{"ind": 0, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $20.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $20.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $739.50.", " $1069.50.", " $841.50.", " $790.50."], "source_id": "deeparithmark_v1_money_rate_depth5_0000", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "79050", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at the normal rate", "added the tax instead of withholding it", "paid overtime at double rate", "correct"], "solution_steps": ["regular pay: 36 x 2000 = 72000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 6 x 3000 = 18000", "gross with bonus: 72000 + 18000 + 3000 = 93000", "take-home: 93000 - 13950 = 79050"], "option_values": [73950, 106950, 84150, 79050], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 1, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $8.00 was split between two teams in the ratio 3:2 after a $5.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $8.00 was split between two teams in the ratio 3:2 after a $5.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.36.", " $0.18.", " $0.24.", " $0.45."], "source_id": "deeparithmark_v1_ratio_depth5_0001", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "18", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the charity cut", "correct", "gave the larger share to the smaller ratio", "divided between the teams instead of the players"], "solution_steps": ["after the fee: 800 - 500 = 300", "one ratio part: 300 / 5 = 60", "larger share: 3 x 60 = 180", "after charity: 180 - 90 = 90", "per player: 90 / 5 = 18"], "option_values": [36, 18, 24, 45], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 2, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:12 a.m.. The first session lasted 55 minutes, the break lasted 25 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:12 a.m.. The first session lasted 55 minutes, the break lasted 25 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 9:12 a.m.", " 7:12 a.m.", " 10:07 a.m.", " 9:37 a.m."], "source_id": "deeparithmark_v1_time_depth3_0002", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "552", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["correct", "dropped the hour carry", "counted the first session twice", "counted the break twice"], "solution_steps": ["after the first session: 432 + 55 = 487 minutes after midnight", "after the break: 487 + 25 = 512", "after the second session: 512 + 40 = 552"], "option_values": [552, 432, 607, 577], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 3, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 420 units. A delivery added 260, then 210 units were shipped out, and 40 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 420 units. A delivery added 260, then 210 units were shipped out, and 40 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 26 crates.", " 29 crates.", " 27 crates.", " 31 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0003", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "26", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "forgot the damaged units", "counted the loose units as a crate", "added the damaged units"], "solution_steps": ["after delivery: 420 + 260 = 680", "after shipping: 680 - 210 = 470", "good units: 470 - 40 = 430", "full crates: 430 / 16 = 26 (remainder 14)"], "option_values": [26, 29, 27, 31], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 4, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 98 pallets.", " 76 pallets.", " 85 pallets.", " 77 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0004", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "76", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["forgot Monday", "correct", "forgot Tuesday", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 20% of 1600 = 320", "left after Monday: 1600 - 320 = 1280", "Tuesday: 10% of 1280 = 128", "left after Tuesday: 1280 - 128 = 1152", "full pallets: 1152 / 15 = 76"], "option_values": [98, 76, 85, 77], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 5, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $0.75 each and 3 erasers at $0.30 each. She split the total cost equally between herself and 3 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $0.75 each and 3 erasers at $0.30 each. She split the total cost equally between herself and 3 friends. Each person paid", "endings": [" $1.01.", " $1.35.", " $1.08.", " $1.68."], "source_id": "deeparithmark_v1_money_depth4_0005", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "135", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["swapped the two unit prices", "correct", "split among one more person", "charged the marker price for everything"], "solution_steps": ["markers: 6 x 75 = 450", "erasers: 3 x 30 = 90", "total cost: 450 + 90 = 540", "split between 4 people: 540 / 4 = 135"], "option_values": [101, 135, 108, 168], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 6, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $24.00. A 25% discount came off it, then 5% tax was added to the discounted price, and a $1.20 coupon was applied last. 3 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $24.00. A 25% discount came off it, then 5% tax was added to the discounted price, and a $1.20 coupon was applied last. 3 people split the final cost equally. Each paid", "endings": [" $3.80.", " $5.90.", " $5.50.", " $6.30."], "source_id": "deeparithmark_v1_percent_money_depth4_0006", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "590", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "correct", "used the coupon twice", "forgot the coupon"], "solution_steps": ["discount: 2400 - 600 = 1800", "tax on the discounted price: 1800 + 90 = 1890", "coupon: 1890 - 120 = 1770", "split 3 ways: 1770 / 3 = 590"], "option_values": [380, 590, 550, 630], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 7, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 60 km at 20 km/h, rested 20 minutes, then walked 10 km at 5 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 60 km at 20 km/h, rested 20 minutes, then walked 10 km at 5 km/h. Her total time, in minutes, was", "endings": [" 80 minutes.", " 320 minutes.", " 230 minutes.", " 860 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0007", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "320", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["divided by the speed twice", "correct", "used the cycling speed for both legs", "used the walking speed for both legs"], "solution_steps": ["cycling time: 60 x 60 / 20 = 180 minutes", "walking time: 60 x 10 / 5 = 120 minutes", "add the rest: 180 + 20 + 120 = 320 minutes"], "option_values": [80, 320, 230, 860], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 8, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 15 km at 15 km/h, rested 30 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 15 km at 15 km/h, rested 30 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "endings": [" 60 minutes.", " 90 minutes.", " 210 minutes.", " 180 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0008", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "210", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["divided by the speed twice", "forgot the walking leg", "correct", "forgot the rest"], "solution_steps": ["cycling time: 60 x 15 / 15 = 60 minutes", "walking time: 60 x 12 / 6 = 120 minutes", "add the rest: 60 + 30 + 120 = 210 minutes"], "option_values": [60, 90, 210, 180], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 9, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $4.02.", " $3.96.", " $3.42.", " $4.62."], "source_id": "deeparithmark_v1_money_percent_depth2_0009", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "402", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the discount off the fee as well", "forgot the fee", "charged the handling fee twice"], "solution_steps": ["take 10% of 380 off: 380 - 38 = 342", "add the 60-cent fee: 342 + 60 = 402"], "option_values": [402, 396, 342, 462], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 10, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 5 hours at $14.00 an hour, and then 2 hours at $18.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 5 hours at $14.00 an hour, and then 2 hours at $18.00 an hour. He earned", "endings": [" $224.00.", " $106.00.", " $118.00.", " $126.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0010", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "10600", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["added the rates together", "correct", "swapped the two rates", "paid every hour at the second rate"], "solution_steps": ["first stretch: 5 x 1400 = 7000", "second stretch: 2 x 1800 = 3600", "total pay: 7000 + 3600 = 10600"], "option_values": [22400, 10600, 11800, 12600], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 11, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 50% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 50% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $14.75.", " $5.15.", " $9.95.", " $9.45."], "source_id": "deeparithmark_v1_money_percent_depth2_0011", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "515", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["added the discount instead of removing it", "correct", "forgot the discount", "read the percentage as a flat number of cents"], "solution_steps": ["take 50% of 960 off: 960 - 480 = 480", "add the 35-cent fee: 480 + 35 = 515"], "option_values": [1475, 515, 995, 945], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 12, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:17 a.m.. The first session lasted 60 minutes, the break lasted 25 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:17 a.m.. The first session lasted 60 minutes, the break lasted 25 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "endings": [" 10:27 a.m.", " 11:27 a.m.", " 10:52 a.m.", " 11:22 a.m."], "source_id": "deeparithmark_v1_time_depth3_0012", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "627", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["correct", "counted the first session twice", "counted the break twice", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 497 + 60 = 557 minutes after midnight", "after the break: 557 + 25 = 582", "after the second session: 582 + 45 = 627"], "option_values": [627, 687, 652, 682], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 13, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $1.20 each and 4 erasers at $0.30 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $1.20 each and 4 erasers at $0.30 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.44.", " $1.68.", " $1.32.", " $1.98."], "source_id": "deeparithmark_v1_money_depth4_0013", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "168", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["forgot the erasers", "correct", "swapped the two unit prices", "bought one extra of each item"], "solution_steps": ["markers: 6 x 120 = 720", "erasers: 4 x 30 = 120", "total cost: 720 + 120 = 840", "split between 5 people: 840 / 5 = 168"], "option_values": [144, 168, 132, 198], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 14, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 480 units. A delivery added 180, then 90 units were shipped out, and 18 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 480 units. A delivery added 180, then 90 units were shipped out, and 18 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 13 crates.", " 38 crates.", " 31 crates.", " 46 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0014", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "46", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed the arriving units only", "shipped out twice", "forgot the delivery", "correct"], "solution_steps": ["after delivery: 480 + 180 = 660", "after shipping: 660 - 90 = 570", "good units: 570 - 18 = 552", "full crates: 552 / 12 = 46 (remainder 0)"], "option_values": [13, 38, 31, 46], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 15, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 6 litres per minute for 4 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 6 litres per minute for 4 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 209 litres.", " 254 litres.", " 284 litres.", " 279 litres."], "source_id": "deeparithmark_v1_rate_depth4_0015", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "279", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "forgot the second fill", "used the first rate for both stages", "correct"], "solution_steps": ["first fill: 6 x 4 = 24 litres", "second fill: 5 x 5 = 25 litres", "before draining: 300 + 24 + 25 = 349", "after draining: 349 - 70 = 279"], "option_values": [209, 254, 284, 279], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 16, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 5 hours at $12.50 an hour, and then 2 hours at $14.50 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 5 hours at $12.50 an hour, and then 2 hours at $14.50 an hour. He earned", "endings": [" $64.50.", " $87.50.", " $91.50.", " $62.50."], "source_id": "deeparithmark_v1_rate_pay_depth3_0016", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "9150", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["worked one hour less in each stretch", "paid every hour at the first rate", "correct", "forgot the second stretch"], "solution_steps": ["first stretch: 5 x 1250 = 6250", "second stretch: 2 x 1450 = 2900", "total pay: 6250 + 2900 = 9150"], "option_values": [6450, 8750, 9150, 6250], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 17, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 96 pallets.", " 66 pallets.", " 105 pallets.", " 108 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0017", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "108", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "took both percentages twice", "took both percentages off the original stock", "correct"], "solution_steps": ["Monday: 10% of 1200 = 120", "left after Monday: 1200 - 120 = 1080", "Tuesday: 20% of 1080 = 216", "left after Tuesday: 1080 - 216 = 864", "full pallets: 864 / 8 = 108"], "option_values": [96, 66, 105, 108], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 18, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $28.00. A 25% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $28.00. A 25% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $11.15.", " $7.43.", " $10.75.", " $11.95."], "source_id": "deeparithmark_v1_percent_money_depth4_0018", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "1115", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "split the total among one more person", "used the coupon twice", "added the coupon instead of subtracting it"], "solution_steps": ["discount: 2800 - 700 = 2100", "tax on the discounted price: 2100 + 210 = 2310", "coupon: 2310 - 80 = 2230", "split 2 ways: 2230 / 2 = 1115"], "option_values": [1115, 743, 1075, 1195], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 19, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $20.00 an hour and 10 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $20.00 an hour and 10 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $872.00.", " $1188.00.", " $792.00.", " $862.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0019", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "79200", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at double rate", "added the tax instead of withholding it", "correct", "taxed only the regular pay"], "solution_steps": ["regular pay: 32 x 2000 = 64000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 10 x 3000 = 30000", "gross with bonus: 64000 + 30000 + 5000 = 99000", "take-home: 99000 - 19800 = 79200"], "option_values": [87200, 118800, 79200, 86200], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 20, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Samir baked 108 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Samir baked 108 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 72 muffins.", " 27 muffins.", " 21 muffins.", " 18 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0020", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "18", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["stopped after giving the third away", "split all the cookies, not the rest", "split all the cookies among one more child", "correct"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 4: 72 / 4 = 18"], "option_values": [72, 27, 21, 18], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 21, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:14 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:14 a.m. for 95 minutes. The booking ended at", "endings": [" 7:34 a.m.", " 8:19 a.m.", " 7:49 a.m.", " 9:19 a.m."], "source_id": "deeparithmark_v1_time_depth2_0021", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "469", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "ran half an hour long", "correct", "ran an hour and a half long"], "solution_steps": ["convert the start: 374 minutes after midnight", "add the duration: 374 + 95 = 469 minutes"], "option_values": [454, 499, 469, 559], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 22, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 840 units. A delivery added 260, then 210 units were shipped out, and 32 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 840 units. A delivery added 260, then 210 units were shipped out, and 32 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 71 crates.", " 89 crates.", " 74 crates.", " 72 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0022", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "71", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "forgot the shipping", "forgot the damaged units", "counted the loose units as a crate"], "solution_steps": ["after delivery: 840 + 260 = 1100", "after shipping: 1100 - 210 = 890", "good units: 890 - 32 = 858", "full crates: 858 / 12 = 71 (remainder 6)"], "option_values": [71, 89, 74, 72], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 23, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:37 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:37 a.m. for 50 minutes. The booking ended at", "endings": [" 9:57 a.m.", " 8:27 a.m.", " 8:57 a.m.", " 9:27 a.m."], "source_id": "deeparithmark_v1_time_depth2_0023", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "507", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran an hour and a half long", "correct", "ran half an hour long", "added an extra hour"], "solution_steps": ["convert the start: 457 minutes after midnight", "add the duration: 457 + 50 = 507 minutes"], "option_values": [597, 507, 537, 567], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 24, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $4.80 was split between two teams in the ratio 5:2 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $4.80 was split between two teams in the ratio 5:2 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.16.", " $0.32.", " $0.12.", " $0.44."], "source_id": "deeparithmark_v1_ratio_depth5_0024", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "32", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["gave the larger share to the smaller ratio", "correct", "swapped the ratio parts", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 480 - 200 = 280", "one ratio part: 280 / 7 = 40", "larger share: 5 x 40 = 200", "after charity: 200 - 40 = 160", "per player: 160 / 5 = 32"], "option_values": [16, 32, 12, 44], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 25, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 40 km at 20 km/h, rested 30 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 40 km at 20 km/h, rested 30 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "endings": [" 270 minutes.", " 70 minutes.", " 240 minutes.", " 150 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0025", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "270", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["correct", "divided by the speed twice", "forgot the rest", "forgot the walking leg"], "solution_steps": ["cycling time: 60 x 40 / 20 = 120 minutes", "walking time: 60 x 12 / 6 = 120 minutes", "add the rest: 120 + 30 + 120 = 270 minutes"], "option_values": [270, 70, 240, 150], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 26, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $1.20 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $1.20 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $2.40.", " $3.80.", " $11.40.", " $4.80."], "source_id": "deeparithmark_v1_money_depth4_0026", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "380", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["forgot the erasers", "correct", "did not split the total at all", "charged the marker price for everything"], "solution_steps": ["markers: 6 x 120 = 720", "erasers: 6 x 70 = 420", "total cost: 720 + 420 = 1140", "split between 3 people: 1140 / 3 = 380"], "option_values": [240, 380, 1140, 480], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 27, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 560 units. A delivery added 240, then 170 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 560 units. A delivery added 240, then 170 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 41 crates.", " 48 crates.", " 37 crates.", " 39 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0027", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "37", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["added the damaged units", "forgot the shipping", "correct", "forgot the damaged units"], "solution_steps": ["after delivery: 560 + 240 = 800", "after shipping: 800 - 170 = 630", "good units: 630 - 32 = 598", "full crates: 598 / 16 = 37 (remainder 6)"], "option_values": [41, 48, 37, 39], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 28, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.60 was split between two teams in the ratio 4:2 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.60 was split between two teams in the ratio 4:2 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.22.", " $0.13.", " $0.24.", " $0.27."], "source_id": "deeparithmark_v1_ratio_depth5_0028", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "27", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the fee and the charity cut", "swapped the ratio parts", "split among one more player", "correct"], "solution_steps": ["after the fee: 760 - 400 = 360", "one ratio part: 360 / 6 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 24 = 216", "per player: 216 / 8 = 27"], "option_values": [22, 13, 24, 27], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 29, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $604.80.", " $579.20.", " $588.80.", " $453.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0029", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "60480", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "paid overtime at the normal rate", "forgot the bonus", "taxed twice"], "solution_steps": ["regular pay: 40 x 1600 = 64000", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 4 x 2400 = 9600", "gross with bonus: 64000 + 9600 + 2000 = 75600", "take-home: 75600 - 15120 = 60480"], "option_values": [60480, 57920, 58880, 45360], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 30, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.50 was split between two teams in the ratio 3:2 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.50 was split between two teams in the ratio 3:2 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.18.", " $0.22.", " $0.78.", " $0.27."], "source_id": "deeparithmark_v1_ratio_depth5_0030", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "27", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "split among one more player", "forgot to deduct the fee", "correct"], "solution_steps": ["after the fee: 650 - 400 = 250", "one ratio part: 250 / 5 = 50", "larger share: 3 x 50 = 150", "after charity: 150 - 15 = 135", "per player: 135 / 5 = 27"], "option_values": [18, 22, 78, 27], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 31, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $14.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $14.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $496.80.", " $572.40.", " $547.20.", " $699.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0031", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "57240", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the overtime", "correct", "paid overtime at the normal rate", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 38 x 1400 = 53200", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 4 x 2100 = 8400", "gross with bonus: 53200 + 8400 + 2000 = 63600", "take-home: 63600 - 6360 = 57240"], "option_values": [49680, 57240, 54720, 69960], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 32, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:32 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:32 a.m. for 110 minutes. The booking ended at", "endings": [" 9:22 a.m.", " 10:22 a.m.", " 11:22 a.m.", " 11:52 a.m."], "source_id": "deeparithmark_v1_time_depth2_0032", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "622", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added the minutes without the hours", "correct", "added an extra hour", "ran an hour and a half long"], "solution_steps": ["convert the start: 512 minutes after midnight", "add the duration: 512 + 110 = 622 minutes"], "option_values": [562, 622, 682, 712], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 33, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 25% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 25% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $6.75.", " $6.64.", " $8.85.", " $10.95."], "source_id": "deeparithmark_v1_money_percent_depth2_0033", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "675", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the discount off the fee as well", "forgot the discount", "added the discount instead of removing it"], "solution_steps": ["take 25% of 840 off: 840 - 210 = 630", "add the 45-cent fee: 630 + 45 = 675"], "option_values": [675, 664, 885, 1095], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 34, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 700 units. A delivery added 180, then 170 units were shipped out, and 24 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 700 units. A delivery added 180, then 170 units were shipped out, and 24 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 32 crates.", " 42 crates.", " 43 crates.", " 45 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0034", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "42", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped out twice", "correct", "counted the loose units as a crate", "added the damaged units"], "solution_steps": ["after delivery: 700 + 180 = 880", "after shipping: 880 - 170 = 710", "good units: 710 - 24 = 686", "full crates: 686 / 16 = 42 (remainder 14)"], "option_values": [32, 42, 43, 45], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 35, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 3 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 3 people split the final cost equally. Each paid", "endings": [" $4.80.", " $6.40.", " $6.80.", " $6.60."], "source_id": "deeparithmark_v1_percent_money_depth4_0035", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "640", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["split the total among one more person", "correct", "added the coupon instead of subtracting it", "forgot the coupon"], "solution_steps": ["discount: 2000 - 200 = 1800", "tax on the discounted price: 1800 + 180 = 1980", "coupon: 1980 - 60 = 1920", "split 3 ways: 1920 / 3 = 640"], "option_values": [480, 640, 680, 660], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 36, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $4.53.", " $5.44.", " $6.34.", " $5.89."], "source_id": "deeparithmark_v1_money_percent_depth2_0036", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "589", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "forgot the fee", "charged the handling fee twice", "correct"], "solution_steps": ["take 20% of 680 off: 680 - 136 = 544", "add the 45-cent fee: 544 + 45 = 589"], "option_values": [453, 544, 634, 589], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 37, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:18 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:18 a.m. for 110 minutes. The booking ended at", "endings": [" 6:28 a.m.", " 11:38 a.m.", " 10:08 a.m.", " 10:38 a.m."], "source_id": "deeparithmark_v1_time_depth2_0037", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "608", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "ran an hour and a half long", "correct", "ran half an hour long"], "solution_steps": ["convert the start: 498 minutes after midnight", "add the duration: 498 + 110 = 608 minutes"], "option_values": [388, 698, 608, 638], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 38, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 400 shirts. It sold 15% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 400 shirts. It sold 15% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "endings": [" 28 boxes.", " 29 boxes.", " 33 boxes.", " 85 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0038", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "28", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "rounded the box count up", "packed the whole stock, not the rest", "divided by the number of boxes left over"], "solution_steps": ["sold: 15% of 400 = 60", "left over: 400 - 60 = 340", "full boxes: 340 / 12 = 28 (remainder 4)"], "option_values": [28, 29, 33, 85], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 39, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.60 was split between two teams in the ratio 3:1 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.60 was split between two teams in the ratio 3:1 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.09.", " $0.21.", " $0.27.", " $0.24."], "source_id": "deeparithmark_v1_ratio_depth5_0039", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "27", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "split among one more player", "correct", "gave twice the share away to charity"], "solution_steps": ["after the fee: 660 - 500 = 160", "one ratio part: 160 / 4 = 40", "larger share: 3 x 40 = 120", "after charity: 120 - 12 = 108", "per player: 108 / 4 = 27"], "option_values": [9, 21, 27, 24], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 40, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 700 units. A delivery added 310, then 90 units were shipped out, and 32 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 700 units. A delivery added 310, then 90 units were shipped out, and 32 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "endings": [" 57 crates.", " 63 crates.", " 64 crates.", " 68 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0040", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "63", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped out twice", "correct", "counted the loose units as a crate", "added the damaged units"], "solution_steps": ["after delivery: 700 + 310 = 1010", "after shipping: 1010 - 90 = 920", "good units: 920 - 32 = 888", "full crates: 888 / 14 = 63 (remainder 6)"], "option_values": [57, 63, 64, 68], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 41, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 33 pallets.", " 52 pallets.", " 48 pallets.", " 54 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0041", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "54", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "took both percentages off the original stock", "stacked on larger pallets", "correct"], "solution_steps": ["Monday: 20% of 600 = 120", "left after Monday: 600 - 120 = 480", "Tuesday: 10% of 480 = 48", "left after Tuesday: 480 - 48 = 432", "full pallets: 432 / 8 = 54"], "option_values": [33, 52, 48, 54], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 42, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:39 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:39 a.m. for 80 minutes. The booking ended at", "endings": [" 8:59 a.m.", " 10:29 a.m.", " 9:59 a.m.", " 10:59 a.m."], "source_id": "deeparithmark_v1_time_depth2_0042", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "599", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "ran half an hour long", "correct", "added an extra hour"], "solution_steps": ["convert the start: 519 minutes after midnight", "add the duration: 519 + 80 = 599 minutes"], "option_values": [539, 629, 599, 659], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 43, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:23 a.m.. The first session lasted 55 minutes, the break lasted 15 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:23 a.m.. The first session lasted 55 minutes, the break lasted 15 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 8:08 a.m.", " 8:38 a.m.", " 8:23 a.m.", " 9:08 a.m."], "source_id": "deeparithmark_v1_time_depth3_0043", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "503", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the break", "counted the break twice", "correct", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 383 + 55 = 438 minutes after midnight", "after the break: 438 + 15 = 453", "after the second session: 453 + 50 = 503"], "option_values": [488, 518, 503, 548], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 44, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $0.60 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $0.60 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $5.52.", " $7.41.", " $9.88.", " $29.64."], "source_id": "deeparithmark_v1_percent_money_depth4_0044", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "741", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "correct", "split the total among one fewer person", "did not split the cost at all"], "solution_steps": ["discount: 3600 - 720 = 2880", "tax on the discounted price: 2880 + 144 = 3024", "coupon: 3024 - 60 = 2964", "split 4 ways: 2964 / 4 = 741"], "option_values": [552, 741, 988, 2964], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 45, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $16.00. A 30% discount came off it, then 15% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $16.00. A 30% discount came off it, then 15% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $1.74.", " $3.12.", " $3.02.", " $2.49."], "source_id": "deeparithmark_v1_percent_money_depth4_0045", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "312", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "correct", "used the coupon twice", "split the total among one more person"], "solution_steps": ["discount: 1600 - 480 = 1120", "tax on the discounted price: 1120 + 168 = 1288", "coupon: 1288 - 40 = 1248", "split 4 ways: 1248 / 4 = 312"], "option_values": [174, 312, 302, 249], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 46, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.40 was split between two teams in the ratio 4:2 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.40 was split between two teams in the ratio 4:2 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.27.", " $0.61.", " $0.72.", " $0.18."], "source_id": "deeparithmark_v1_ratio_depth5_0046", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "18", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["took the charity cut off the whole prize", "forgot to deduct the fee", "divided between the teams instead of the players", "correct"], "solution_steps": ["after the fee: 740 - 500 = 240", "one ratio part: 240 / 6 = 40", "larger share: 4 x 40 = 160", "after charity: 160 - 16 = 144", "per player: 144 / 8 = 18"], "option_values": [27, 61, 72, 18], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 47, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 3 hours at $11.00 an hour, and then 3 hours at $14.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 3 hours at $11.00 an hour, and then 3 hours at $14.00 an hour. He earned", "endings": [" $42.00.", " $33.00.", " $75.00.", " $84.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0047", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "7500", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["forgot the first stretch", "forgot the second stretch", "correct", "paid every hour at the second rate"], "solution_steps": ["first stretch: 3 x 1100 = 3300", "second stretch: 3 x 1400 = 4200", "total pay: 3300 + 4200 = 7500"], "option_values": [4200, 3300, 7500, 8400], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 48, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Hana baked 108 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Hana baked 108 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 9 biscuits.", " 18 biscuits.", " 12 biscuits.", " 72 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0048", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "18", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split the given-away cookies too", "correct", "gave away a third twice", "stopped after giving the third away"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 4: 72 / 4 = 18"], "option_values": [9, 18, 12, 72], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 49, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 40 km at 20 km/h, rested 30 minutes, then walked 12 km at 4 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 40 km at 20 km/h, rested 30 minutes, then walked 12 km at 4 km/h. Her total time, in minutes, was", "endings": [" 150 minutes.", " 330 minutes.", " 360 minutes.", " 810 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0049", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "330", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "correct", "counted the rest twice", "used the walking speed for both legs"], "solution_steps": ["cycling time: 60 x 40 / 20 = 120 minutes", "walking time: 60 x 12 / 4 = 180 minutes", "add the rest: 120 + 30 + 180 = 330 minutes"], "option_values": [150, 330, 360, 810], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 50, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 12 litres per minute for 6 minutes, then 5 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 12 litres per minute for 6 minutes, then 5 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 421 litres.", " 347 litres.", " 356 litres.", " 307 litres."], "source_id": "deeparithmark_v1_rate_depth4_0050", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "307", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["added the rates and multiplied once", "forgot the drain", "used the first rate for both stages", "correct"], "solution_steps": ["first fill: 12 x 6 = 72 litres", "second fill: 5 x 7 = 35 litres", "before draining: 240 + 72 + 35 = 347", "after draining: 347 - 40 = 307"], "option_values": [421, 347, 356, 307], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 51, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 36 km at 18 km/h, rested 25 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 36 km at 18 km/h, rested 25 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "endings": [" 265 minutes.", " 145 minutes.", " 185 minutes.", " 505 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0051", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "265", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["correct", "forgot the walking leg", "used the cycling speed for both legs", "used the walking speed for both legs"], "solution_steps": ["cycling time: 60 x 36 / 18 = 120 minutes", "walking time: 60 x 12 / 6 = 120 minutes", "add the rest: 120 + 25 + 120 = 265 minutes"], "option_values": [265, 145, 185, 505], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 52, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.00 was split between two teams in the ratio 4:1 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.00 was split between two teams in the ratio 4:1 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.25.", " $0.24.", " $0.08.", " $0.32."], "source_id": "deeparithmark_v1_ratio_depth5_0052", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "32", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "gave twice the share away to charity", "swapped the ratio parts", "correct"], "solution_steps": ["after the fee: 600 - 400 = 200", "one ratio part: 200 / 5 = 40", "larger share: 4 x 40 = 160", "after charity: 160 - 32 = 128", "per player: 128 / 4 = 32"], "option_values": [25, 24, 8, 32], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 53, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1000 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1000 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 53 pallets.", " 56 pallets.", " 43 pallets.", " 42 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0053", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "42", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["forgot Tuesday", "forgot Monday", "counted the loose sacks as a pallet", "correct"], "solution_steps": ["Monday: 20% of 1000 = 200", "left after Monday: 1000 - 200 = 800", "Tuesday: 20% of 800 = 160", "left after Tuesday: 800 - 160 = 640", "full pallets: 640 / 15 = 42"], "option_values": [53, 56, 43, 42], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 54, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $28.00. A 25% discount came off it, then 5% tax was added to the discounted price, and a $1.20 coupon was applied last. 5 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $28.00. A 25% discount came off it, then 5% tax was added to the discounted price, and a $1.20 coupon was applied last. 5 people split the final cost equally. Each paid", "endings": [" $5.21.", " $5.88.", " $4.41.", " $4.17."], "source_id": "deeparithmark_v1_percent_money_depth4_0054", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "417", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["split the total among one fewer person", "forgot the discount and the coupon", "forgot the coupon", "correct"], "solution_steps": ["discount: 2800 - 700 = 2100", "tax on the discounted price: 2100 + 105 = 2205", "coupon: 2205 - 120 = 2085", "split 5 ways: 2085 / 5 = 417"], "option_values": [521, 588, 441, 417], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 55, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Farid baked 90 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Farid baked 90 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 15 biscuits.", " 6 biscuits.", " 7 biscuits.", " 18 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0055", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "15", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["correct", "gave away two thirds and split among one more child", "split the given-away cookies too", "split all the cookies among one more child"], "solution_steps": ["one third given away: 90 / 3 = 30", "rest kept: 90 - 30 = 60", "split among 4: 60 / 4 = 15"], "option_values": [15, 6, 7, 18], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 56, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 360 shirts. It sold 15% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 360 shirts. It sold 15% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 32 boxes.", " 31 boxes.", " 38 boxes.", " 45 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0056", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "38", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["took the percentage off the remainder again", "sold twice as many", "correct", "packed the whole stock, not the rest"], "solution_steps": ["sold: 15% of 360 = 54", "left over: 360 - 54 = 306", "full boxes: 306 / 8 = 38 (remainder 2)"], "option_values": [32, 31, 38, 45], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 57, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:02 a.m.. The first session lasted 70 minutes, the break lasted 25 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:02 a.m.. The first session lasted 70 minutes, the break lasted 25 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 10:22 a.m.", " 9:27 a.m.", " 9:52 a.m.", " 10:37 a.m."], "source_id": "deeparithmark_v1_time_depth3_0057", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "567", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["finished half an hour late on top of the break", "correct", "counted the break twice", "counted the first session twice"], "solution_steps": ["after the first session: 422 + 70 = 492 minutes after midnight", "after the break: 492 + 25 = 517", "after the second session: 517 + 50 = 567"], "option_values": [622, 567, 592, 637], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 58, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:52 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:52 a.m. for 95 minutes. The booking ended at", "endings": [" 7:27 a.m.", " 9:27 a.m.", " 9:12 a.m.", " 10:57 a.m."], "source_id": "deeparithmark_v1_time_depth2_0058", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "567", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "correct", "stopped a quarter of an hour early", "ran an hour and a half long"], "solution_steps": ["convert the start: 472 minutes after midnight", "add the duration: 472 + 95 = 567 minutes"], "option_values": [447, 567, 552, 657], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 59, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 420 units. A delivery added 240, then 170 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 420 units. A delivery added 240, then 170 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 39 crates.", " 32 crates.", " 29 crates.", " 28 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0059", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "28", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the shipping", "added the damaged units", "counted the loose units as a crate", "correct"], "solution_steps": ["after delivery: 420 + 240 = 660", "after shipping: 660 - 170 = 490", "good units: 490 - 32 = 458", "full crates: 458 / 16 = 28 (remainder 10)"], "option_values": [39, 32, 29, 28], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 60, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 24 km at 12 km/h, rested 12 minutes, then walked 4 km at 4 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 24 km at 12 km/h, rested 12 minutes, then walked 4 km at 4 km/h. Her total time, in minutes, was", "endings": [" 192 minutes.", " 132 minutes.", " 57 minutes.", " 152 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0060", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "192", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["correct", "forgot the walking leg", "divided by the speed twice", "used the cycling speed for both legs"], "solution_steps": ["cycling time: 60 x 24 / 12 = 120 minutes", "walking time: 60 x 4 / 4 = 60 minutes", "add the rest: 120 + 12 + 60 = 192 minutes"], "option_values": [192, 132, 57, 152], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 61, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 9 litres per minute for 10 minutes, then 7 litres per minute for 7 minutes. A drain then removed 55 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 9 litres per minute for 10 minutes, then 7 litres per minute for 7 minutes. A drain then removed 55 litres. The tank then held", "endings": [" 149 litres.", " 204 litres.", " 114 litres.", " 314 litres."], "source_id": "deeparithmark_v1_rate_depth4_0061", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "204", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "correct", "forgot the first fill", "added the drain instead of removing it"], "solution_steps": ["first fill: 9 x 10 = 90 litres", "second fill: 7 x 7 = 49 litres", "before draining: 120 + 90 + 49 = 259", "after draining: 259 - 55 = 204"], "option_values": [149, 204, 114, 314], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 62, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 5 metres and 38 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 5 metres and 38 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 503 centimetres.", " 493 centimetres.", " 583 centimetres.", " 531 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0062", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "493", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["stopped ten centimetres short of the cut", "correct", "added the cut instead of removing it", "counted the extra centimetres twice"], "solution_steps": ["convert metres: 5 x 100 = 500 cm", "add the extra centimetres: 500 + 38 = 538 cm", "subtract the cut: 538 - 45 = 493 cm"], "option_values": [503, 493, 583, 531], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 63, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 25% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 25% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $4.35.", " $8.55.", " $10.65.", " $6.45."], "source_id": "deeparithmark_v1_money_percent_depth2_0063", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "645", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "forgot the discount", "added the discount instead of removing it", "correct"], "solution_steps": ["take 25% of 840 off: 840 - 210 = 630", "add the 15-cent fee: 630 + 15 = 645"], "option_values": [435, 855, 1065, 645], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 64, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $0.45 each and 4 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $0.45 each and 4 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $0.85.", " $1.19.", " $0.63.", " $0.99."], "source_id": "deeparithmark_v1_money_depth4_0064", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "119", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among two more people", "correct", "forgot the erasers", "charged the marker price for everything"], "solution_steps": ["markers: 7 x 45 = 315", "erasers: 4 x 70 = 280", "total cost: 315 + 280 = 595", "split between 5 people: 595 / 5 = 119"], "option_values": [85, 119, 63, 99], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 65, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $12.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $0.60 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $12.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $0.60 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $1.47.", " $3.24.", " $9.12.", " $2.28."], "source_id": "deeparithmark_v1_percent_money_depth4_0065", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "228", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "forgot the discount and the coupon", "did not split the cost at all", "correct"], "solution_steps": ["discount: 1200 - 300 = 900", "tax on the discounted price: 900 + 72 = 972", "coupon: 972 - 60 = 912", "split 4 ways: 912 / 4 = 228"], "option_values": [147, 324, 912, 228], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 66, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $2.30.", " $2.90.", " $2.60.", " $4.70."], "source_id": "deeparithmark_v1_money_percent_depth2_0066", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "290", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "correct", "took the discount off the fee as well", "read the percentage as a flat number of cents"], "solution_steps": ["take 50% of 460 off: 460 - 230 = 230", "add the 60-cent fee: 230 + 60 = 290"], "option_values": [230, 290, 260, 470], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 67, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $3.21.", " $4.85.", " $4.13.", " $5.05."], "source_id": "deeparithmark_v1_money_percent_depth2_0067", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "413", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "read the percentage as a flat number of cents", "correct", "forgot the discount"], "solution_steps": ["take 20% of 460 off: 460 - 92 = 368", "add the 45-cent fee: 368 + 45 = 413"], "option_values": [321, 485, 413, 505], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 68, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $20.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $20.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $945.00.", " $914.00.", " $891.00.", " $1089.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0068", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "89100", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at double rate", "taxed only the regular pay", "correct", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 38 x 2000 = 76000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 6 x 3000 = 18000", "gross with bonus: 76000 + 18000 + 5000 = 99000", "take-home: 99000 - 9900 = 89100"], "option_values": [94500, 91400, 89100, 108900], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 69, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:32 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:32 a.m. for 95 minutes. The booking ended at", "endings": [" 9:07 a.m.", " 10:37 a.m.", " 9:37 a.m.", " 10:07 a.m."], "source_id": "deeparithmark_v1_time_depth2_0069", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "547", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "ran an hour and a half long", "ran half an hour long", "added an extra hour"], "solution_steps": ["convert the start: 452 minutes after midnight", "add the duration: 452 + 95 = 547 minutes"], "option_values": [547, 637, 577, 607], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 70, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:35 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:35 a.m. for 50 minutes. The booking ended at", "endings": [" 6:45 a.m.", " 8:25 a.m.", " 7:25 a.m.", " 8:55 a.m."], "source_id": "deeparithmark_v1_time_depth2_0070", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "505", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "correct", "dropped the hour carry", "ran half an hour long"], "solution_steps": ["convert the start: 455 minutes after midnight", "add the duration: 455 + 50 = 505 minutes"], "option_values": [405, 505, 445, 535], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 71, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 6 litres per minute for 6 minutes, then 3 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 6 litres per minute for 6 minutes, then 3 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 176 litres.", " 151 litres.", " 191 litres.", " 155 litres."], "source_id": "deeparithmark_v1_rate_depth4_0071", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "191", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the second fill", "drained twice", "correct", "forgot the first fill"], "solution_steps": ["first fill: 6 x 6 = 36 litres", "second fill: 3 x 5 = 15 litres", "before draining: 180 + 36 + 15 = 231", "after draining: 231 - 40 = 191"], "option_values": [176, 151, 191, 155], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 72, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:36 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:36 a.m. for 65 minutes. The booking ended at", "endings": [" 7:41 a.m.", " 5:31 a.m.", " 9:11 a.m.", " 8:11 a.m."], "source_id": "deeparithmark_v1_time_depth2_0072", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "461", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "subtracted the duration instead of adding it", "ran an hour and a half long", "ran half an hour long"], "solution_steps": ["convert the start: 396 minutes after midnight", "add the duration: 396 + 65 = 461 minutes"], "option_values": [461, 331, 551, 491], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 73, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 440 shirts. It sold 25% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 440 shirts. It sold 25% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "endings": [" 12 boxes.", " 36 boxes.", " 27 boxes.", " 24 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0073", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "36", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the sold shirts", "correct", "took the percentage off the remainder again", "sold twice as many"], "solution_steps": ["sold: 25% of 440 = 110", "left over: 440 - 110 = 330", "full boxes: 330 / 9 = 36 (remainder 6)"], "option_values": [12, 36, 27, 24], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 74, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $310.50.", " $391.50.", " $364.50.", " $652.50."], "source_id": "deeparithmark_v1_money_rate_depth5_0074", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "39150", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the overtime", "correct", "paid overtime at the normal rate", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 32 x 1200 = 38400", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 6 x 1800 = 10800", "gross with bonus: 38400 + 10800 + 3000 = 52200", "take-home: 52200 - 13050 = 39150"], "option_values": [31050, 39150, 36450, 65250], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 75, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 45 km at 15 km/h, rested 25 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 45 km at 15 km/h, rested 25 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "endings": [" 205 minutes.", " 97 minutes.", " 745 minutes.", " 385 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0075", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "385", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "divided by the speed twice", "used the walking speed for both legs", "correct"], "solution_steps": ["cycling time: 60 x 45 / 15 = 180 minutes", "walking time: 60 x 15 / 5 = 180 minutes", "add the rest: 180 + 25 + 180 = 385 minutes"], "option_values": [205, 97, 745, 385], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 76, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $0.95 each and 5 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $0.95 each and 5 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.17.", " $1.65.", " $1.67.", " $1.98."], "source_id": "deeparithmark_v1_money_depth4_0076", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "165", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among two more people", "correct", "added the unit prices instead of multiplying", "bought one extra of each item"], "solution_steps": ["markers: 5 x 95 = 475", "erasers: 5 x 70 = 350", "total cost: 475 + 350 = 825", "split between 5 people: 825 / 5 = 165"], "option_values": [117, 165, 167, 198], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 77, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $4.10 was split between two teams in the ratio 4:3 after a $2.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $4.10 was split between two teams in the ratio 4:3 after a $2.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.13.", " $0.18.", " $0.12.", " $0.15."], "source_id": "deeparithmark_v1_ratio_depth5_0077", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "18", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "correct", "gave twice the share away to charity", "split among one more player"], "solution_steps": ["after the fee: 410 - 200 = 210", "one ratio part: 210 / 7 = 30", "larger share: 4 x 30 = 120", "after charity: 120 - 30 = 90", "per player: 90 / 5 = 18"], "option_values": [13, 18, 12, 15], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 78, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:09 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:09 a.m. for 80 minutes. The booking ended at", "endings": [" 10:59 a.m.", " 10:29 a.m.", " 9:29 a.m.", " 9:59 a.m."], "source_id": "deeparithmark_v1_time_depth2_0078", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "569", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran an hour and a half long", "added an extra hour", "correct", "ran half an hour long"], "solution_steps": ["convert the start: 489 minutes after midnight", "add the duration: 489 + 80 = 569 minutes"], "option_values": [659, 629, 569, 599], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 79, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 10% discount came off it, then 15% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 10% discount came off it, then 15% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $15.96.", " $17.43.", " $18.63.", " $18.03."], "source_id": "deeparithmark_v1_percent_money_depth4_0079", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "1803", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "used the coupon twice", "forgot the coupon", "correct"], "solution_steps": ["discount: 3600 - 360 = 3240", "tax on the discounted price: 3240 + 486 = 3726", "coupon: 3726 - 120 = 3606", "split 2 ways: 3606 / 2 = 1803"], "option_values": [1596, 1743, 1863, 1803], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 80, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 20 km at 20 km/h, rested 20 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 20 km at 20 km/h, rested 20 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "endings": [" 260 minutes.", " 240 minutes.", " 80 minutes.", " 440 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0080", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "260", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["correct", "forgot the rest", "forgot the walking leg", "used the walking speed for both legs"], "solution_steps": ["cycling time: 60 x 20 / 20 = 60 minutes", "walking time: 60 x 15 / 5 = 180 minutes", "add the rest: 60 + 20 + 180 = 260 minutes"], "option_values": [260, 240, 80, 440], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 81, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.00 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.00 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.18.", " $0.37.", " $0.96.", " $0.24."], "source_id": "deeparithmark_v1_ratio_depth5_0081", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "24", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["gave twice the share away to charity", "split the whole prize among one team", "divided between the teams instead of the players", "correct"], "solution_steps": ["after the fee: 600 - 300 = 300", "one ratio part: 300 / 5 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 48 = 192", "per player: 192 / 8 = 24"], "option_values": [18, 37, 96, 24], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 82, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 12 litres per minute for 8 minutes, then 3 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 12 litres per minute for 8 minutes, then 3 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "endings": [" 253 litres.", " 212 litres.", " 389 litres.", " 308 litres."], "source_id": "deeparithmark_v1_rate_depth4_0082", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "308", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "forgot the first fill", "used the first rate for both stages", "correct"], "solution_steps": ["first fill: 12 x 8 = 96 litres", "second fill: 3 x 9 = 27 litres", "before draining: 240 + 96 + 27 = 363", "after draining: 363 - 55 = 308"], "option_values": [253, 212, 389, 308], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 83, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:42 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:42 a.m. for 95 minutes. The booking ended at", "endings": [" 8:17 a.m.", " 5:07 a.m.", " 9:47 a.m.", " 8:47 a.m."], "source_id": "deeparithmark_v1_time_depth2_0083", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "497", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "subtracted the duration instead of adding it", "ran an hour and a half long", "ran half an hour long"], "solution_steps": ["convert the start: 402 minutes after midnight", "add the duration: 402 + 95 = 497 minutes"], "option_values": [497, 307, 587, 527], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 84, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $424.00.", " $555.00.", " $636.00.", " $621.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0084", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "63600", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "forgot the overtime", "correct", "forgot the bonus"], "solution_steps": ["regular pay: 40 x 1800 = 72000", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 4 x 2700 = 10800", "gross with bonus: 72000 + 10800 + 2000 = 84800", "take-home: 84800 - 21200 = 63600"], "option_values": [42400, 55500, 63600, 62100], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 85, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 99 pallets.", " 147 pallets.", " 112 pallets.", " 113 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0085", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "112", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "forgot Monday", "correct", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 20% of 1400 = 280", "left after Monday: 1400 - 280 = 1120", "Tuesday: 20% of 1120 = 224", "left after Tuesday: 1120 - 224 = 896", "full pallets: 896 / 8 = 112"], "option_values": [99, 147, 112, 113], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 86, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Chen baked 144 buns. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Chen baked 144 buns. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 28 buns.", " 36 buns.", " 96 buns.", " 24 buns."], "source_id": "deeparithmark_v1_fractions_depth3_0086", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "24", "unit": "buns", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split all the cookies among one more child", "split all the cookies, not the rest", "stopped after giving the third away", "correct"], "solution_steps": ["one third given away: 144 / 3 = 48", "rest kept: 144 - 48 = 96", "split among 4: 96 / 4 = 24"], "option_values": [28, 36, 96, 24], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 87, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:01 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:01 a.m. for 110 minutes. The booking ended at", "endings": [" 8:51 a.m.", " 9:36 a.m.", " 9:51 a.m.", " 6:11 a.m."], "source_id": "deeparithmark_v1_time_depth2_0087", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "591", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "stopped a quarter of an hour early", "correct", "subtracted the duration instead of adding it"], "solution_steps": ["convert the start: 481 minutes after midnight", "add the duration: 481 + 110 = 591 minutes"], "option_values": [531, 576, 591, 371], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 88, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $529.20.", " $597.60.", " $690.80.", " $565.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0088", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "56520", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "paid overtime at double rate", "added the tax instead of withholding it", "correct"], "solution_steps": ["regular pay: 40 x 1200 = 48000", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 6 x 1800 = 10800", "gross with bonus: 48000 + 10800 + 4000 = 62800", "take-home: 62800 - 6280 = 56520"], "option_values": [52920, 59760, 69080, 56520], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 89, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 130, then 140 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 130, then 140 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 34 crates.", " 36 crates.", " 53 crates.", " 44 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0089", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "44", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped twice and damaged twice", "shipped out twice", "forgot the shipping", "correct"], "solution_steps": ["after delivery: 760 + 130 = 890", "after shipping: 890 - 140 = 750", "good units: 750 - 32 = 718", "full crates: 718 / 16 = 44 (remainder 14)"], "option_values": [34, 36, 53, 44], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 90, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 6 litres per minute for 6 minutes, then 7 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 6 litres per minute for 6 minutes, then 7 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 249 litres.", " 278 litres.", " 236 litres.", " 285 litres."], "source_id": "deeparithmark_v1_rate_depth4_0090", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "285", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the first fill", "used the first rate for both stages", "forgot the second fill", "correct"], "solution_steps": ["first fill: 6 x 6 = 36 litres", "second fill: 7 x 7 = 49 litres", "before draining: 240 + 36 + 49 = 325", "after draining: 325 - 40 = 285"], "option_values": [249, 278, 236, 285], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 91, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 6 metres and 55 centimetres long. A worker cut off 90 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 6 metres and 55 centimetres long. A worker cut off 90 centimetres. The board left was", "endings": [" 565 centimetres.", " 465 centimetres.", " 575 centimetres.", " 745 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0091", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "565", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["correct", "cut a whole metre off as well", "stopped ten centimetres short of the cut", "added the cut instead of removing it"], "solution_steps": ["convert metres: 6 x 100 = 600 cm", "add the extra centimetres: 600 + 55 = 655 cm", "subtract the cut: 655 - 90 = 565 cm"], "option_values": [565, 465, 575, 745], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 92, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $18.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $18.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $492.80.", " $708.80.", " $676.80.", " $636.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0092", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "70880", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the overtime", "correct", "forgot the bonus", "paid overtime at the normal rate"], "solution_steps": ["regular pay: 32 x 1800 = 57600", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 10 x 2700 = 27000", "gross with bonus: 57600 + 27000 + 4000 = 88600", "take-home: 88600 - 17720 = 70880"], "option_values": [49280, 70880, 67680, 63680], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 93, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 15 litres per minute for 6 minutes, then 5 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 15 litres per minute for 6 minutes, then 5 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 95 litres.", " 185 litres.", " 275 litres.", " 325 litres."], "source_id": "deeparithmark_v1_rate_depth4_0093", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "185", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the first fill", "correct", "used the first rate for both stages", "added the drain instead of removing it"], "solution_steps": ["first fill: 15 x 6 = 90 litres", "second fill: 5 x 9 = 45 litres", "before draining: 120 + 90 + 45 = 255", "after draining: 255 - 70 = 185"], "option_values": [95, 185, 275, 325], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 94, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.20 was split between two teams in the ratio 2:1 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.20 was split between two teams in the ratio 2:1 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.09.", " $0.04.", " $0.07.", " $0.05."], "source_id": "deeparithmark_v1_ratio_depth5_0094", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "9", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "swapped the ratio parts", "forgot the fee and the charity cut", "gave the larger share to the smaller ratio"], "solution_steps": ["after the fee: 520 - 400 = 120", "one ratio part: 120 / 3 = 40", "larger share: 2 x 40 = 80", "after charity: 80 - 8 = 72", "per player: 72 / 8 = 9"], "option_values": [9, 4, 7, 5], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 95, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $5.40. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $5.40. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $6.29.", " $5.65.", " $5.21.", " $5.56."], "source_id": "deeparithmark_v1_money_percent_depth2_0095", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "521", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["added the discount instead of removing it", "read the percentage as a flat number of cents", "correct", "charged the handling fee twice"], "solution_steps": ["take 10% of 540 off: 540 - 54 = 486", "add the 35-cent fee: 486 + 35 = 521"], "option_values": [629, 565, 521, 556], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 96, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 180, then 250 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 180, then 250 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 23 crates.", " 45 crates.", " 41 crates.", " 42 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0096", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "41", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped twice and damaged twice", "added the damaged units", "correct", "counted the loose units as a crate"], "solution_steps": ["after delivery: 760 + 180 = 940", "after shipping: 940 - 250 = 690", "good units: 690 - 32 = 658", "full crates: 658 / 16 = 41 (remainder 2)"], "option_values": [23, 45, 41, 42], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 97, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $5.40. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $5.40. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $3.49.", " $4.32.", " $4.52.", " $4.57."], "source_id": "deeparithmark_v1_money_percent_depth2_0097", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "457", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "forgot the fee", "took the discount off the fee as well", "correct"], "solution_steps": ["take 20% of 540 off: 540 - 108 = 432", "add the 25-cent fee: 432 + 25 = 457"], "option_values": [349, 432, 452, 457], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 98, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $24.00. A 25% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $24.00. A 25% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $8.70.", " $9.30.", " $9.90.", " $13.20."], "source_id": "deeparithmark_v1_percent_money_depth4_0098", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "930", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["used the coupon twice", "correct", "forgot the coupon", "forgot the discount and the coupon"], "solution_steps": ["discount: 2400 - 600 = 1800", "tax on the discounted price: 1800 + 180 = 1980", "coupon: 1980 - 120 = 1860", "split 2 ways: 1860 / 2 = 930"], "option_values": [870, 930, 990, 1320], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 99, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 3 hours at $12.50 an hour, and then 4 hours at $15.50 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 3 hours at $12.50 an hour, and then 4 hours at $15.50 an hour. He earned", "endings": [" $71.50.", " $96.50.", " $108.50.", " $99.50."], "source_id": "deeparithmark_v1_rate_pay_depth3_0099", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "9950", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["worked one hour less in each stretch", "swapped the two rates", "paid every hour at the second rate", "correct"], "solution_steps": ["first stretch: 3 x 1250 = 3750", "second stretch: 4 x 1550 = 6200", "total pay: 3750 + 6200 = 9950"], "option_values": [7150, 9650, 10850, 9950], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 100, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 20% discount came off it, then 15% tax was added to the discounted price, and a $1.20 coupon was applied last. 5 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 20% discount came off it, then 15% tax was added to the discounted price, and a $1.20 coupon was applied last. 5 people split the final cost equally. Each paid", "endings": [" $2.86.", " $3.92.", " $3.44.", " $4.36."], "source_id": "deeparithmark_v1_percent_money_depth4_0100", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "344", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["split the total among one more person", "added the coupon instead of subtracting it", "correct", "forgot the discount"], "solution_steps": ["discount: 2000 - 400 = 1600", "tax on the discounted price: 1600 + 240 = 1840", "coupon: 1840 - 120 = 1720", "split 5 ways: 1720 / 5 = 344"], "option_values": [286, 392, 344, 436], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 101, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.80 was split between two teams in the ratio 4:3 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.80 was split between two teams in the ratio 4:3 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.35.", " $0.28.", " $0.63.", " $0.36."], "source_id": "deeparithmark_v1_ratio_depth5_0101", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "36", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the fee and the charity cut", "split among one more player", "took the charity cut off the whole prize", "correct"], "solution_steps": ["after the fee: 780 - 500 = 280", "one ratio part: 280 / 7 = 40", "larger share: 4 x 40 = 160", "after charity: 160 - 16 = 144", "per player: 144 / 4 = 36"], "option_values": [35, 28, 63, 36], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 102, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $11.00 an hour, and then 3 hours at $16.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $11.00 an hour, and then 3 hours at $16.00 an hour. He earned", "endings": [" $112.00.", " $97.00.", " $189.00.", " $92.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0102", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "9200", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid every hour at the second rate", "swapped the two rates", "added the rates together", "correct"], "solution_steps": ["first stretch: 4 x 1100 = 4400", "second stretch: 3 x 1600 = 4800", "total pay: 4400 + 4800 = 9200"], "option_values": [11200, 9700, 18900, 9200], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 103, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.90 was split between two teams in the ratio 2:1 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.90 was split between two teams in the ratio 2:1 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.09.", " $0.06.", " $0.07.", " $0.12."], "source_id": "deeparithmark_v1_ratio_depth5_0103", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "12", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "swapped the ratio parts", "gave the larger share to the smaller ratio", "correct"], "solution_steps": ["after the fee: 590 - 500 = 90", "one ratio part: 90 / 3 = 30", "larger share: 2 x 30 = 60", "after charity: 60 - 12 = 48", "per player: 48 / 4 = 12"], "option_values": [9, 6, 7, 12], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 104, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $3.01.", " $3.68.", " $3.93.", " $4.65."], "source_id": "deeparithmark_v1_money_percent_depth2_0104", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "393", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "forgot the fee", "correct", "read the percentage as a flat number of cents"], "solution_steps": ["take 20% of 460 off: 460 - 92 = 368", "add the 25-cent fee: 368 + 25 = 393"], "option_values": [301, 368, 393, 465], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 105, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $14.00 an hour and 10 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $14.00 an hour and 10 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $596.70.", " $887.80.", " $692.20.", " $656.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0105", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "65620", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at the normal rate", "added the tax instead of withholding it", "taxed only the regular pay", "correct"], "solution_steps": ["regular pay: 38 x 1400 = 53200", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 10 x 2100 = 21000", "gross with bonus: 53200 + 21000 + 3000 = 77200", "take-home: 77200 - 11580 = 65620"], "option_values": [59670, 88780, 69220, 65620], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 106, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $0.45 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 3 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $0.45 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 3 friends. Each person paid", "endings": [" $1.56.", " $1.95.", " $1.57.", " $2.07."], "source_id": "deeparithmark_v1_money_depth4_0106", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "195", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among one more person", "correct", "charged the marker price for everything", "swapped the two unit prices"], "solution_steps": ["markers: 8 x 45 = 360", "erasers: 6 x 70 = 420", "total cost: 360 + 420 = 780", "split between 4 people: 780 / 4 = 195"], "option_values": [156, 195, 157, 207], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 107, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Vera baked 144 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Vera baked 144 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 19 muffins.", " 18 muffins.", " 24 muffins.", " 28 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0107", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "24", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split the rest among one more child", "gave away a half instead of a third", "correct", "split all the cookies among one more child"], "solution_steps": ["one third given away: 144 / 3 = 48", "rest kept: 144 - 48 = 96", "split among 4: 96 / 4 = 24"], "option_values": [19, 18, 24, 28], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 108, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:37 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:37 a.m. for 65 minutes. The booking ended at", "endings": [" 8:42 a.m.", " 7:42 a.m.", " 10:12 a.m.", " 9:12 a.m."], "source_id": "deeparithmark_v1_time_depth2_0108", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "522", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "dropped the hour carry", "ran an hour and a half long", "ran half an hour long"], "solution_steps": ["convert the start: 457 minutes after midnight", "add the duration: 457 + 65 = 522 minutes"], "option_values": [522, 462, 612, 552], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 109, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 700 units. A delivery added 260, then 250 units were shipped out, and 12 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 700 units. A delivery added 260, then 250 units were shipped out, and 12 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 77 crates.", " 48 crates.", " 69 crates.", " 49 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0109", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "77", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "shipped twice and damaged twice", "packed into larger crates", "shipped out twice"], "solution_steps": ["after delivery: 700 + 260 = 960", "after shipping: 960 - 250 = 710", "good units: 710 - 12 = 698", "full crates: 698 / 9 = 77 (remainder 5)"], "option_values": [77, 48, 69, 49], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 110, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:27 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:27 a.m. for 110 minutes. The booking ended at", "endings": [" 10:17 a.m.", " 9:47 a.m.", " 9:17 a.m.", " 10:47 a.m."], "source_id": "deeparithmark_v1_time_depth2_0110", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "557", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added an extra hour", "ran half an hour long", "correct", "ran an hour and a half long"], "solution_steps": ["convert the start: 447 minutes after midnight", "add the duration: 447 + 110 = 557 minutes"], "option_values": [617, 587, 557, 647], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 111, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:12 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:12 a.m. for 50 minutes. The booking ended at", "endings": [" 7:02 a.m.", " 6:22 a.m.", " 9:02 a.m.", " 8:02 a.m."], "source_id": "deeparithmark_v1_time_depth2_0111", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "482", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "subtracted the duration instead of adding it", "added an extra hour", "correct"], "solution_steps": ["convert the start: 432 minutes after midnight", "add the duration: 432 + 50 = 482 minutes"], "option_values": [422, 382, 542, 482], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 112, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 4 markers at $0.60 each and 3 erasers at $0.70 each. She split the total cost equally between herself and 5 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 4 markers at $0.60 each and 3 erasers at $0.70 each. She split the total cost equally between herself and 5 friends. Each person paid", "endings": [" $0.64.", " $0.56.", " $0.75.", " $0.76."], "source_id": "deeparithmark_v1_money_depth4_0112", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "75", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among one more person", "split among two more people", "correct", "swapped the two unit prices"], "solution_steps": ["markers: 4 x 60 = 240", "erasers: 3 x 70 = 210", "total cost: 240 + 210 = 450", "split between 6 people: 450 / 6 = 75"], "option_values": [64, 56, 75, 76], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 113, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 25% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 25% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $1.55.", " $2.15.", " $3.35.", " $2.75."], "source_id": "deeparithmark_v1_money_percent_depth2_0113", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "215", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "correct", "added the discount instead of removing it", "forgot the discount"], "solution_steps": ["take 25% of 240 off: 240 - 60 = 180", "add the 35-cent fee: 180 + 35 = 215"], "option_values": [155, 215, 335, 275], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 114, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $16.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $16.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $506.80.", " $832.60.", " $615.40.", " $647.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0114", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "61540", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "added the tax instead of withholding it", "correct", "taxed only the regular pay"], "solution_steps": ["regular pay: 32 x 1600 = 51200", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 8 x 2400 = 19200", "gross with bonus: 51200 + 19200 + 2000 = 72400", "take-home: 72400 - 10860 = 61540"], "option_values": [50680, 83260, 61540, 64720], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 115, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $11.00 an hour, and then 3 hours at $15.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $11.00 an hour, and then 3 hours at $15.00 an hour. He earned", "endings": [" $135.00.", " $123.00.", " $234.00.", " $111.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0115", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "11100", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid every hour at the second rate", "swapped the two rates", "added the rates together", "correct"], "solution_steps": ["first stretch: 6 x 1100 = 6600", "second stretch: 3 x 1500 = 4500", "total pay: 6600 + 4500 = 11100"], "option_values": [13500, 12300, 23400, 11100], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 116, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 5 metres and 74 centimetres long. A worker cut off 115 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 5 metres and 74 centimetres long. A worker cut off 115 centimetres. The board left was", "endings": [" 359 centimetres.", " 385 centimetres.", " 459 centimetres.", " 789 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0116", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "459", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["cut a whole metre off as well", "forgot the extra centimetres", "correct", "added the cut and a whole metre"], "solution_steps": ["convert metres: 5 x 100 = 500 cm", "add the extra centimetres: 500 + 74 = 574 cm", "subtract the cut: 574 - 115 = 459 cm"], "option_values": [359, 385, 459, 789], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 117, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:18 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:18 a.m. for 65 minutes. The booking ended at", "endings": [" 9:23 a.m.", " 7:13 a.m.", " 8:23 a.m.", " 9:08 a.m."], "source_id": "deeparithmark_v1_time_depth2_0117", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "563", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "subtracted the duration instead of adding it", "dropped the hour carry", "stopped a quarter of an hour early"], "solution_steps": ["convert the start: 498 minutes after midnight", "add the duration: 498 + 65 = 563 minutes"], "option_values": [563, 433, 503, 548], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 118, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 25% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 25% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $4.55.", " $6.57.", " $6.65.", " $10.85."], "source_id": "deeparithmark_v1_money_percent_depth2_0118", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "665", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "took the discount off the fee as well", "correct", "added the discount instead of removing it"], "solution_steps": ["take 25% of 840 off: 840 - 210 = 630", "add the 35-cent fee: 630 + 35 = 665"], "option_values": [455, 657, 665, 1085], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 119, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $24.00. A 10% discount came off it, then 5% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $24.00. A 10% discount came off it, then 5% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $11.04.", " $11.64.", " $11.34.", " $22.08."], "source_id": "deeparithmark_v1_percent_money_depth4_0119", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "1104", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "added the coupon instead of subtracting it", "forgot the coupon", "split the total among one fewer person"], "solution_steps": ["discount: 2400 - 240 = 2160", "tax on the discounted price: 2160 + 108 = 2268", "coupon: 2268 - 60 = 2208", "split 2 ways: 2208 / 2 = 1104"], "option_values": [1104, 1164, 1134, 2208], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 120, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 480 shirts. It sold 25% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 480 shirts. It sold 25% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "endings": [" 51 boxes.", " 17 boxes.", " 34 boxes.", " 52 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0120", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "51", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "packed the sold shirts", "sold twice as many", "rounded the box count up"], "solution_steps": ["sold: 25% of 480 = 120", "left over: 480 - 120 = 360", "full boxes: 360 / 7 = 51 (remainder 3)"], "option_values": [51, 17, 34, 52], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 121, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 4 markers at $0.60 each and 4 erasers at $0.30 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 4 markers at $0.60 each and 4 erasers at $0.30 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $0.51.", " $0.73.", " $0.72.", " $0.96."], "source_id": "deeparithmark_v1_money_depth4_0121", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "72", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among two more people", "added the unit prices instead of multiplying", "correct", "charged the marker price for everything"], "solution_steps": ["markers: 4 x 60 = 240", "erasers: 4 x 30 = 120", "total cost: 240 + 120 = 360", "split between 5 people: 360 / 5 = 72"], "option_values": [51, 73, 72, 96], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 122, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:44 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:44 a.m. for 50 minutes. The booking ended at", "endings": [" 6:34 a.m.", " 7:19 a.m.", " 5:54 a.m.", " 7:34 a.m."], "source_id": "deeparithmark_v1_time_depth2_0122", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "454", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "stopped a quarter of an hour early", "subtracted the duration instead of adding it", "correct"], "solution_steps": ["convert the start: 404 minutes after midnight", "add the duration: 404 + 50 = 454 minutes"], "option_values": [394, 439, 354, 454], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 123, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:53 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:53 a.m. for 65 minutes. The booking ended at", "endings": [" 8:43 a.m.", " 6:48 a.m.", " 8:58 a.m.", " 7:58 a.m."], "source_id": "deeparithmark_v1_time_depth2_0123", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "538", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "subtracted the duration instead of adding it", "correct", "dropped the hour carry"], "solution_steps": ["convert the start: 473 minutes after midnight", "add the duration: 473 + 65 = 538 minutes"], "option_values": [523, 408, 538, 478], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 124, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 560 units. A delivery added 260, then 90 units were shipped out, and 40 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 560 units. A delivery added 260, then 90 units were shipped out, and 40 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "endings": [" 15 crates.", " 49 crates.", " 46 crates.", " 55 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0124", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "49", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed the arriving units only", "correct", "packed into larger crates", "forgot the shipping"], "solution_steps": ["after delivery: 560 + 260 = 820", "after shipping: 820 - 90 = 730", "good units: 730 - 40 = 690", "full crates: 690 / 14 = 49 (remainder 4)"], "option_values": [15, 49, 46, 55], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 125, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 36 km at 12 km/h, rested 25 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 36 km at 12 km/h, rested 25 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "endings": [" 205 minutes.", " 97 minutes.", " 385 minutes.", " 637 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0125", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "385", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "divided by the speed twice", "correct", "used the walking speed for both legs"], "solution_steps": ["cycling time: 60 x 36 / 12 = 180 minutes", "walking time: 60 x 15 / 5 = 180 minutes", "add the rest: 180 + 25 + 180 = 385 minutes"], "option_values": [205, 97, 385, 637], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 126, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 6 litres per minute for 6 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 6 litres per minute for 6 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 116 litres.", " 251 litres.", " 111 litres.", " 181 litres."], "source_id": "deeparithmark_v1_rate_depth4_0126", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "111", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["used the first rate for both stages", "added the drain instead of removing it", "correct", "forgot the drain"], "solution_steps": ["first fill: 6 x 6 = 36 litres", "second fill: 5 x 5 = 25 litres", "before draining: 120 + 36 + 25 = 181", "after draining: 181 - 70 = 111"], "option_values": [116, 251, 111, 181], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 127, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 25% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 25% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 49 pallets.", " 42 pallets.", " 54 pallets.", " 55 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0127", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "54", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "took both percentages off the original stock", "correct", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 25% of 1200 = 300", "left after Monday: 1200 - 300 = 900", "Tuesday: 40% of 900 = 360", "left after Tuesday: 900 - 360 = 540", "full pallets: 540 / 10 = 54"], "option_values": [49, 42, 54, 55], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 128, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 30% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 30% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 37 pallets.", " 15 pallets.", " 42 pallets.", " 55 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0128", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "37", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "took both percentages twice", "forgot Tuesday", "forgot Monday"], "solution_steps": ["Monday: 30% of 600 = 180", "left after Monday: 600 - 180 = 420", "Tuesday: 10% of 420 = 42", "left after Tuesday: 420 - 42 = 378", "full pallets: 378 / 10 = 37"], "option_values": [37, 15, 42, 55], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 129, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 50% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 50% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $7.15.", " $4.05.", " $7.65.", " $11.25."], "source_id": "deeparithmark_v1_money_percent_depth2_0129", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "405", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["read the percentage as a flat number of cents", "correct", "forgot the discount", "added the discount instead of removing it"], "solution_steps": ["take 50% of 720 off: 720 - 360 = 360", "add the 45-cent fee: 360 + 45 = 405"], "option_values": [715, 405, 765, 1125], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 130, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Amara baked 162 cookies. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Amara baked 162 cookies. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "endings": [" 18 cookies.", " 15 cookies.", " 9 cookies.", " 7 cookies."], "source_id": "deeparithmark_v1_fractions_depth3_0130", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "18", "unit": "cookies", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["correct", "split the rest among one more child", "split the given-away cookies too", "gave away two thirds and split among one more child"], "solution_steps": ["one third given away: 162 / 3 = 54", "rest kept: 162 - 54 = 108", "split among 6: 108 / 6 = 18"], "option_values": [18, 15, 9, 7], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 131, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $12.00 an hour and 4 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $12.00 an hour and 4 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $587.40.", " $490.80.", " $480.60.", " $502.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0131", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "48060", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["added the tax instead of withholding it", "taxed only the regular pay", "correct", "paid overtime at double rate"], "solution_steps": ["regular pay: 36 x 1200 = 43200", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 4 x 1800 = 7200", "gross with bonus: 43200 + 7200 + 3000 = 53400", "take-home: 53400 - 5340 = 48060"], "option_values": [58740, 49080, 48060, 50220], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 132, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $3.77.", " $3.39.", " $3.74.", " $4.15."], "source_id": "deeparithmark_v1_money_percent_depth2_0132", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "377", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the percentage off twice", "took the discount off the fee as well", "forgot the discount"], "solution_steps": ["take 10% of 380 off: 380 - 38 = 342", "add the 35-cent fee: 342 + 35 = 377"], "option_values": [377, 339, 374, 415], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 133, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $5.40. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $5.40. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $4.57.", " $5.11.", " $6.19.", " $5.36."], "source_id": "deeparithmark_v1_money_percent_depth2_0133", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "511", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "correct", "added the discount instead of removing it", "charged the handling fee twice"], "solution_steps": ["take 10% of 540 off: 540 - 54 = 486", "add the 25-cent fee: 486 + 25 = 511"], "option_values": [457, 511, 619, 536], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 134, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 6 metres and 68 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 6 metres and 68 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 555 centimetres.", " 813 centimetres.", " 713 centimetres.", " 623 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0134", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "623", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["forgot the extra centimetres", "added the cut and a whole metre", "added the cut instead of removing it", "correct"], "solution_steps": ["convert metres: 6 x 100 = 600 cm", "add the extra centimetres: 600 + 68 = 668 cm", "subtract the cut: 668 - 45 = 623 cm"], "option_values": [555, 813, 713, 623], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 135, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $565.20.", " $633.60.", " $651.60.", " $663.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0135", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "65160", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the overtime", "forgot the bonus", "correct", "taxed only the regular pay"], "solution_steps": ["regular pay: 38 x 1600 = 60800", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 4 x 2400 = 9600", "gross with bonus: 60800 + 9600 + 2000 = 72400", "take-home: 72400 - 7240 = 65160"], "option_values": [56520, 63360, 65160, 66320], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 136, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $14.00 an hour and 10 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $14.00 an hour and 10 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $354.00.", " $708.00.", " $531.00.", " $885.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0136", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "53100", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "forgot the tax", "correct", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 32 x 1400 = 44800", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 10 x 2100 = 21000", "gross with bonus: 44800 + 21000 + 5000 = 70800", "take-home: 70800 - 17700 = 53100"], "option_values": [35400, 70800, 53100, 88500], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 137, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $18.00 an hour and 8 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $18.00 an hour and 8 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $724.50.", " $670.50.", " $1207.50.", " $778.50."], "source_id": "deeparithmark_v1_money_rate_depth5_0137", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "72450", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "paid overtime at the normal rate", "added the tax instead of withholding it", "paid overtime at double rate"], "solution_steps": ["regular pay: 40 x 1800 = 72000", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 8 x 2700 = 21600", "gross with bonus: 72000 + 21600 + 3000 = 96600", "take-home: 96600 - 24150 = 72450"], "option_values": [72450, 67050, 120750, 77850], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 138, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $14.00 an hour, and then 3 hours at $18.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $14.00 an hour, and then 3 hours at $18.00 an hour. He earned", "endings": [" $84.00.", " $138.00.", " $288.00.", " $162.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0138", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "13800", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["forgot the second stretch", "correct", "added the rates together", "paid every hour at the second rate"], "solution_steps": ["first stretch: 6 x 1400 = 8400", "second stretch: 3 x 1800 = 5400", "total pay: 8400 + 5400 = 13800"], "option_values": [8400, 13800, 28800, 16200], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 139, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 840 units. A delivery added 130, then 250 units were shipped out, and 40 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 840 units. A delivery added 130, then 250 units were shipped out, and 40 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 75 crates.", " 68 crates.", " 43 crates.", " 61 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0139", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "75", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "packed into larger crates", "shipped twice and damaged twice", "forgot the delivery"], "solution_steps": ["after delivery: 840 + 130 = 970", "after shipping: 970 - 250 = 720", "good units: 720 - 40 = 680", "full crates: 680 / 9 = 75 (remainder 5)"], "option_values": [75, 68, 43, 61], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 140, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $8.00 was split between two teams in the ratio 5:1 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $8.00 was split between two teams in the ratio 5:1 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $1.33.", " $0.54.", " $0.45.", " $1.12."], "source_id": "deeparithmark_v1_ratio_depth5_0140", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "45", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot to deduct the fee", "took the charity cut off the whole prize", "correct", "divided between the teams instead of the players"], "solution_steps": ["after the fee: 800 - 500 = 300", "one ratio part: 300 / 6 = 50", "larger share: 5 x 50 = 250", "after charity: 250 - 25 = 225", "per player: 225 / 5 = 45"], "option_values": [133, 54, 45, 112], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 141, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $5.40. The booth took 50% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $5.40. The booth took 50% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $3.05.", " $2.88.", " $5.75.", " $8.45."], "source_id": "deeparithmark_v1_money_percent_depth2_0141", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "305", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the discount off the fee as well", "forgot the discount", "added the discount instead of removing it"], "solution_steps": ["take 50% of 540 off: 540 - 270 = 270", "add the 35-cent fee: 270 + 35 = 305"], "option_values": [305, 288, 575, 845], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 142, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $0.95 each and 5 erasers at $0.50 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $0.95 each and 5 erasers at $0.50 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.75.", " $2.02.", " $2.52.", " $2.04."], "source_id": "deeparithmark_v1_money_depth4_0142", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "202", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["swapped the two unit prices", "correct", "split only between the friends", "added the unit prices instead of multiplying"], "solution_steps": ["markers: 8 x 95 = 760", "erasers: 5 x 50 = 250", "total cost: 760 + 250 = 1010", "split between 5 people: 1010 / 5 = 202"], "option_values": [175, 202, 252, 204], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 143, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $12.00. A 20% discount came off it, then 15% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $12.00. A 20% discount came off it, then 15% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $2.66.", " $1.97.", " $2.12.", " $2.56."], "source_id": "deeparithmark_v1_percent_money_depth4_0143", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "266", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "applied the discount twice", "split the total among one more person", "used the coupon twice"], "solution_steps": ["discount: 1200 - 240 = 960", "tax on the discounted price: 960 + 144 = 1104", "coupon: 1104 - 40 = 1064", "split 4 ways: 1064 / 4 = 266"], "option_values": [266, 197, 212, 256], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 144, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $5.59.", " $6.26.", " $6.12.", " $6.27."], "source_id": "deeparithmark_v1_money_percent_depth2_0144", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "627", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "took the discount off the fee as well", "forgot the fee", "correct"], "solution_steps": ["take 10% of 680 off: 680 - 68 = 612", "add the 15-cent fee: 612 + 15 = 627"], "option_values": [559, 626, 612, 627], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 145, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $3.36.", " $4.16.", " $3.68.", " $4.28."], "source_id": "deeparithmark_v1_money_percent_depth2_0145", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "428", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "took the discount off the fee as well", "forgot the fee", "correct"], "solution_steps": ["take 20% of 460 off: 460 - 92 = 368", "add the 60-cent fee: 368 + 60 = 428"], "option_values": [336, 416, 368, 428], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 146, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $3.11.", " $4.03.", " $3.68.", " $4.38."], "source_id": "deeparithmark_v1_money_percent_depth2_0146", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "403", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "correct", "forgot the fee", "charged the handling fee twice"], "solution_steps": ["take 20% of 460 off: 460 - 92 = 368", "add the 35-cent fee: 368 + 35 = 403"], "option_values": [311, 403, 368, 438], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 147, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 4 metres and 12 centimetres long. A worker cut off 60 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 4 metres and 12 centimetres long. A worker cut off 60 centimetres. The board left was", "endings": [" 252 centimetres.", " 362 centimetres.", " 352 centimetres.", " 472 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0147", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "352", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["cut a whole metre off as well", "stopped ten centimetres short of the cut", "correct", "added the cut instead of removing it"], "solution_steps": ["convert metres: 4 x 100 = 400 cm", "add the extra centimetres: 400 + 12 = 412 cm", "subtract the cut: 412 - 60 = 352 cm"], "option_values": [252, 362, 352, 472], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 148, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:04 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:04 a.m. for 65 minutes. The booking ended at", "endings": [" 4:59 a.m.", " 6:09 a.m.", " 6:54 a.m.", " 7:09 a.m."], "source_id": "deeparithmark_v1_time_depth2_0148", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "429", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "dropped the hour carry", "stopped a quarter of an hour early", "correct"], "solution_steps": ["convert the start: 364 minutes after midnight", "add the duration: 364 + 65 = 429 minutes"], "option_values": [299, 369, 414, 429], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 149, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $0.95 each and 3 erasers at $0.30 each. She split the total cost equally between herself and 3 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $0.95 each and 3 erasers at $0.30 each. She split the total cost equally between herself and 3 friends. Each person paid", "endings": [" $1.16.", " $1.96.", " $1.65.", " $2.13."], "source_id": "deeparithmark_v1_money_depth4_0149", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "165", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["swapped the two unit prices", "bought one extra of each item", "correct", "charged the marker price for everything"], "solution_steps": ["markers: 6 x 95 = 570", "erasers: 3 x 30 = 90", "total cost: 570 + 90 = 660", "split between 4 people: 660 / 4 = 165"], "option_values": [116, 196, 165, 213], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 150, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $3.39.", " $3.04.", " $3.74.", " $4.91."], "source_id": "deeparithmark_v1_money_percent_depth2_0150", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "339", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "forgot the fee", "charged the handling fee twice", "added the discount instead of removing it"], "solution_steps": ["take 20% of 380 off: 380 - 76 = 304", "add the 35-cent fee: 304 + 35 = 339"], "option_values": [339, 304, 374, 491], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 151, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $6.97.", " $5.29.", " $6.92.", " $10.33."], "source_id": "deeparithmark_v1_money_percent_depth2_0151", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "697", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the percentage off twice", "took the discount off the fee as well", "added the discount instead of removing it"], "solution_steps": ["take 20% of 840 off: 840 - 168 = 672", "add the 25-cent fee: 672 + 25 = 697"], "option_values": [697, 529, 692, 1033], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 152, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $0.45 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $0.45 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $1.25.", " $0.93.", " $0.75.", " $1.15."], "source_id": "deeparithmark_v1_money_depth4_0152", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "125", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "split among one more person", "split among two more people", "swapped the two unit prices"], "solution_steps": ["markers: 6 x 45 = 270", "erasers: 3 x 35 = 105", "total cost: 270 + 105 = 375", "split between 3 people: 375 / 3 = 125"], "option_values": [125, 93, 75, 115], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 153, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $817.50.", " $637.50.", " $1362.50.", " $877.50."], "source_id": "deeparithmark_v1_money_rate_depth5_0153", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "81750", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "forgot the overtime", "added the tax instead of withholding it", "paid overtime at double rate"], "solution_steps": ["regular pay: 40 x 2000 = 80000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 8 x 3000 = 24000", "gross with bonus: 80000 + 24000 + 5000 = 109000", "take-home: 109000 - 27250 = 81750"], "option_values": [81750, 63750, 136250, 87750], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 154, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 3 hours at $12.50 an hour, and then 4 hours at $14.50 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 3 hours at $12.50 an hour, and then 4 hours at $14.50 an hour. He earned", "endings": [" $87.50.", " $37.50.", " $93.50.", " $95.50."], "source_id": "deeparithmark_v1_rate_pay_depth3_0154", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "9550", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid every hour at the first rate", "forgot the second stretch", "swapped the two rates", "correct"], "solution_steps": ["first stretch: 3 x 1250 = 3750", "second stretch: 4 x 1450 = 5800", "total pay: 3750 + 5800 = 9550"], "option_values": [8750, 3750, 9350, 9550], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 155, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:16 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:16 a.m. for 110 minutes. The booking ended at", "endings": [" 8:51 a.m.", " 10:36 a.m.", " 9:06 a.m.", " 10:06 a.m."], "source_id": "deeparithmark_v1_time_depth2_0155", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "546", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "ran an hour and a half long", "correct", "added an extra hour"], "solution_steps": ["convert the start: 436 minutes after midnight", "add the duration: 436 + 110 = 546 minutes"], "option_values": [531, 636, 546, 606], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 156, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $5.76.", " $4.67.", " $7.55.", " $6.11."], "source_id": "deeparithmark_v1_money_percent_depth2_0156", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "611", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "took the percentage off twice", "forgot the discount", "correct"], "solution_steps": ["take 20% of 720 off: 720 - 144 = 576", "add the 35-cent fee: 576 + 35 = 611"], "option_values": [576, 467, 755, 611], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 157, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 6 metres and 38 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 6 metres and 38 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 593 centimetres.", " 783 centimetres.", " 631 centimetres.", " 603 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0157", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "593", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["correct", "added the cut and a whole metre", "counted the extra centimetres twice", "stopped ten centimetres short of the cut"], "solution_steps": ["convert metres: 6 x 100 = 600 cm", "add the extra centimetres: 600 + 38 = 638 cm", "subtract the cut: 638 - 45 = 593 cm"], "option_values": [593, 783, 631, 603], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 158, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 20% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 20% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 16 pallets.", " 48 pallets.", " 44 pallets.", " 45 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0158", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "48", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "correct", "took both percentages off the original stock", "stacked on larger pallets"], "solution_steps": ["Monday: 20% of 1200 = 240", "left after Monday: 1200 - 240 = 960", "Tuesday: 25% of 960 = 240", "left after Tuesday: 960 - 240 = 720", "full pallets: 720 / 15 = 48"], "option_values": [16, 48, 44, 45], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 159, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:25 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:25 a.m. for 110 minutes. The booking ended at", "endings": [" 7:15 a.m.", " 8:15 a.m.", " 9:15 a.m.", " 9:45 a.m."], "source_id": "deeparithmark_v1_time_depth2_0159", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "495", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added the minutes without the hours", "correct", "added an extra hour", "ran an hour and a half long"], "solution_steps": ["convert the start: 385 minutes after midnight", "add the duration: 385 + 110 = 495 minutes"], "option_values": [435, 495, 555, 585], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 160, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:18 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:18 a.m. for 65 minutes. The booking ended at", "endings": [" 8:23 a.m.", " 7:23 a.m.", " 8:08 a.m.", " 6:13 a.m."], "source_id": "deeparithmark_v1_time_depth2_0160", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "503", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "dropped the hour carry", "stopped a quarter of an hour early", "subtracted the duration instead of adding it"], "solution_steps": ["convert the start: 438 minutes after midnight", "add the duration: 438 + 65 = 503 minutes"], "option_values": [503, 443, 488, 373], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 161, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:38 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:38 a.m. for 125 minutes. The booking ended at", "endings": [" 8:43 a.m.", " 10:43 a.m.", " 10:28 a.m.", " 11:43 a.m."], "source_id": "deeparithmark_v1_time_depth2_0161", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "643", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "correct", "stopped a quarter of an hour early", "added an extra hour"], "solution_steps": ["convert the start: 518 minutes after midnight", "add the duration: 518 + 125 = 643 minutes"], "option_values": [523, 643, 628, 703], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 162, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 50% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 50% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $7.05.", " $7.55.", " $11.15.", " $3.95."], "source_id": "deeparithmark_v1_money_percent_depth2_0162", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "395", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["read the percentage as a flat number of cents", "forgot the discount", "added the discount instead of removing it", "correct"], "solution_steps": ["take 50% of 720 off: 720 - 360 = 360", "add the 35-cent fee: 360 + 35 = 395"], "option_values": [705, 755, 1115, 395], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 163, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $16.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $16.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $622.80.", " $676.80.", " $720.80.", " $694.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0163", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "69480", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at the normal rate", "forgot the bonus", "taxed only the regular pay", "correct"], "solution_steps": ["regular pay: 32 x 1600 = 51200", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 10 x 2400 = 24000", "gross with bonus: 51200 + 24000 + 2000 = 77200", "take-home: 77200 - 7720 = 69480"], "option_values": [62280, 67680, 72080, 69480], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 164, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $1.20 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $1.20 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $5.59.", " $4.56.", " $6.69.", " $6.99."], "source_id": "deeparithmark_v1_percent_money_depth4_0164", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "699", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["split the total among one more person", "applied the discount twice", "used the coupon twice", "correct"], "solution_steps": ["discount: 3600 - 900 = 2700", "tax on the discounted price: 2700 + 216 = 2916", "coupon: 2916 - 120 = 2796", "split 4 ways: 2796 / 4 = 699"], "option_values": [559, 456, 669, 699], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 165, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:55 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:55 a.m. for 95 minutes. The booking ended at", "endings": [" 6:20 a.m.", " 9:30 a.m.", " 8:30 a.m.", " 10:30 a.m."], "source_id": "deeparithmark_v1_time_depth2_0165", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "570", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "correct", "added the minutes without the hours", "added an extra hour"], "solution_steps": ["convert the start: 475 minutes after midnight", "add the duration: 475 + 95 = 570 minutes"], "option_values": [380, 570, 510, 630], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 166, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $3.03.", " $2.22.", " $2.35.", " $2.07."], "source_id": "deeparithmark_v1_money_percent_depth2_0166", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "207", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["added the discount instead of removing it", "charged the handling fee twice", "read the percentage as a flat number of cents", "correct"], "solution_steps": ["take 20% of 240 off: 240 - 48 = 192", "add the 15-cent fee: 192 + 15 = 207"], "option_values": [303, 222, 235, 207], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 167, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:03 a.m.. The first session lasted 50 minutes, the break lasted 10 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:03 a.m.. The first session lasted 50 minutes, the break lasted 10 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 8:33 a.m.", " 7:53 a.m.", " 7:43 a.m.", " 8:43 a.m."], "source_id": "deeparithmark_v1_time_depth3_0167", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "523", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the break", "forgot the last session and the break", "dropped the hour carry", "correct"], "solution_steps": ["after the first session: 423 + 50 = 473 minutes after midnight", "after the break: 473 + 10 = 483", "after the second session: 483 + 40 = 523"], "option_values": [513, 473, 463, 523], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 168, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:36 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:36 a.m. for 65 minutes. The booking ended at", "endings": [" 8:41 a.m.", " 6:31 a.m.", " 7:41 a.m.", " 9:41 a.m."], "source_id": "deeparithmark_v1_time_depth2_0168", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "521", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "subtracted the duration instead of adding it", "dropped the hour carry", "added an extra hour"], "solution_steps": ["convert the start: 456 minutes after midnight", "add the duration: 456 + 65 = 521 minutes"], "option_values": [521, 391, 461, 581], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 169, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $3.04.", " $2.56.", " $3.16.", " $2.52."], "source_id": "deeparithmark_v1_money_percent_depth2_0169", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "316", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "forgot the fee", "correct", "took the percentage off twice"], "solution_steps": ["take 20% of 320 off: 320 - 64 = 256", "add the 60-cent fee: 256 + 60 = 316"], "option_values": [304, 256, 316, 252], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 170, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $4.00 was split between two teams in the ratio 4:1 after a $2.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $4.00 was split between two teams in the ratio 4:1 after a $2.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.06.", " $0.16.", " $0.08.", " $0.24."], "source_id": "deeparithmark_v1_ratio_depth5_0170", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "24", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "gave twice the share away to charity", "gave the larger share to the smaller ratio", "correct"], "solution_steps": ["after the fee: 400 - 200 = 200", "one ratio part: 200 / 5 = 40", "larger share: 4 x 40 = 160", "after charity: 160 - 40 = 120", "per player: 120 / 5 = 24"], "option_values": [6, 16, 8, 24], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 171, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $0.60 each and 6 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $0.60 each and 6 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $0.96.", " $2.17.", " $1.74.", " $1.76."], "source_id": "deeparithmark_v1_money_depth4_0171", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "174", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["forgot the erasers", "split only between the friends", "correct", "swapped the two unit prices"], "solution_steps": ["markers: 8 x 60 = 480", "erasers: 6 x 65 = 390", "total cost: 480 + 390 = 870", "split between 5 people: 870 / 5 = 174"], "option_values": [96, 217, 174, 176], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 172, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:48 a.m.. The first session lasted 55 minutes, the break lasted 10 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:48 a.m.. The first session lasted 55 minutes, the break lasted 10 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 6:33 a.m.", " 8:33 a.m.", " 9:13 a.m.", " 8:43 a.m."], "source_id": "deeparithmark_v1_time_depth3_0172", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "513", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["dropped the hour carry", "correct", "finished half an hour late on top of the break", "counted the break twice"], "solution_steps": ["after the first session: 408 + 55 = 463 minutes after midnight", "after the break: 463 + 10 = 473", "after the second session: 473 + 40 = 513"], "option_values": [393, 513, 553, 523], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 173, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:01 a.m.. The first session lasted 45 minutes, the break lasted 20 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:01 a.m.. The first session lasted 45 minutes, the break lasted 20 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "endings": [" 10:01 a.m.", " 10:26 a.m.", " 10:31 a.m.", " 9:41 a.m."], "source_id": "deeparithmark_v1_time_depth3_0173", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "581", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["counted the break twice", "counted the first session twice", "finished half an hour late on top of the break", "correct"], "solution_steps": ["after the first session: 481 + 45 = 526 minutes after midnight", "after the break: 526 + 20 = 546", "after the second session: 546 + 35 = 581"], "option_values": [601, 626, 631, 581], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 174, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:39 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:39 a.m. for 125 minutes. The booking ended at", "endings": [" 5:34 a.m.", " 11:14 a.m.", " 9:44 a.m.", " 10:44 a.m."], "source_id": "deeparithmark_v1_time_depth2_0174", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "584", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "ran an hour and a half long", "correct", "added an extra hour"], "solution_steps": ["convert the start: 459 minutes after midnight", "add the duration: 459 + 125 = 584 minutes"], "option_values": [334, 674, 584, 644], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 175, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $11.00 an hour, and then 3 hours at $16.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $11.00 an hour, and then 3 hours at $16.00 an hour. He earned", "endings": [" $87.00.", " $144.00.", " $243.00.", " $114.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0175", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "11400", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["worked one hour less in each stretch", "paid every hour at the second rate", "added the rates together", "correct"], "solution_steps": ["first stretch: 6 x 1100 = 6600", "second stretch: 3 x 1600 = 4800", "total pay: 6600 + 4800 = 11400"], "option_values": [8700, 14400, 24300, 11400], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 176, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $5.40. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $5.40. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $4.47.", " $6.63.", " $4.62.", " $5.35."], "source_id": "deeparithmark_v1_money_percent_depth2_0176", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "447", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "added the discount instead of removing it", "charged the handling fee twice", "read the percentage as a flat number of cents"], "solution_steps": ["take 20% of 540 off: 540 - 108 = 432", "add the 15-cent fee: 432 + 15 = 447"], "option_values": [447, 663, 462, 535], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 177, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:05 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:05 a.m. for 50 minutes. The booking ended at", "endings": [" 8:55 a.m.", " 7:15 a.m.", " 9:55 a.m.", " 9:25 a.m."], "source_id": "deeparithmark_v1_time_depth2_0177", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "535", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "subtracted the duration instead of adding it", "added an extra hour", "ran half an hour long"], "solution_steps": ["convert the start: 485 minutes after midnight", "add the duration: 485 + 50 = 535 minutes"], "option_values": [535, 435, 595, 565], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 178, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 4 markers at $1.20 each and 6 erasers at $0.50 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 4 markers at $1.20 each and 6 erasers at $0.50 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $1.60.", " $3.90.", " $7.80.", " $2.60."], "source_id": "deeparithmark_v1_money_depth4_0178", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "260", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["forgot the erasers", "split only between the friends", "did not split the total at all", "correct"], "solution_steps": ["markers: 4 x 120 = 480", "erasers: 6 x 50 = 300", "total cost: 480 + 300 = 780", "split between 3 people: 780 / 3 = 260"], "option_values": [160, 390, 780, 260], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 179, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:34 a.m.. The first session lasted 45 minutes, the break lasted 25 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:34 a.m.. The first session lasted 45 minutes, the break lasted 25 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 9:24 a.m.", " 8:44 a.m.", " 7:24 a.m.", " 8:19 a.m."], "source_id": "deeparithmark_v1_time_depth3_0179", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "564", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["correct", "forgot the second session", "dropped the hour carry", "forgot the last session and the break"], "solution_steps": ["after the first session: 454 + 45 = 499 minutes after midnight", "after the break: 499 + 25 = 524", "after the second session: 524 + 40 = 564"], "option_values": [564, 524, 444, 499], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 180, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $8.79.", " $9.75.", " $9.65.", " $8.94."], "source_id": "deeparithmark_v1_money_percent_depth2_0180", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "879", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "forgot the discount", "read the percentage as a flat number of cents", "charged the handling fee twice"], "solution_steps": ["take 10% of 960 off: 960 - 96 = 864", "add the 15-cent fee: 864 + 15 = 879"], "option_values": [879, 975, 965, 894], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 181, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $16.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $0.60 coupon was applied last. 3 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $16.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $0.60 coupon was applied last. 3 people split the final cost equally. Each paid", "endings": [" $4.28.", " $5.33.", " $4.48.", " $4.68."], "source_id": "deeparithmark_v1_percent_money_depth4_0181", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "428", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "split the price before the discount", "forgot the coupon", "added the coupon instead of subtracting it"], "solution_steps": ["discount: 1600 - 320 = 1280", "tax on the discounted price: 1280 + 64 = 1344", "coupon: 1344 - 60 = 1284", "split 3 ways: 1284 / 3 = 428"], "option_values": [428, 533, 448, 468], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 182, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Ivo baked 144 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Ivo baked 144 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 96 muffins.", " 24 muffins.", " 36 muffins.", " 28 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0182", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "24", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["stopped after giving the third away", "correct", "split all the cookies, not the rest", "split all the cookies among one more child"], "solution_steps": ["one third given away: 144 / 3 = 48", "rest kept: 144 - 48 = 96", "split among 4: 96 / 4 = 24"], "option_values": [96, 24, 36, 28], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 183, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 9 litres per minute for 10 minutes, then 3 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 9 litres per minute for 10 minutes, then 3 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "endings": [" 127 litres.", " 92 litres.", " 155 litres.", " 182 litres."], "source_id": "deeparithmark_v1_rate_depth4_0183", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "182", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "forgot the first fill", "forgot the second fill", "correct"], "solution_steps": ["first fill: 9 x 10 = 90 litres", "second fill: 3 x 9 = 27 litres", "before draining: 120 + 90 + 27 = 237", "after draining: 237 - 55 = 182"], "option_values": [127, 92, 155, 182], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 184, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 4 markers at $0.80 each and 5 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 4 markers at $0.80 each and 5 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.22.", " $0.99.", " $1.08.", " $1.44."], "source_id": "deeparithmark_v1_money_depth4_0184", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "99", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["bought one extra of each item", "correct", "swapped the two unit prices", "charged the marker price for everything"], "solution_steps": ["markers: 4 x 80 = 320", "erasers: 5 x 35 = 175", "total cost: 320 + 175 = 495", "split between 5 people: 495 / 5 = 99"], "option_values": [122, 99, 108, 144], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 185, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $18.00 an hour and 10 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $18.00 an hour and 10 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $792.00.", " $816.00.", " $744.00.", " $612.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0185", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "81600", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "correct", "paid overtime at the normal rate", "taxed twice"], "solution_steps": ["regular pay: 40 x 1800 = 72000", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 10 x 2700 = 27000", "gross with bonus: 72000 + 27000 + 3000 = 102000", "take-home: 102000 - 20400 = 81600"], "option_values": [79200, 81600, 74400, 61200], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 186, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1000 sacks. It sent out 10% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1000 sacks. It sent out 10% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 81 pallets.", " 73 pallets.", " 62 pallets.", " 82 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0186", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "81", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "stacked on larger pallets", "took both percentages twice", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 10% of 1000 = 100", "left after Monday: 1000 - 100 = 900", "Tuesday: 10% of 900 = 90", "left after Tuesday: 900 - 90 = 810", "full pallets: 810 / 10 = 81"], "option_values": [81, 73, 62, 82], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 187, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 75 pallets.", " 68 pallets.", " 67 pallets.", " 92 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0187", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "67", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["forgot Tuesday", "counted the loose sacks as a pallet", "correct", "forgot Monday"], "solution_steps": ["Monday: 25% of 800 = 200", "left after Monday: 800 - 200 = 600", "Tuesday: 10% of 600 = 60", "left after Tuesday: 600 - 60 = 540", "full pallets: 540 / 8 = 67"], "option_values": [75, 68, 67, 92], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 188, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $6.84.", " $6.87.", " $5.19.", " $10.23."], "source_id": "deeparithmark_v1_money_percent_depth2_0188", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "687", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "correct", "took the percentage off twice", "added the discount instead of removing it"], "solution_steps": ["take 20% of 840 off: 840 - 168 = 672", "add the 15-cent fee: 672 + 15 = 687"], "option_values": [684, 687, 519, 1023], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 189, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 15 km at 15 km/h, rested 15 minutes, then walked 4 km at 4 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 15 km at 15 km/h, rested 15 minutes, then walked 4 km at 4 km/h. Her total time, in minutes, was", "endings": [" 135 minutes.", " 75 minutes.", " 45 minutes.", " 91 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0189", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "135", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["correct", "forgot the walking leg", "divided by the speed twice", "used the cycling speed for both legs"], "solution_steps": ["cycling time: 60 x 15 / 15 = 60 minutes", "walking time: 60 x 4 / 4 = 60 minutes", "add the rest: 60 + 15 + 60 = 135 minutes"], "option_values": [135, 75, 45, 91], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 190, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 5 hours at $15.00 an hour, and then 4 hours at $17.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 5 hours at $15.00 an hour, and then 4 hours at $17.00 an hour. He earned", "endings": [" $143.00.", " $145.00.", " $153.00.", " $288.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0190", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "14300", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["correct", "swapped the two rates", "paid every hour at the second rate", "added the rates together"], "solution_steps": ["first stretch: 5 x 1500 = 7500", "second stretch: 4 x 1700 = 6800", "total pay: 7500 + 6800 = 14300"], "option_values": [14300, 14500, 15300, 28800], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 191, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 6 litres per minute for 8 minutes, then 5 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 6 litres per minute for 8 minutes, then 5 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 323 litres.", " 275 litres.", " 253 litres.", " 393 litres."], "source_id": "deeparithmark_v1_rate_depth4_0191", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "323", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "forgot the first fill", "drained twice", "forgot the drain"], "solution_steps": ["first fill: 6 x 8 = 48 litres", "second fill: 5 x 9 = 45 litres", "before draining: 300 + 48 + 45 = 393", "after draining: 393 - 70 = 323"], "option_values": [323, 275, 253, 393], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 192, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:29 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:29 a.m. for 110 minutes. The booking ended at", "endings": [" 9:04 a.m.", " 9:19 a.m.", " 8:19 a.m.", " 9:49 a.m."], "source_id": "deeparithmark_v1_time_depth2_0192", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "559", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "correct", "added the minutes without the hours", "ran half an hour long"], "solution_steps": ["convert the start: 449 minutes after midnight", "add the duration: 449 + 110 = 559 minutes"], "option_values": [544, 559, 499, 589], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 193, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $14.00 an hour and 8 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $14.00 an hour and 8 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $516.80.", " $561.60.", " $556.40.", " $775.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0193", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "51680", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "paid overtime at double rate", "taxed only the regular pay", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 32 x 1400 = 44800", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 8 x 2100 = 16800", "gross with bonus: 44800 + 16800 + 3000 = 64600", "take-home: 64600 - 12920 = 51680"], "option_values": [51680, 56160, 55640, 77520], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 194, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 30% discount came off it, then 15% tax was added to the discounted price, and a $0.40 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 30% discount came off it, then 15% tax was added to the discounted price, and a $0.40 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $7.85.", " $5.23.", " $8.25.", " $8.05."], "source_id": "deeparithmark_v1_percent_money_depth4_0194", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "785", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "split the total among one more person", "added the coupon instead of subtracting it", "forgot the coupon"], "solution_steps": ["discount: 2000 - 600 = 1400", "tax on the discounted price: 1400 + 210 = 1610", "coupon: 1610 - 40 = 1570", "split 2 ways: 1570 / 2 = 785"], "option_values": [785, 523, 825, 805], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 195, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $15.00 an hour, and then 4 hours at $20.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $15.00 an hour, and then 4 hours at $20.00 an hour. He earned", "endings": [" $200.00.", " $350.00.", " $170.00.", " $180.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0195", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "17000", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid every hour at the second rate", "added the rates together", "correct", "swapped the two rates"], "solution_steps": ["first stretch: 6 x 1500 = 9000", "second stretch: 4 x 2000 = 8000", "total pay: 9000 + 8000 = 17000"], "option_values": [20000, 35000, 17000, 18000], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 196, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $24.00. A 30% discount came off it, then 15% tax was added to the discounted price, and a $1.20 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $24.00. A 30% discount came off it, then 15% tax was added to the discounted price, and a $1.20 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $4.53.", " $2.46.", " $4.23.", " $18.12."], "source_id": "deeparithmark_v1_percent_money_depth4_0196", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "453", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "applied the discount twice", "used the coupon twice", "did not split the cost at all"], "solution_steps": ["discount: 2400 - 720 = 1680", "tax on the discounted price: 1680 + 252 = 1932", "coupon: 1932 - 120 = 1812", "split 4 ways: 1812 / 4 = 453"], "option_values": [453, 246, 423, 1812], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 197, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:49 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:49 a.m. for 50 minutes. The booking ended at", "endings": [" 5:59 a.m.", " 7:24 a.m.", " 6:39 a.m.", " 7:39 a.m."], "source_id": "deeparithmark_v1_time_depth2_0197", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "459", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "stopped a quarter of an hour early", "dropped the hour carry", "correct"], "solution_steps": ["convert the start: 409 minutes after midnight", "add the duration: 409 + 50 = 459 minutes"], "option_values": [359, 444, 399, 459], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 198, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 6 litres per minute for 4 minutes, then 5 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 6 litres per minute for 4 minutes, then 5 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 209 litres.", " 225 litres.", " 249 litres.", " 224 litres."], "source_id": "deeparithmark_v1_rate_depth4_0198", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "249", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "forgot the first fill", "correct", "forgot the second fill"], "solution_steps": ["first fill: 6 x 4 = 24 litres", "second fill: 5 x 5 = 25 litres", "before draining: 240 + 24 + 25 = 289", "after draining: 289 - 40 = 249"], "option_values": [209, 225, 249, 224], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 199, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Chen baked 162 biscuits. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Chen baked 162 biscuits. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "endings": [" 11 biscuits.", " 15 biscuits.", " 18 biscuits.", " 27 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0199", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "18", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away a half and split among one more child", "split the rest among one more child", "correct", "split all the cookies, not the rest"], "solution_steps": ["one third given away: 162 / 3 = 54", "rest kept: 162 - 54 = 108", "split among 6: 108 / 6 = 18"], "option_values": [11, 15, 18, 27], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 200, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:15 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:15 a.m. for 95 minutes. The booking ended at", "endings": [" 6:50 a.m.", " 4:40 a.m.", " 7:50 a.m.", " 9:20 a.m."], "source_id": "deeparithmark_v1_time_depth2_0200", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "470", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "subtracted the duration instead of adding it", "correct", "ran an hour and a half long"], "solution_steps": ["convert the start: 375 minutes after midnight", "add the duration: 375 + 95 = 470 minutes"], "option_values": [410, 280, 470, 560], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 201, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:50 a.m.. The first session lasted 55 minutes, the break lasted 20 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:50 a.m.. The first session lasted 55 minutes, the break lasted 20 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 7:45 a.m.", " 9:45 a.m.", " 10:05 a.m.", " 10:35 a.m."], "source_id": "deeparithmark_v1_time_depth3_0201", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "585", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["dropped the hour carry", "correct", "counted the break twice", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 470 + 55 = 525 minutes after midnight", "after the break: 525 + 20 = 545", "after the second session: 545 + 40 = 585"], "option_values": [465, 585, 605, 635], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 202, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $9.20 was split between two teams in the ratio 4:3 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $9.20 was split between two teams in the ratio 4:3 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.48.", " $0.36.", " $1.05.", " $0.52."], "source_id": "deeparithmark_v1_ratio_depth5_0202", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "48", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "swapped the ratio parts", "split the whole prize among one team", "forgot the fee and the charity cut"], "solution_steps": ["after the fee: 920 - 500 = 420", "one ratio part: 420 / 7 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 48 = 192", "per player: 192 / 4 = 48"], "option_values": [48, 36, 105, 52], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 203, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 50% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 50% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $7.15.", " $4.35.", " $4.85.", " $2.55."], "source_id": "deeparithmark_v1_money_percent_depth2_0203", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "255", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["added the discount instead of removing it", "read the percentage as a flat number of cents", "forgot the discount", "correct"], "solution_steps": ["take 50% of 460 off: 460 - 230 = 230", "add the 25-cent fee: 230 + 25 = 255"], "option_values": [715, 435, 485, 255], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 204, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Nia baked 108 muffins. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Nia baked 108 muffins. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "endings": [" 5 muffins.", " 18 muffins.", " 12 muffins.", " 15 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0204", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "12", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away two thirds and split among one more child", "split all the cookies, not the rest", "correct", "split all the cookies among one more child"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 6: 72 / 6 = 12"], "option_values": [5, 18, 12, 15], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 205, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $12.50 an hour, and then 2 hours at $16.50 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $12.50 an hour, and then 2 hours at $16.50 an hour. He earned", "endings": [" $75.00.", " $91.00.", " $83.00.", " $174.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0205", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "8300", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid every hour at the first rate", "swapped the two rates", "correct", "added the rates together"], "solution_steps": ["first stretch: 4 x 1250 = 5000", "second stretch: 2 x 1650 = 3300", "total pay: 5000 + 3300 = 8300"], "option_values": [7500, 9100, 8300, 17400], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 206, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Yara baked 135 buns. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Yara baked 135 buns. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "endings": [" 11 buns.", " 15 buns.", " 7 buns.", " 6 buns."], "source_id": "deeparithmark_v1_fractions_depth3_0206", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "15", "unit": "buns", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away a half instead of a third", "correct", "split the given-away cookies too", "gave away two thirds and split among one more child"], "solution_steps": ["one third given away: 135 / 3 = 45", "rest kept: 135 - 45 = 90", "split among 6: 90 / 6 = 15"], "option_values": [11, 15, 7, 6], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 207, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 50% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 50% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $1.98.", " $3.95.", " $5.85.", " $2.05."], "source_id": "deeparithmark_v1_money_percent_depth2_0207", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "205", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "forgot the discount", "added the discount instead of removing it", "correct"], "solution_steps": ["take 50% of 380 off: 380 - 190 = 190", "add the 15-cent fee: 190 + 15 = 205"], "option_values": [198, 395, 585, 205], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 208, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.80 was split between two teams in the ratio 3:1 after a $4.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.80 was split between two teams in the ratio 3:1 after a $4.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.21.", " $0.07.", " $0.14.", " $0.52."], "source_id": "deeparithmark_v1_ratio_depth5_0208", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "21", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "swapped the ratio parts", "gave the larger share to the smaller ratio", "divided between the teams instead of the players"], "solution_steps": ["after the fee: 680 - 400 = 280", "one ratio part: 280 / 4 = 70", "larger share: 3 x 70 = 210", "after charity: 210 - 105 = 105", "per player: 105 / 5 = 21"], "option_values": [21, 7, 14, 52], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 209, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $6.48.", " $6.62.", " $8.07.", " $6.63."], "source_id": "deeparithmark_v1_money_percent_depth2_0209", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "663", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "took the discount off the fee as well", "added the discount instead of removing it", "correct"], "solution_steps": ["take 10% of 720 off: 720 - 72 = 648", "add the 15-cent fee: 648 + 15 = 663"], "option_values": [648, 662, 807, 663], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 210, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Tara baked 90 muffins. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Tara baked 90 muffins. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "endings": [" 12 muffins.", " 7 muffins.", " 9 muffins.", " 5 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0210", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "12", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["correct", "gave away a half and split among one more child", "gave away a half instead of a third", "gave away two thirds and split among one more child"], "solution_steps": ["one third given away: 90 / 3 = 30", "rest kept: 90 - 30 = 60", "split among 5: 60 / 5 = 12"], "option_values": [12, 7, 9, 5], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 211, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.00 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.00 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.32.", " $0.25.", " $0.08.", " $0.24."], "source_id": "deeparithmark_v1_ratio_depth5_0211", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "32", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "split among one more player", "swapped the ratio parts", "gave twice the share away to charity"], "solution_steps": ["after the fee: 500 - 300 = 200", "one ratio part: 200 / 5 = 40", "larger share: 4 x 40 = 160", "after charity: 160 - 32 = 128", "per player: 128 / 4 = 32"], "option_values": [32, 25, 8, 24], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 212, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.00 was split between two teams in the ratio 3:2 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.00 was split between two teams in the ratio 3:2 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.27.", " $0.36.", " $0.28.", " $1.05."], "source_id": "deeparithmark_v1_ratio_depth5_0212", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "36", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["gave twice the share away to charity", "correct", "split among one more player", "forgot to deduct the fee"], "solution_steps": ["after the fee: 700 - 400 = 300", "one ratio part: 300 / 5 = 60", "larger share: 3 x 60 = 180", "after charity: 180 - 36 = 144", "per player: 144 / 4 = 36"], "option_values": [27, 36, 28, 105], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 213, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 6 litres per minute for 10 minutes, then 7 litres per minute for 7 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 6 litres per minute for 10 minutes, then 7 litres per minute for 7 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 212 litres.", " 159 litres.", " 359 litres.", " 219 litres."], "source_id": "deeparithmark_v1_rate_depth4_0213", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "219", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["used the first rate for both stages", "forgot the first fill", "added the drain instead of removing it", "correct"], "solution_steps": ["first fill: 6 x 10 = 60 litres", "second fill: 7 x 7 = 49 litres", "before draining: 180 + 60 + 49 = 289", "after draining: 289 - 70 = 219"], "option_values": [212, 159, 359, 219], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 214, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $0.45 each and 4 erasers at $0.30 each. She split the total cost equally between herself and 5 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $0.45 each and 4 erasers at $0.30 each. She split the total cost equally between herself and 5 friends. Each person paid", "endings": [" $0.45.", " $0.66.", " $0.65.", " $0.77."], "source_id": "deeparithmark_v1_money_depth4_0214", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "65", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["forgot the erasers", "added the unit prices instead of multiplying", "correct", "bought one extra of each item"], "solution_steps": ["markers: 6 x 45 = 270", "erasers: 4 x 30 = 120", "total cost: 270 + 120 = 390", "split between 6 people: 390 / 6 = 65"], "option_values": [45, 66, 65, 77], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 215, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 25% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 25% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 16 pallets.", " 44 pallets.", " 48 pallets.", " 49 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0215", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "48", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "took both percentages off the original stock", "correct", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 25% of 800 = 200", "left after Monday: 800 - 200 = 600", "Tuesday: 20% of 600 = 120", "left after Tuesday: 600 - 120 = 480", "full pallets: 480 / 10 = 48"], "option_values": [16, 44, 48, 49], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 216, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 240, then 170 units were shipped out, and 40 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 240, then 170 units were shipped out, and 40 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 98 crates.", " 103 crates.", " 108 crates.", " 99 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0216", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "98", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "forgot the damaged units", "added the damaged units", "counted the loose units as a crate"], "solution_steps": ["after delivery: 760 + 240 = 1000", "after shipping: 1000 - 170 = 830", "good units: 830 - 40 = 790", "full crates: 790 / 8 = 98 (remainder 6)"], "option_values": [98, 103, 108, 99], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 217, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 5 metres and 68 centimetres long. A worker cut off 115 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 5 metres and 68 centimetres long. A worker cut off 115 centimetres. The board left was", "endings": [" 385 centimetres.", " 353 centimetres.", " 683 centimetres.", " 453 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0217", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "453", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["forgot the extra centimetres", "cut a whole metre off as well", "added the cut instead of removing it", "correct"], "solution_steps": ["convert metres: 5 x 100 = 500 cm", "add the extra centimetres: 500 + 68 = 568 cm", "subtract the cut: 568 - 115 = 453 cm"], "option_values": [385, 353, 683, 453], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 218, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:08 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:08 a.m. for 65 minutes. The booking ended at", "endings": [" 7:03 a.m.", " 9:13 a.m.", " 8:13 a.m.", " 8:58 a.m."], "source_id": "deeparithmark_v1_time_depth2_0218", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "553", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "correct", "dropped the hour carry", "stopped a quarter of an hour early"], "solution_steps": ["convert the start: 488 minutes after midnight", "add the duration: 488 + 65 = 553 minutes"], "option_values": [423, 553, 493, 538], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 219, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:19 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:19 a.m. for 125 minutes. The booking ended at", "endings": [" 6:14 a.m.", " 10:24 a.m.", " 10:09 a.m.", " 9:24 a.m."], "source_id": "deeparithmark_v1_time_depth2_0219", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "624", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "correct", "stopped a quarter of an hour early", "forgot the last full hour"], "solution_steps": ["convert the start: 499 minutes after midnight", "add the duration: 499 + 125 = 624 minutes"], "option_values": [374, 624, 609, 564], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 220, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $4.40 was split between two teams in the ratio 5:3 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $4.40 was split between two teams in the ratio 5:3 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.09.", " $0.11.", " $0.15.", " $0.13."], "source_id": "deeparithmark_v1_ratio_depth5_0220", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "15", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "gave the larger share to the smaller ratio", "correct", "split among one more player"], "solution_steps": ["after the fee: 440 - 200 = 240", "one ratio part: 240 / 8 = 30", "larger share: 5 x 30 = 150", "after charity: 150 - 30 = 120", "per player: 120 / 8 = 15"], "option_values": [9, 11, 15, 13], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 221, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $0.75 each and 6 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $0.75 each and 6 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.09.", " $1.53.", " $1.55.", " $1.91."], "source_id": "deeparithmark_v1_money_depth4_0221", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "153", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among two more people", "correct", "swapped the two unit prices", "split only between the friends"], "solution_steps": ["markers: 5 x 75 = 375", "erasers: 6 x 65 = 390", "total cost: 375 + 390 = 765", "split between 5 people: 765 / 5 = 153"], "option_values": [109, 153, 155, 191], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 222, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $2.55.", " $2.41.", " $2.89.", " $2.65."], "source_id": "deeparithmark_v1_money_percent_depth2_0222", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "241", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["read the percentage as a flat number of cents", "correct", "added the discount instead of removing it", "forgot the discount"], "solution_steps": ["take 10% of 240 off: 240 - 24 = 216", "add the 25-cent fee: 216 + 25 = 241"], "option_values": [255, 241, 289, 265], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 223, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $9.50.", " $10.60.", " $9.90.", " $10.30."], "source_id": "deeparithmark_v1_percent_money_depth4_0223", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "950", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "forgot the discount", "forgot the coupon", "added the coupon instead of subtracting it"], "solution_steps": ["discount: 2000 - 200 = 1800", "tax on the discounted price: 1800 + 180 = 1980", "coupon: 1980 - 80 = 1900", "split 2 ways: 1900 / 2 = 950"], "option_values": [950, 1060, 990, 1030], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 224, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 30% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 30% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 61 pallets.", " 68 pallets.", " 67 pallets.", " 84 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0224", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "67", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "counted the loose sacks as a pallet", "correct", "forgot Tuesday"], "solution_steps": ["Monday: 30% of 1200 = 360", "left after Monday: 1200 - 360 = 840", "Tuesday: 20% of 840 = 168", "left after Tuesday: 840 - 168 = 672", "full pallets: 672 / 10 = 67"], "option_values": [61, 68, 67, 84], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 225, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $9.00 an hour, and then 2 hours at $14.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $9.00 an hour, and then 2 hours at $14.00 an hour. He earned", "endings": [" $84.00.", " $74.00.", " $64.00.", " $138.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0225", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "6400", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid every hour at the second rate", "swapped the two rates", "correct", "added the rates together"], "solution_steps": ["first stretch: 4 x 900 = 3600", "second stretch: 2 x 1400 = 2800", "total pay: 3600 + 2800 = 6400"], "option_values": [8400, 7400, 6400, 13800], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 226, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 6 litres per minute for 8 minutes, then 7 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 6 litres per minute for 8 minutes, then 7 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 237 litres.", " 189 litres.", " 188 litres.", " 335 litres."], "source_id": "deeparithmark_v1_rate_depth4_0226", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "237", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "forgot the first fill", "forgot the second fill", "added the rates and multiplied once"], "solution_steps": ["first fill: 6 x 8 = 48 litres", "second fill: 7 x 7 = 49 litres", "before draining: 180 + 48 + 49 = 277", "after draining: 277 - 40 = 237"], "option_values": [237, 189, 188, 335], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 227, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $20.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $20.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $858.00.", " $837.00.", " $891.00.", " $1023.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0227", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "83700", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed only the regular pay", "correct", "paid overtime at double rate", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 36 x 2000 = 72000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 6 x 3000 = 18000", "gross with bonus: 72000 + 18000 + 3000 = 93000", "take-home: 93000 - 9300 = 83700"], "option_values": [85800, 83700, 89100, 102300], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 228, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 5 hours at $14.00 an hour, and then 3 hours at $17.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 5 hours at $14.00 an hour, and then 3 hours at $17.00 an hour. He earned", "endings": [" $121.00.", " $51.00.", " $248.00.", " $136.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0228", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "12100", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["correct", "forgot the first stretch", "added the rates together", "paid every hour at the second rate"], "solution_steps": ["first stretch: 5 x 1400 = 7000", "second stretch: 3 x 1700 = 5100", "total pay: 7000 + 5100 = 12100"], "option_values": [12100, 5100, 24800, 13600], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 229, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $18.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $18.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $476.80.", " $692.80.", " $620.80.", " $676.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0229", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "69280", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the overtime", "correct", "paid overtime at the normal rate", "forgot the bonus"], "solution_steps": ["regular pay: 32 x 1800 = 57600", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 10 x 2700 = 27000", "gross with bonus: 57600 + 27000 + 2000 = 86600", "take-home: 86600 - 17320 = 69280"], "option_values": [47680, 69280, 62080, 67680], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 230, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:41 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:41 a.m. for 65 minutes. The booking ended at", "endings": [" 9:31 a.m.", " 8:46 a.m.", " 9:46 a.m.", " 7:36 a.m."], "source_id": "deeparithmark_v1_time_depth2_0230", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "586", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "dropped the hour carry", "correct", "subtracted the duration instead of adding it"], "solution_steps": ["convert the start: 521 minutes after midnight", "add the duration: 521 + 65 = 586 minutes"], "option_values": [571, 526, 586, 456], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 231, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 280 shirts. It sold 40% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 280 shirts. It sold 40% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 31 boxes.", " 21 boxes.", " 22 boxes.", " 35 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0231", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "21", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold only a tenth of the stock", "correct", "counted the loose shirts as a box", "packed the whole stock, not the rest"], "solution_steps": ["sold: 40% of 280 = 112", "left over: 280 - 112 = 168", "full boxes: 168 / 8 = 21 (remainder 0)"], "option_values": [31, 21, 22, 35], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 232, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:14 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:14 a.m. for 50 minutes. The booking ended at", "endings": [" 8:49 a.m.", " 9:04 a.m.", " 7:24 a.m.", " 8:04 a.m."], "source_id": "deeparithmark_v1_time_depth2_0232", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "544", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "correct", "subtracted the duration instead of adding it", "dropped the hour carry"], "solution_steps": ["convert the start: 494 minutes after midnight", "add the duration: 494 + 50 = 544 minutes"], "option_values": [529, 544, 444, 484], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 233, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $12.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $12.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $4.08.", " $3.12.", " $3.36.", " $4.68."], "source_id": "deeparithmark_v1_percent_money_depth4_0233", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "468", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["used the coupon twice", "split the total among one more person", "applied the discount twice", "correct"], "solution_steps": ["discount: 1200 - 240 = 960", "tax on the discounted price: 960 + 96 = 1056", "coupon: 1056 - 120 = 936", "split 2 ways: 936 / 2 = 468"], "option_values": [408, 312, 336, 468], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 234, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $4.80 was split between two teams in the ratio 5:2 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $4.80 was split between two teams in the ratio 5:2 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.50.", " $0.80.", " $0.70.", " $0.40."], "source_id": "deeparithmark_v1_ratio_depth5_0234", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "40", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the charity cut", "divided between the teams instead of the players", "split the whole prize among one team", "correct"], "solution_steps": ["after the fee: 480 - 200 = 280", "one ratio part: 280 / 7 = 40", "larger share: 5 x 40 = 200", "after charity: 200 - 40 = 160", "per player: 160 / 4 = 40"], "option_values": [50, 80, 70, 40], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 235, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 56 pallets.", " 52 pallets.", " 64 pallets.", " 57 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0235", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "57", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "stacked on larger pallets", "forgot Tuesday", "correct"], "solution_steps": ["Monday: 20% of 800 = 160", "left after Monday: 800 - 160 = 640", "Tuesday: 10% of 640 = 64", "left after Tuesday: 640 - 64 = 576", "full pallets: 576 / 10 = 57"], "option_values": [56, 52, 64, 57], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 236, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $16.00. A 30% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $16.00. A 30% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $12.08.", " $6.84.", " $6.04.", " $6.44."], "source_id": "deeparithmark_v1_percent_money_depth4_0236", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "604", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["split the total among one fewer person", "added the coupon instead of subtracting it", "correct", "forgot the coupon"], "solution_steps": ["discount: 1600 - 480 = 1120", "tax on the discounted price: 1120 + 168 = 1288", "coupon: 1288 - 80 = 1208", "split 2 ways: 1208 / 2 = 604"], "option_values": [1208, 684, 604, 644], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 237, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:06 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:06 a.m. for 65 minutes. The booking ended at", "endings": [" 8:11 a.m.", " 6:01 a.m.", " 7:11 a.m.", " 7:56 a.m."], "source_id": "deeparithmark_v1_time_depth2_0237", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "491", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "subtracted the duration instead of adding it", "dropped the hour carry", "stopped a quarter of an hour early"], "solution_steps": ["convert the start: 426 minutes after midnight", "add the duration: 426 + 65 = 491 minutes"], "option_values": [491, 361, 431, 476], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 238, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:59 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:59 a.m. for 50 minutes. The booking ended at", "endings": [" 8:49 a.m.", " 8:19 a.m.", " 7:49 a.m.", " 9:19 a.m."], "source_id": "deeparithmark_v1_time_depth2_0238", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "469", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added an extra hour", "ran half an hour long", "correct", "ran an hour and a half long"], "solution_steps": ["convert the start: 419 minutes after midnight", "add the duration: 419 + 50 = 469 minutes"], "option_values": [529, 499, 469, 559], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 239, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 5 hours at $11.00 an hour, and then 4 hours at $16.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 5 hours at $11.00 an hour, and then 4 hours at $16.00 an hour. He earned", "endings": [" $108.00.", " $92.00.", " $119.00.", " $243.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0239", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "11900", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["worked one hour less in the first stretch", "worked one hour less in each stretch", "correct", "added the rates together"], "solution_steps": ["first stretch: 5 x 1100 = 5500", "second stretch: 4 x 1600 = 6400", "total pay: 5500 + 6400 = 11900"], "option_values": [10800, 9200, 11900, 24300], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 240, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.60 was split between two teams in the ratio 4:2 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.60 was split between two teams in the ratio 4:2 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.24.", " $0.12.", " $0.15.", " $0.21."], "source_id": "deeparithmark_v1_ratio_depth5_0240", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "24", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "swapped the ratio parts", "gave the larger share to the smaller ratio", "split among one more player"], "solution_steps": ["after the fee: 660 - 300 = 360", "one ratio part: 360 / 6 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 48 = 192", "per player: 192 / 8 = 24"], "option_values": [24, 12, 15, 21], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 241, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $1.90.", " $2.20.", " $3.90.", " $2.50."], "source_id": "deeparithmark_v1_money_percent_depth2_0241", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "250", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "took the discount off the fee as well", "read the percentage as a flat number of cents", "correct"], "solution_steps": ["take 50% of 380 off: 380 - 190 = 190", "add the 60-cent fee: 190 + 60 = 250"], "option_values": [190, 220, 390, 250], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 242, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 15 litres per minute for 4 minutes, then 7 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 15 litres per minute for 4 minutes, then 7 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 173 litres.", " 163 litres.", " 233 litres.", " 396 litres."], "source_id": "deeparithmark_v1_rate_depth4_0242", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "233", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the first fill", "drained twice", "correct", "added the rates and multiplied once"], "solution_steps": ["first fill: 15 x 4 = 60 litres", "second fill: 7 x 9 = 63 litres", "before draining: 180 + 60 + 63 = 303", "after draining: 303 - 70 = 233"], "option_values": [173, 163, 233, 396], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 243, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:35 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:35 a.m. for 65 minutes. The booking ended at", "endings": [" 11:10 a.m.", " 9:40 a.m.", " 10:40 a.m.", " 10:10 a.m."], "source_id": "deeparithmark_v1_time_depth2_0243", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "580", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran an hour and a half long", "correct", "added an extra hour", "ran half an hour long"], "solution_steps": ["convert the start: 515 minutes after midnight", "add the duration: 515 + 65 = 580 minutes"], "option_values": [670, 580, 640, 610], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 244, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 58 pallets.", " 96 pallets.", " 88 pallets.", " 93 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0244", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "96", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "correct", "stacked on larger pallets", "took both percentages off the original stock"], "solution_steps": ["Monday: 10% of 1600 = 160", "left after Monday: 1600 - 160 = 1440", "Tuesday: 20% of 1440 = 288", "left after Tuesday: 1440 - 288 = 1152", "full pallets: 1152 / 12 = 96"], "option_values": [58, 96, 88, 93], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 245, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $16.00 an hour and 6 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $16.00 an hour and 6 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $618.00.", " $412.00.", " $582.00.", " $654.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0245", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "61800", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "taxed twice", "paid overtime at the normal rate", "paid overtime at double rate"], "solution_steps": ["regular pay: 40 x 1600 = 64000", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 6 x 2400 = 14400", "gross with bonus: 64000 + 14400 + 4000 = 82400", "take-home: 82400 - 20600 = 61800"], "option_values": [61800, 41200, 58200, 65400], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 246, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $0.80 coupon was applied last. 5 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $0.80 coupon was applied last. 5 people split the final cost equally. Each paid", "endings": [" $2.92.", " $2.56.", " $3.08.", " $3.24."], "source_id": "deeparithmark_v1_percent_money_depth4_0246", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "308", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["used the coupon twice", "split the total among one more person", "correct", "forgot the coupon"], "solution_steps": ["discount: 2000 - 500 = 1500", "tax on the discounted price: 1500 + 120 = 1620", "coupon: 1620 - 80 = 1540", "split 5 ways: 1540 / 5 = 308"], "option_values": [292, 256, 308, 324], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 247, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $4.28.", " $4.14.", " $4.29.", " $3.83."], "source_id": "deeparithmark_v1_money_percent_depth2_0247", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "429", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "forgot the fee", "correct", "took the percentage off twice"], "solution_steps": ["take 10% of 460 off: 460 - 46 = 414", "add the 15-cent fee: 414 + 15 = 429"], "option_values": [428, 414, 429, 383], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 248, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $0.95 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $0.95 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $0.96.", " $0.95.", " $1.16.", " $1.42."], "source_id": "deeparithmark_v1_money_depth4_0248", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "116", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among one more person", "forgot the erasers", "correct", "bought one extra of each item"], "solution_steps": ["markers: 5 x 95 = 475", "erasers: 3 x 35 = 105", "total cost: 475 + 105 = 580", "split between 5 people: 580 / 5 = 116"], "option_values": [96, 95, 116, 142], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 249, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 130, then 250 units were shipped out, and 24 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 130, then 250 units were shipped out, and 24 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 68 crates.", " 77 crates.", " 78 crates.", " 108 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0249", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "77", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed into larger crates", "correct", "counted the loose units as a crate", "forgot the shipping"], "solution_steps": ["after delivery: 760 + 130 = 890", "after shipping: 890 - 250 = 640", "good units: 640 - 24 = 616", "full crates: 616 / 8 = 77 (remainder 0)"], "option_values": [68, 77, 78, 108], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 250, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:28 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:28 a.m. for 95 minutes. The booking ended at", "endings": [" 8:03 a.m.", " 9:03 a.m.", " 9:33 a.m.", " 10:03 a.m."], "source_id": "deeparithmark_v1_time_depth2_0250", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "543", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added the minutes without the hours", "correct", "ran half an hour long", "added an extra hour"], "solution_steps": ["convert the start: 448 minutes after midnight", "add the duration: 448 + 95 = 543 minutes"], "option_values": [483, 543, 573, 603], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 251, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 480 shirts. It sold 55% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 480 shirts. It sold 55% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "endings": [" 36 boxes.", " 18 boxes.", " 22 boxes.", " 19 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0251", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "18", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold only a tenth of the stock", "correct", "packed the sold shirts", "counted the loose shirts as a box"], "solution_steps": ["sold: 55% of 480 = 264", "left over: 480 - 264 = 216", "full boxes: 216 / 12 = 18 (remainder 0)"], "option_values": [36, 18, 22, 19], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 252, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $28.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $0.60 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $28.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $0.60 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $7.56.", " $7.36.", " $5.52.", " $7.41."], "source_id": "deeparithmark_v1_percent_money_depth4_0252", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "552", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["forgot the discount and the coupon", "split the total among one fewer person", "correct", "forgot the discount"], "solution_steps": ["discount: 2800 - 700 = 2100", "tax on the discounted price: 2100 + 168 = 2268", "coupon: 2268 - 60 = 2208", "split 4 ways: 2208 / 4 = 552"], "option_values": [756, 736, 552, 741], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 253, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.40 was split between two teams in the ratio 5:3 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.40 was split between two teams in the ratio 5:3 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.24.", " $0.92.", " $0.48.", " $0.38."], "source_id": "deeparithmark_v1_ratio_depth5_0253", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "24", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "forgot to deduct the fee", "split the whole prize among one team", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 740 - 500 = 240", "one ratio part: 240 / 8 = 30", "larger share: 5 x 30 = 150", "after charity: 150 - 30 = 120", "per player: 120 / 5 = 24"], "option_values": [24, 92, 48, 38], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 254, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:11 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:11 a.m. for 110 minutes. The booking ended at", "endings": [" 9:01 a.m.", " 10:01 a.m.", " 6:21 a.m.", " 8:01 a.m."], "source_id": "deeparithmark_v1_time_depth2_0254", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "601", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added the minutes without the hours", "correct", "subtracted the duration instead of adding it", "dropped the hour carry"], "solution_steps": ["convert the start: 491 minutes after midnight", "add the duration: 491 + 110 = 601 minutes"], "option_values": [541, 601, 381, 481], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 255, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:27 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:27 a.m. for 80 minutes. The booking ended at", "endings": [" 8:47 a.m.", " 9:32 a.m.", " 10:47 a.m.", " 9:47 a.m."], "source_id": "deeparithmark_v1_time_depth2_0255", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "587", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "stopped a quarter of an hour early", "added an extra hour", "correct"], "solution_steps": ["convert the start: 507 minutes after midnight", "add the duration: 507 + 80 = 587 minutes"], "option_values": [527, 572, 647, 587], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 256, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 64 pallets.", " 72 pallets.", " 44 pallets.", " 73 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0256", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "72", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "correct", "took both percentages twice", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 10% of 800 = 80", "left after Monday: 800 - 80 = 720", "Tuesday: 20% of 720 = 144", "left after Tuesday: 720 - 144 = 576", "full pallets: 576 / 8 = 72"], "option_values": [64, 72, 44, 73], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 257, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $8.50.", " $9.60.", " $6.40.", " $9.30."], "source_id": "deeparithmark_v1_percent_money_depth4_0257", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "960", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "correct", "split the total among one more person", "used the coupon twice"], "solution_steps": ["discount: 2000 - 200 = 1800", "tax on the discounted price: 1800 + 180 = 1980", "coupon: 1980 - 60 = 1920", "split 2 ways: 1920 / 2 = 960"], "option_values": [850, 960, 640, 930], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 258, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 10% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 10% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 37 pallets.", " 44 pallets.", " 48 pallets.", " 49 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0258", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "48", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "stacked on larger pallets", "correct", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 10% of 600 = 60", "left after Monday: 600 - 60 = 540", "Tuesday: 10% of 540 = 54", "left after Tuesday: 540 - 54 = 486", "full pallets: 486 / 10 = 48"], "option_values": [37, 44, 48, 49], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 259, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $11.00 an hour, and then 2 hours at $16.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $11.00 an hour, and then 2 hours at $16.00 an hour. He earned", "endings": [" $66.00.", " $98.00.", " $216.00.", " $118.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0259", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "9800", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["forgot the second stretch", "correct", "added the rates together", "swapped the two rates"], "solution_steps": ["first stretch: 6 x 1100 = 6600", "second stretch: 2 x 1600 = 3200", "total pay: 6600 + 3200 = 9800"], "option_values": [6600, 9800, 21600, 11800], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 260, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:38 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:38 a.m. for 65 minutes. The booking ended at", "endings": [" 7:43 a.m.", " 5:33 a.m.", " 6:43 a.m.", " 7:28 a.m."], "source_id": "deeparithmark_v1_time_depth2_0260", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "463", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "subtracted the duration instead of adding it", "dropped the hour carry", "stopped a quarter of an hour early"], "solution_steps": ["convert the start: 398 minutes after midnight", "add the duration: 398 + 65 = 463 minutes"], "option_values": [463, 333, 403, 448], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 261, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $0.95 each and 6 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $0.95 each and 6 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.56.", " $1.11.", " $1.95.", " $1.82."], "source_id": "deeparithmark_v1_money_depth4_0261", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "156", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "split among two more people", "split only between the friends", "bought one extra of each item"], "solution_steps": ["markers: 6 x 95 = 570", "erasers: 6 x 35 = 210", "total cost: 570 + 210 = 780", "split between 5 people: 780 / 5 = 156"], "option_values": [156, 111, 195, 182], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 262, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $14.00 an hour, and then 4 hours at $19.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $14.00 an hour, and then 4 hours at $19.00 an hour. He earned", "endings": [" $70.00.", " $160.00.", " $330.00.", " $190.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0262", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "16000", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid the slower rate for the whole day", "correct", "added the rates together", "paid every hour at the second rate"], "solution_steps": ["first stretch: 6 x 1400 = 8400", "second stretch: 4 x 1900 = 7600", "total pay: 8400 + 7600 = 16000"], "option_values": [7000, 16000, 33000, 19000], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 263, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 25% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 25% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 18 pallets.", " 56 pallets.", " 52 pallets.", " 51 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0263", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "56", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "correct", "stacked on larger pallets", "took both percentages off the original stock"], "solution_steps": ["Monday: 25% of 1400 = 350", "left after Monday: 1400 - 350 = 1050", "Tuesday: 20% of 1050 = 210", "left after Tuesday: 1050 - 210 = 840", "full pallets: 840 / 15 = 56"], "option_values": [18, 56, 52, 51], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 264, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.50 was split between two teams in the ratio 4:3 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.50 was split between two teams in the ratio 4:3 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.26.", " $0.24.", " $0.73.", " $0.32."], "source_id": "deeparithmark_v1_ratio_depth5_0264", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "32", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "swapped the ratio parts", "forgot to deduct the fee", "correct"], "solution_steps": ["after the fee: 650 - 300 = 350", "one ratio part: 350 / 7 = 50", "larger share: 4 x 50 = 200", "after charity: 200 - 40 = 160", "per player: 160 / 5 = 32"], "option_values": [26, 24, 73, 32], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 265, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 240 shirts. It sold 40% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 240 shirts. It sold 40% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 15 boxes.", " 18 boxes.", " 12 boxes.", " 6 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0265", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "18", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold half the stock regardless of the percentage", "correct", "packed the sold shirts", "sold twice as many"], "solution_steps": ["sold: 40% of 240 = 96", "left over: 240 - 96 = 144", "full boxes: 144 / 8 = 18 (remainder 0)"], "option_values": [15, 18, 12, 6], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 266, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $0.75 each and 6 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $0.75 each and 6 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $1.46.", " $1.95.", " $1.17.", " $1.98."], "source_id": "deeparithmark_v1_money_depth4_0266", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "195", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among one more person", "correct", "split among two more people", "added the unit prices instead of multiplying"], "solution_steps": ["markers: 5 x 75 = 375", "erasers: 6 x 35 = 210", "total cost: 375 + 210 = 585", "split between 3 people: 585 / 3 = 195"], "option_values": [146, 195, 117, 198], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 267, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.50 was split between two teams in the ratio 2:1 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.50 was split between two teams in the ratio 2:1 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.18.", " $0.15.", " $0.16.", " $0.27."], "source_id": "deeparithmark_v1_ratio_depth5_0267", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "18", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "split among one more player", "gave twice the share away to charity", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 550 - 400 = 150", "one ratio part: 150 / 3 = 50", "larger share: 2 x 50 = 100", "after charity: 100 - 10 = 90", "per player: 90 / 5 = 18"], "option_values": [18, 15, 16, 27], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 268, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $5.40. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $5.40. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $5.85.", " $5.65.", " $4.77.", " $6.93."], "source_id": "deeparithmark_v1_money_percent_depth2_0268", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "477", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the discount", "read the percentage as a flat number of cents", "correct", "added the discount instead of removing it"], "solution_steps": ["take 20% of 540 off: 540 - 108 = 432", "add the 45-cent fee: 432 + 45 = 477"], "option_values": [585, 565, 477, 693], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 269, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 22 pallets.", " 52 pallets.", " 51 pallets.", " 67 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0269", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "51", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "counted the loose sacks as a pallet", "correct", "forgot Monday"], "solution_steps": ["Monday: 20% of 1200 = 240", "left after Monday: 1200 - 240 = 960", "Tuesday: 20% of 960 = 192", "left after Tuesday: 960 - 192 = 768", "full pallets: 768 / 15 = 51"], "option_values": [22, 52, 51, 67], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 270, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $12.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $12.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $3.69.", " $5.14.", " $5.54.", " $4.88."], "source_id": "deeparithmark_v1_percent_money_depth4_0270", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "554", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["split the total among one more person", "used the coupon twice", "correct", "applied the discount twice"], "solution_steps": ["discount: 1200 - 120 = 1080", "tax on the discounted price: 1080 + 108 = 1188", "coupon: 1188 - 80 = 1108", "split 2 ways: 1108 / 2 = 554"], "option_values": [369, 514, 554, 488], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 271, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 25% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 25% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $6.49.", " $4.45.", " $6.55.", " $10.75."], "source_id": "deeparithmark_v1_money_percent_depth2_0271", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "655", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "took the percentage off twice", "correct", "added the discount instead of removing it"], "solution_steps": ["take 25% of 840 off: 840 - 210 = 630", "add the 25-cent fee: 630 + 25 = 655"], "option_values": [649, 445, 655, 1075], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 272, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 38 pallets.", " 36 pallets.", " 42 pallets.", " 43 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0272", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "42", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "took both percentages off the original stock", "correct", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 30% of 800 = 240", "left after Monday: 800 - 240 = 560", "Tuesday: 25% of 560 = 140", "left after Tuesday: 560 - 140 = 420", "full pallets: 420 / 10 = 42"], "option_values": [38, 36, 42, 43], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 273, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.50 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.50 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.12.", " $0.45.", " $0.36.", " $0.62."], "source_id": "deeparithmark_v1_ratio_depth5_0273", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "45", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["gave the larger share to the smaller ratio", "correct", "split among one more player", "split the whole prize among one team"], "solution_steps": ["after the fee: 550 - 300 = 250", "one ratio part: 250 / 5 = 50", "larger share: 4 x 50 = 200", "after charity: 200 - 20 = 180", "per player: 180 / 4 = 45"], "option_values": [12, 45, 36, 62], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 274, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 12 litres per minute for 6 minutes, then 3 litres per minute for 7 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 12 litres per minute for 6 minutes, then 3 litres per minute for 7 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 182 litres.", " 203 litres.", " 133 litres.", " 266 litres."], "source_id": "deeparithmark_v1_rate_depth4_0274", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "203", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the second fill", "correct", "drained twice", "used the first rate for both stages"], "solution_steps": ["first fill: 12 x 6 = 72 litres", "second fill: 3 x 7 = 21 litres", "before draining: 180 + 72 + 21 = 273", "after draining: 273 - 70 = 203"], "option_values": [182, 203, 133, 266], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 275, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $24.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $0.80 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $24.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $0.80 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $6.28.", " $4.66.", " $6.21.", " $6.48."], "source_id": "deeparithmark_v1_percent_money_depth4_0275", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "466", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["forgot the discount", "correct", "split the total among one fewer person", "forgot the discount and the coupon"], "solution_steps": ["discount: 2400 - 600 = 1800", "tax on the discounted price: 1800 + 144 = 1944", "coupon: 1944 - 80 = 1864", "split 4 ways: 1864 / 4 = 466"], "option_values": [628, 466, 621, 648], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 276, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.20 was split between two teams in the ratio 3:1 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.20 was split between two teams in the ratio 3:1 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.15.", " $0.12.", " $0.09.", " $0.11."], "source_id": "deeparithmark_v1_ratio_depth5_0276", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "9", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split the whole prize among one team", "took the charity cut off the whole prize", "correct", "forgot the charity cut"], "solution_steps": ["after the fee: 620 - 500 = 120", "one ratio part: 120 / 4 = 30", "larger share: 3 x 30 = 90", "after charity: 90 - 18 = 72", "per player: 72 / 8 = 9"], "option_values": [15, 12, 9, 11], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 277, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $1.20 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 5 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $1.20 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 5 friends. Each person paid", "endings": [" $1.40.", " $1.80.", " $2.60.", " $2.10."], "source_id": "deeparithmark_v1_money_depth4_0277", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "210", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["forgot the erasers", "split among one more person", "charged the marker price for everything", "correct"], "solution_steps": ["markers: 7 x 120 = 840", "erasers: 6 x 70 = 420", "total cost: 840 + 420 = 1260", "split between 6 people: 1260 / 6 = 210"], "option_values": [140, 180, 260, 210], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 278, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 4 markers at $0.45 each and 4 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 4 markers at $0.45 each and 4 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $0.36.", " $0.45.", " $0.53.", " $0.64."], "source_id": "deeparithmark_v1_money_depth4_0278", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "64", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["forgot the erasers", "split among two more people", "split among one more person", "correct"], "solution_steps": ["markers: 4 x 45 = 180", "erasers: 4 x 35 = 140", "total cost: 180 + 140 = 320", "split between 5 people: 320 / 5 = 64"], "option_values": [36, 45, 53, 64], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 279, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Samir baked 72 buns. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Samir baked 72 buns. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 48 buns.", " 12 buns.", " 18 buns.", " 14 buns."], "source_id": "deeparithmark_v1_fractions_depth3_0279", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "12", "unit": "buns", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["stopped after giving the third away", "correct", "split all the cookies, not the rest", "split all the cookies among one more child"], "solution_steps": ["one third given away: 72 / 3 = 24", "rest kept: 72 - 24 = 48", "split among 4: 48 / 4 = 12"], "option_values": [48, 12, 18, 14], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 280, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 480 shirts. It sold 40% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 480 shirts. It sold 40% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "endings": [" 8 boxes.", " 25 boxes.", " 24 boxes.", " 36 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0280", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "24", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold twice as many", "counted the loose shirts as a box", "correct", "sold only a tenth of the stock"], "solution_steps": ["sold: 40% of 480 = 192", "left over: 480 - 192 = 288", "full boxes: 288 / 12 = 24 (remainder 0)"], "option_values": [8, 25, 24, 36], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 281, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.60 was split between two teams in the ratio 5:1 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.60 was split between two teams in the ratio 5:1 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.45.", " $0.54.", " $0.48.", " $0.64."], "source_id": "deeparithmark_v1_ratio_depth5_0281", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "54", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "correct", "gave twice the share away to charity", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 760 - 400 = 360", "one ratio part: 360 / 6 = 60", "larger share: 5 x 60 = 300", "after charity: 300 - 30 = 270", "per player: 270 / 5 = 54"], "option_values": [45, 54, 48, 64], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 282, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Nia baked 144 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Nia baked 144 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 12 biscuits.", " 96 biscuits.", " 24 biscuits.", " 36 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0282", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "24", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split the given-away cookies too", "stopped after giving the third away", "correct", "split all the cookies, not the rest"], "solution_steps": ["one third given away: 144 / 3 = 48", "rest kept: 144 - 48 = 96", "split among 4: 96 / 4 = 24"], "option_values": [12, 96, 24, 36], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 283, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $7.08.", " $7.02.", " $6.36.", " $7.68."], "source_id": "deeparithmark_v1_money_percent_depth2_0283", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "708", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the discount off the fee as well", "took the percentage off twice", "charged the handling fee twice"], "solution_steps": ["take 10% of 720 off: 720 - 72 = 648", "add the 60-cent fee: 648 + 60 = 708"], "option_values": [708, 702, 636, 768], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 284, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $9.20 was split between two teams in the ratio 4:3 after a $5.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $9.20 was split between two teams in the ratio 4:3 after a $5.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.15.", " $0.22.", " $0.52.", " $0.26."], "source_id": "deeparithmark_v1_ratio_depth5_0284", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "15", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "gave the larger share to the smaller ratio", "split the whole prize among one team", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 920 - 500 = 420", "one ratio part: 420 / 7 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 120 = 120", "per player: 120 / 8 = 15"], "option_values": [15, 22, 52, 26], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 285, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 36 km at 12 km/h, rested 30 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 36 km at 12 km/h, rested 30 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "endings": [" 390 minutes.", " 210 minutes.", " 360 minutes.", " 420 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0285", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "390", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["correct", "forgot the walking leg", "forgot the rest", "counted the rest twice"], "solution_steps": ["cycling time: 60 x 36 / 12 = 180 minutes", "walking time: 60 x 15 / 5 = 180 minutes", "add the rest: 180 + 30 + 180 = 390 minutes"], "option_values": [390, 210, 360, 420], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 286, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 23 pallets.", " 43 pallets.", " 46 pallets.", " 45 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0286", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "45", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "took both percentages off the original stock", "counted the loose sacks as a pallet", "correct"], "solution_steps": ["Monday: 25% of 800 = 200", "left after Monday: 800 - 200 = 600", "Tuesday: 10% of 600 = 60", "left after Tuesday: 600 - 60 = 540", "full pallets: 540 / 12 = 45"], "option_values": [23, 43, 46, 45], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 287, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $5.79.", " $6.12.", " $6.44.", " $6.47."], "source_id": "deeparithmark_v1_money_percent_depth2_0287", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "647", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "forgot the fee", "took the discount off the fee as well", "correct"], "solution_steps": ["take 10% of 680 off: 680 - 68 = 612", "add the 35-cent fee: 612 + 35 = 647"], "option_values": [579, 612, 644, 647], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 288, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 4 metres and 38 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 4 metres and 38 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 431 centimetres.", " 583 centimetres.", " 483 centimetres.", " 393 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0288", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "393", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["counted the extra centimetres twice", "added the cut and a whole metre", "added the cut instead of removing it", "correct"], "solution_steps": ["convert metres: 4 x 100 = 400 cm", "add the extra centimetres: 400 + 38 = 438 cm", "subtract the cut: 438 - 45 = 393 cm"], "option_values": [431, 583, 483, 393], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 289, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 2 metres and 47 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 2 metres and 47 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 202 centimetres.", " 102 centimetres.", " 155 centimetres.", " 212 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0289", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "202", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["correct", "cut a whole metre off as well", "forgot the extra centimetres", "stopped ten centimetres short of the cut"], "solution_steps": ["convert metres: 2 x 100 = 200 cm", "add the extra centimetres: 200 + 47 = 247 cm", "subtract the cut: 247 - 45 = 202 cm"], "option_values": [202, 102, 155, 212], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 290, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $16.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $16.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $627.00.", " $836.00.", " $1045.00.", " $687.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0290", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "62700", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "forgot the tax", "added the tax instead of withholding it", "paid overtime at double rate"], "solution_steps": ["regular pay: 36 x 1600 = 57600", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 10 x 2400 = 24000", "gross with bonus: 57600 + 24000 + 2000 = 83600", "take-home: 83600 - 20900 = 62700"], "option_values": [62700, 83600, 104500, 68700], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 291, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:01 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:01 a.m. for 95 minutes. The booking ended at", "endings": [" 9:36 a.m.", " 10:36 a.m.", " 10:06 a.m.", " 11:06 a.m."], "source_id": "deeparithmark_v1_time_depth2_0291", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "576", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "added an extra hour", "ran half an hour long", "ran an hour and a half long"], "solution_steps": ["convert the start: 481 minutes after midnight", "add the duration: 481 + 95 = 576 minutes"], "option_values": [576, 636, 606, 666], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 292, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 5 metres and 12 centimetres long. A worker cut off 60 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 5 metres and 12 centimetres long. A worker cut off 60 centimetres. The board left was", "endings": [" 352 centimetres.", " 452 centimetres.", " 462 centimetres.", " 464 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0292", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "452", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["cut a whole metre off as well", "correct", "stopped ten centimetres short of the cut", "counted the extra centimetres twice"], "solution_steps": ["convert metres: 5 x 100 = 500 cm", "add the extra centimetres: 500 + 12 = 512 cm", "subtract the cut: 512 - 60 = 452 cm"], "option_values": [352, 452, 462, 464], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 293, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:30 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:30 a.m. for 125 minutes. The booking ended at", "endings": [" 9:35 a.m.", " 9:05 a.m.", " 10:05 a.m.", " 8:35 a.m."], "source_id": "deeparithmark_v1_time_depth2_0293", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "515", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added an extra hour", "ran half an hour long", "ran an hour and a half long", "correct"], "solution_steps": ["convert the start: 390 minutes after midnight", "add the duration: 390 + 125 = 515 minutes"], "option_values": [575, 545, 605, 515], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 294, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 440 shirts. It sold 15% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 440 shirts. It sold 15% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 47 boxes.", " 62 boxes.", " 46 boxes.", " 49 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0294", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "46", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["rounded the box count up", "divided by the number of boxes left over", "correct", "sold only a tenth of the stock"], "solution_steps": ["sold: 15% of 440 = 66", "left over: 440 - 66 = 374", "full boxes: 374 / 8 = 46 (remainder 6)"], "option_values": [47, 62, 46, 49], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 295, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.50 was split between two teams in the ratio 3:2 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.50 was split between two teams in the ratio 3:2 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.20.", " $0.60.", " $0.50.", " $0.30."], "source_id": "deeparithmark_v1_ratio_depth5_0295", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "30", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "divided between the teams instead of the players", "took the charity cut off the whole prize", "correct"], "solution_steps": ["after the fee: 650 - 400 = 250", "one ratio part: 250 / 5 = 50", "larger share: 3 x 50 = 150", "after charity: 150 - 30 = 120", "per player: 120 / 4 = 30"], "option_values": [20, 60, 50, 30], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 296, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $6.09.", " $7.32.", " $7.62.", " $5.64."], "source_id": "deeparithmark_v1_percent_money_depth4_0296", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "762", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["split the total among one more person", "used the coupon twice", "correct", "applied the discount twice"], "solution_steps": ["discount: 3600 - 720 = 2880", "tax on the discounted price: 2880 + 288 = 3168", "coupon: 3168 - 120 = 3048", "split 4 ways: 3048 / 4 = 762"], "option_values": [609, 732, 762, 564], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 297, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:04 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:04 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "endings": [" 7:04 a.m.", " 8:04 a.m.", " 7:19 a.m.", " 8:19 a.m."], "source_id": "deeparithmark_v1_time_depth3_0297", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "484", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the last session and the break", "correct", "forgot the second session", "counted the break twice"], "solution_steps": ["after the first session: 364 + 60 = 424 minutes after midnight", "after the break: 424 + 15 = 439", "after the second session: 439 + 45 = 484"], "option_values": [424, 484, 439, 499], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 298, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 2 metres and 74 centimetres long. A worker cut off 60 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 2 metres and 74 centimetres long. A worker cut off 60 centimetres. The board left was", "endings": [" 334 centimetres.", " 214 centimetres.", " 288 centimetres.", " 224 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0298", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "214", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["added the cut instead of removing it", "correct", "counted the extra centimetres twice", "stopped ten centimetres short of the cut"], "solution_steps": ["convert metres: 2 x 100 = 200 cm", "add the extra centimetres: 200 + 74 = 274 cm", "subtract the cut: 274 - 60 = 214 cm"], "option_values": [334, 214, 288, 224], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 299, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $2.88.", " $3.03.", " $3.02.", " $2.71."], "source_id": "deeparithmark_v1_money_percent_depth2_0299", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "303", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "correct", "took the discount off the fee as well", "took the percentage off twice"], "solution_steps": ["take 10% of 320 off: 320 - 32 = 288", "add the 15-cent fee: 288 + 15 = 303"], "option_values": [288, 303, 302, 271], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 300, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:38 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:38 a.m. for 50 minutes. The booking ended at", "endings": [" 5:48 a.m.", " 7:28 a.m.", " 8:28 a.m.", " 8:58 a.m."], "source_id": "deeparithmark_v1_time_depth2_0300", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "448", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "correct", "added an extra hour", "ran an hour and a half long"], "solution_steps": ["convert the start: 398 minutes after midnight", "add the duration: 398 + 50 = 448 minutes"], "option_values": [348, 448, 508, 538], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 301, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:36 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:36 a.m. for 95 minutes. The booking ended at", "endings": [" 8:11 a.m.", " 7:56 a.m.", " 6:11 a.m.", " 7:11 a.m."], "source_id": "deeparithmark_v1_time_depth2_0301", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "491", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "stopped a quarter of an hour early", "dropped the hour carry", "added the minutes without the hours"], "solution_steps": ["convert the start: 396 minutes after midnight", "add the duration: 396 + 95 = 491 minutes"], "option_values": [491, 476, 371, 431], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 302, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 14 pallets.", " 37 pallets.", " 27 pallets.", " 28 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0302", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "27", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "forgot Monday", "correct", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 25% of 600 = 150", "left after Monday: 600 - 150 = 450", "Tuesday: 10% of 450 = 45", "left after Tuesday: 450 - 45 = 405", "full pallets: 405 / 15 = 27"], "option_values": [14, 37, 27, 28], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 303, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $12.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $1.20 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $12.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $1.20 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $1.92.", " $1.59.", " $2.22.", " $1.77."], "source_id": "deeparithmark_v1_percent_money_depth4_0303", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "222", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["used the coupon twice", "applied the discount twice", "correct", "split the total among one more person"], "solution_steps": ["discount: 1200 - 240 = 960", "tax on the discounted price: 960 + 48 = 1008", "coupon: 1008 - 120 = 888", "split 4 ways: 888 / 4 = 222"], "option_values": [192, 159, 222, 177], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 304, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $748.00.", " $765.00.", " $561.00.", " $1035.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0304", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "76500", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "correct", "forgot the overtime", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 32 x 2000 = 64000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 8 x 3000 = 24000", "gross with bonus: 64000 + 24000 + 2000 = 90000", "take-home: 90000 - 13500 = 76500"], "option_values": [74800, 76500, 56100, 103500], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 305, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 30% discount came off it, then 8% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 30% discount came off it, then 8% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $4.64.", " $6.96.", " $6.36.", " $13.92."], "source_id": "deeparithmark_v1_percent_money_depth4_0305", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "696", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["split the total among one more person", "correct", "used the coupon twice", "split the total among one fewer person"], "solution_steps": ["discount: 2000 - 600 = 1400", "tax on the discounted price: 1400 + 112 = 1512", "coupon: 1512 - 120 = 1392", "split 2 ways: 1392 / 2 = 696"], "option_values": [464, 696, 636, 1392], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 306, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $761.20.", " $634.40.", " $651.60.", " $622.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0306", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "62280", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["added the tax instead of withholding it", "taxed only the regular pay", "paid overtime at double rate", "correct"], "solution_steps": ["regular pay: 36 x 1600 = 57600", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 4 x 2400 = 9600", "gross with bonus: 57600 + 9600 + 2000 = 69200", "take-home: 69200 - 6920 = 62280"], "option_values": [76120, 63440, 65160, 62280], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 307, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $1.20 each and 4 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $1.20 each and 4 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.74.", " $1.63.", " $1.44.", " $1.96."], "source_id": "deeparithmark_v1_money_depth4_0307", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "196", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["swapped the two unit prices", "split among one more person", "forgot the erasers", "correct"], "solution_steps": ["markers: 6 x 120 = 720", "erasers: 4 x 65 = 260", "total cost: 720 + 260 = 980", "split between 5 people: 980 / 5 = 196"], "option_values": [174, 163, 144, 196], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 308, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $566.10.", " $540.60.", " $617.10.", " $597.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0308", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "56610", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "forgot the bonus", "paid overtime at double rate", "taxed only the regular pay"], "solution_steps": ["regular pay: 38 x 1200 = 45600", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 10 x 1800 = 18000", "gross with bonus: 45600 + 18000 + 3000 = 66600", "take-home: 66600 - 9990 = 56610"], "option_values": [56610, 54060, 61710, 59760], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 309, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 420 units. A delivery added 180, then 250 units were shipped out, and 18 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 420 units. A delivery added 180, then 250 units were shipped out, and 18 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 18 crates.", " 36 crates.", " 33 crates.", " 9 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0309", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "36", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed the arriving units only", "correct", "packed into larger crates", "shipped out twice"], "solution_steps": ["after delivery: 420 + 180 = 600", "after shipping: 600 - 250 = 350", "good units: 350 - 18 = 332", "full crates: 332 / 9 = 36 (remainder 8)"], "option_values": [18, 36, 33, 9], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 310, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Quinn baked 135 muffins. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Quinn baked 135 muffins. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "endings": [" 12 muffins.", " 15 muffins.", " 9 muffins.", " 8 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0310", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "15", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split the rest among one more child", "correct", "gave away a half and split among one more child", "gave away a third twice and split among one more child"], "solution_steps": ["one third given away: 135 / 3 = 45", "rest kept: 135 - 45 = 90", "split among 6: 90 / 6 = 15"], "option_values": [12, 15, 9, 8], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 311, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 5 hours at $9.00 an hour, and then 2 hours at $12.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 5 hours at $9.00 an hour, and then 2 hours at $12.00 an hour. He earned", "endings": [" $48.00.", " $84.00.", " $69.00.", " $78.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0311", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "6900", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["worked one hour less in each stretch", "paid every hour at the second rate", "correct", "swapped the two rates"], "solution_steps": ["first stretch: 5 x 900 = 4500", "second stretch: 2 x 1200 = 2400", "total pay: 4500 + 2400 = 6900"], "option_values": [4800, 8400, 6900, 7800], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 312, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 6 metres and 74 centimetres long. A worker cut off 75 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 6 metres and 74 centimetres long. A worker cut off 75 centimetres. The board left was", "endings": [" 525 centimetres.", " 599 centimetres.", " 499 centimetres.", " 673 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0312", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "599", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["forgot the extra centimetres", "correct", "cut a whole metre off as well", "counted the extra centimetres twice"], "solution_steps": ["convert metres: 6 x 100 = 600 cm", "add the extra centimetres: 600 + 74 = 674 cm", "subtract the cut: 674 - 75 = 599 cm"], "option_values": [525, 599, 499, 673], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 313, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Samir baked 108 cookies. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Samir baked 108 cookies. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "endings": [" 13 cookies.", " 12 cookies.", " 18 cookies.", " 15 cookies."], "source_id": "deeparithmark_v1_fractions_depth3_0313", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "12", "unit": "cookies", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split all the cookies among two more children", "correct", "split all the cookies, not the rest", "split all the cookies among one more child"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 6: 72 / 6 = 12"], "option_values": [13, 12, 18, 15], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 314, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:22 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:22 a.m. for 95 minutes. The booking ended at", "endings": [" 5:47 a.m.", " 8:42 a.m.", " 8:57 a.m.", " 9:27 a.m."], "source_id": "deeparithmark_v1_time_depth2_0314", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "537", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "stopped a quarter of an hour early", "correct", "ran half an hour long"], "solution_steps": ["convert the start: 442 minutes after midnight", "add the duration: 442 + 95 = 537 minutes"], "option_values": [347, 522, 537, 567], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 315, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $516.80.", " $439.60.", " $722.20.", " $533.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0315", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "53380", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "taxed twice", "added the tax instead of withholding it", "correct"], "solution_steps": ["regular pay: 32 x 1600 = 51200", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 4 x 2400 = 9600", "gross with bonus: 51200 + 9600 + 2000 = 62800", "take-home: 62800 - 9420 = 53380"], "option_values": [51680, 43960, 72220, 53380], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 316, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:48 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:48 a.m. for 80 minutes. The booking ended at", "endings": [" 10:38 a.m.", " 9:38 a.m.", " 9:08 a.m.", " 10:08 a.m."], "source_id": "deeparithmark_v1_time_depth2_0316", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "548", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran an hour and a half long", "ran half an hour long", "correct", "added an extra hour"], "solution_steps": ["convert the start: 468 minutes after midnight", "add the duration: 468 + 80 = 548 minutes"], "option_values": [638, 578, 548, 608], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 317, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $18.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $18.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $537.60.", " $652.80.", " $883.20.", " $698.70."], "source_id": "deeparithmark_v1_money_rate_depth5_0317", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "65280", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "correct", "added the tax instead of withholding it", "paid overtime at double rate"], "solution_steps": ["regular pay: 32 x 1800 = 57600", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 6 x 2700 = 16200", "gross with bonus: 57600 + 16200 + 3000 = 76800", "take-home: 76800 - 11520 = 65280"], "option_values": [53760, 65280, 88320, 69870], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 318, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 480 units. A delivery added 180, then 90 units were shipped out, and 40 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 480 units. A delivery added 180, then 90 units were shipped out, and 40 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 15 crates.", " 68 crates.", " 67 crates.", " 58 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0318", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "58", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed the arriving units only", "forgot the shipping", "added the damaged units", "correct"], "solution_steps": ["after delivery: 480 + 180 = 660", "after shipping: 660 - 90 = 570", "good units: 570 - 40 = 530", "full crates: 530 / 9 = 58 (remainder 8)"], "option_values": [15, 68, 67, 58], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 319, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $3.67.", " $4.43.", " $3.95.", " $4.05."], "source_id": "deeparithmark_v1_money_percent_depth2_0319", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "367", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "added the discount instead of removing it", "read the percentage as a flat number of cents", "forgot the discount"], "solution_steps": ["take 10% of 380 off: 380 - 38 = 342", "add the 25-cent fee: 342 + 25 = 367"], "option_values": [367, 443, 395, 405], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 320, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 15 litres per minute for 6 minutes, then 5 litres per minute for 9 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 15 litres per minute for 6 minutes, then 5 litres per minute for 9 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 435 litres.", " 485 litres.", " 475 litres.", " 395 litres."], "source_id": "deeparithmark_v1_rate_depth4_0320", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "395", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the drain", "used the first rate for both stages", "added the drain instead of removing it", "correct"], "solution_steps": ["first fill: 15 x 6 = 90 litres", "second fill: 5 x 9 = 45 litres", "before draining: 300 + 90 + 45 = 435", "after draining: 435 - 40 = 395"], "option_values": [435, 485, 475, 395], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 321, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 78 pallets.", " 91 pallets.", " 81 pallets.", " 144 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0321", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "91", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "correct", "stacked on larger pallets", "forgot Monday"], "solution_steps": ["Monday: 30% of 1400 = 420", "left after Monday: 1400 - 420 = 980", "Tuesday: 25% of 980 = 245", "left after Tuesday: 980 - 245 = 735", "full pallets: 735 / 8 = 91"], "option_values": [78, 91, 81, 144], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 322, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 12 litres per minute for 4 minutes, then 7 litres per minute for 9 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 12 litres per minute for 4 minutes, then 7 litres per minute for 9 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 447 litres.", " 311 litres.", " 391 litres.", " 356 litres."], "source_id": "deeparithmark_v1_rate_depth4_0322", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "311", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["added the rates and multiplied once", "correct", "added the drain instead of removing it", "used the first rate for both stages"], "solution_steps": ["first fill: 12 x 4 = 48 litres", "second fill: 7 x 9 = 63 litres", "before draining: 240 + 48 + 63 = 351", "after draining: 351 - 40 = 311"], "option_values": [447, 311, 391, 356], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 323, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $6.37.", " $5.69.", " $6.35.", " $6.12."], "source_id": "deeparithmark_v1_money_percent_depth2_0323", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "637", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the percentage off twice", "took the discount off the fee as well", "forgot the fee"], "solution_steps": ["take 10% of 680 off: 680 - 68 = 612", "add the 25-cent fee: 612 + 25 = 637"], "option_values": [637, 569, 635, 612], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 324, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 50% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 50% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $2.65.", " $7.25.", " $4.95.", " $4.45."], "source_id": "deeparithmark_v1_money_percent_depth2_0324", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "265", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "added the discount instead of removing it", "forgot the discount", "read the percentage as a flat number of cents"], "solution_steps": ["take 50% of 460 off: 460 - 230 = 230", "add the 35-cent fee: 230 + 35 = 265"], "option_values": [265, 725, 495, 445], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 325, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $588.80.", " $622.80.", " $695.20.", " $568.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0325", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "56880", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed only the regular pay", "paid overtime at double rate", "added the tax instead of withholding it", "correct"], "solution_steps": ["regular pay: 36 x 1200 = 43200", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 10 x 1800 = 18000", "gross with bonus: 43200 + 18000 + 2000 = 63200", "take-home: 63200 - 6320 = 56880"], "option_values": [58880, 62280, 69520, 56880], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 326, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 130, then 90 units were shipped out, and 24 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 130, then 90 units were shipped out, and 24 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 42 crates.", " 51 crates.", " 49 crates.", " 48 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0326", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "48", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped out twice", "added the damaged units", "counted the loose units as a crate", "correct"], "solution_steps": ["after delivery: 760 + 130 = 890", "after shipping: 890 - 90 = 800", "good units: 800 - 24 = 776", "full crates: 776 / 16 = 48 (remainder 8)"], "option_values": [42, 51, 49, 48], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 327, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 36 pallets.", " 23 pallets.", " 38 pallets.", " 39 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0327", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "38", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "took both percentages twice", "correct", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 10% of 800 = 80", "left after Monday: 800 - 80 = 720", "Tuesday: 20% of 720 = 144", "left after Tuesday: 720 - 144 = 576", "full pallets: 576 / 15 = 38"], "option_values": [36, 23, 38, 39], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 328, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:53 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:53 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 8:48 a.m.", " 9:33 a.m.", " 9:48 a.m.", " 7:48 a.m."], "source_id": "deeparithmark_v1_time_depth3_0328", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "588", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["added the minutes but not the hours", "forgot the break", "correct", "dropped the hour carry"], "solution_steps": ["after the first session: 473 + 60 = 533 minutes after midnight", "after the break: 533 + 15 = 548", "after the second session: 548 + 40 = 588"], "option_values": [528, 573, 588, 468], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 329, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $3.68.", " $5.67.", " $3.83.", " $4.75."], "source_id": "deeparithmark_v1_money_percent_depth2_0329", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "383", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "added the discount instead of removing it", "correct", "forgot the discount"], "solution_steps": ["take 20% of 460 off: 460 - 92 = 368", "add the 15-cent fee: 368 + 15 = 383"], "option_values": [368, 567, 383, 475], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 330, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $8.64.", " $8.03.", " $8.96.", " $8.99."], "source_id": "deeparithmark_v1_money_percent_depth2_0330", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "899", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "took the percentage off twice", "took the discount off the fee as well", "correct"], "solution_steps": ["take 10% of 960 off: 960 - 96 = 864", "add the 35-cent fee: 864 + 35 = 899"], "option_values": [864, 803, 896, 899], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 331, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:20 a.m.. The first session lasted 45 minutes, the break lasted 15 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:20 a.m.. The first session lasted 45 minutes, the break lasted 15 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 6:00 a.m.", " 7:00 a.m.", " 8:00 a.m.", " 7:20 a.m."], "source_id": "deeparithmark_v1_time_depth3_0331", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "480", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["dropped the hour carry", "added the minutes but not the hours", "correct", "forgot the second session"], "solution_steps": ["after the first session: 380 + 45 = 425 minutes after midnight", "after the break: 425 + 15 = 440", "after the second session: 440 + 40 = 480"], "option_values": [360, 420, 480, 440], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 332, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:53 a.m.. The first session lasted 70 minutes, the break lasted 25 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:53 a.m.. The first session lasted 70 minutes, the break lasted 25 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 7:08 a.m.", " 10:08 a.m.", " 11:03 a.m.", " 10:33 a.m."], "source_id": "deeparithmark_v1_time_depth3_0332", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "608", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["dropped the hour carry", "correct", "finished half an hour late on top of the break", "counted the break twice"], "solution_steps": ["after the first session: 473 + 70 = 543 minutes after midnight", "after the break: 543 + 25 = 568", "after the second session: 568 + 40 = 608"], "option_values": [428, 608, 663, 633], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 333, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 30 km at 15 km/h, rested 30 minutes, then walked 8 km at 4 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 30 km at 15 km/h, rested 30 minutes, then walked 8 km at 4 km/h. Her total time, in minutes, was", "endings": [" 240 minutes.", " 150 minutes.", " 270 minutes.", " 90 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0333", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "270", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the rest", "forgot the walking leg", "correct", "divided by the speed twice"], "solution_steps": ["cycling time: 60 x 30 / 15 = 120 minutes", "walking time: 60 x 8 / 4 = 120 minutes", "add the rest: 120 + 30 + 120 = 270 minutes"], "option_values": [240, 150, 270, 90], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 334, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:21 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:21 a.m. for 95 minutes. The booking ended at", "endings": [" 5:46 a.m.", " 7:56 a.m.", " 8:56 a.m.", " 8:41 a.m."], "source_id": "deeparithmark_v1_time_depth2_0334", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "536", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "dropped the hour carry", "correct", "stopped a quarter of an hour early"], "solution_steps": ["convert the start: 441 minutes after midnight", "add the duration: 441 + 95 = 536 minutes"], "option_values": [346, 476, 536, 521], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 335, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $3.20 was split between two teams in the ratio 2:1 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $3.20 was split between two teams in the ratio 2:1 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.32.", " $0.12.", " $0.26.", " $0.08."], "source_id": "deeparithmark_v1_ratio_depth5_0335", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "8", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["divided between the teams instead of the players", "took the charity cut off the whole prize", "forgot to deduct the fee", "correct"], "solution_steps": ["after the fee: 320 - 200 = 120", "one ratio part: 120 / 3 = 40", "larger share: 2 x 40 = 80", "after charity: 80 - 16 = 64", "per player: 64 / 8 = 8"], "option_values": [32, 12, 26, 8], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 336, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 3 hours at $9.00 an hour, and then 2 hours at $12.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 3 hours at $9.00 an hour, and then 2 hours at $12.00 an hour. He earned", "endings": [" $24.00.", " $54.00.", " $105.00.", " $51.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0336", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "5100", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["forgot the first stretch", "swapped the two rates", "added the rates together", "correct"], "solution_steps": ["first stretch: 3 x 900 = 2700", "second stretch: 2 x 1200 = 2400", "total pay: 2700 + 2400 = 5100"], "option_values": [2400, 5400, 10500, 5100], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 337, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.50 was split between two teams in the ratio 5:2 after a $2.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.50 was split between two teams in the ratio 5:2 after a $2.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.62.", " $0.65.", " $0.87.", " $0.47."], "source_id": "deeparithmark_v1_ratio_depth5_0337", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "47", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the charity cut", "took the charity cut off the whole prize", "split the whole prize among one team", "correct"], "solution_steps": ["after the fee: 550 - 200 = 350", "one ratio part: 350 / 7 = 50", "larger share: 5 x 50 = 250", "after charity: 250 - 62 = 188", "per player: 188 / 4 = 47"], "option_values": [62, 65, 87, 47], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 338, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 240 shirts. It sold 55% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 240 shirts. It sold 55% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "endings": [" 18 boxes.", " 8 boxes.", " 19 boxes.", " 22 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0338", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "18", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "took the percentage off the remainder again", "counted the loose shirts as a box", "packed the sold shirts"], "solution_steps": ["sold: 55% of 240 = 132", "left over: 240 - 132 = 108", "full boxes: 108 / 6 = 18 (remainder 0)"], "option_values": [18, 8, 19, 22], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 339, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 5 metres and 47 centimetres long. A worker cut off 75 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 5 metres and 47 centimetres long. A worker cut off 75 centimetres. The board left was", "endings": [" 472 centimetres.", " 425 centimetres.", " 372 centimetres.", " 482 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0339", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "472", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["correct", "forgot the extra centimetres", "cut a whole metre off as well", "stopped ten centimetres short of the cut"], "solution_steps": ["convert metres: 5 x 100 = 500 cm", "add the extra centimetres: 500 + 47 = 547 cm", "subtract the cut: 547 - 75 = 472 cm"], "option_values": [472, 425, 372, 482], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 340, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $0.60 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 3 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $0.60 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 3 friends. Each person paid", "endings": [" $1.80.", " $1.20.", " $2.40.", " $7.20."], "source_id": "deeparithmark_v1_money_depth4_0340", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "180", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "split among two more people", "split only between the friends", "did not split the total at all"], "solution_steps": ["markers: 5 x 60 = 300", "erasers: 6 x 70 = 420", "total cost: 300 + 420 = 720", "split between 4 people: 720 / 4 = 180"], "option_values": [180, 120, 240, 720], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 341, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 420 units. A delivery added 130, then 210 units were shipped out, and 32 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 420 units. A delivery added 130, then 210 units were shipped out, and 32 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 38 crates.", " 22 crates.", " 34 crates.", " 39 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0341", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "38", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "forgot the delivery", "packed into larger crates", "counted the loose units as a crate"], "solution_steps": ["after delivery: 420 + 130 = 550", "after shipping: 550 - 210 = 340", "good units: 340 - 32 = 308", "full crates: 308 / 8 = 38 (remainder 4)"], "option_values": [38, 22, 34, 39], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 342, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 15 litres per minute for 4 minutes, then 3 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 15 litres per minute for 4 minutes, then 3 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "endings": [" 92 litres.", " 97 litres.", " 152 litres.", " 207 litres."], "source_id": "deeparithmark_v1_rate_depth4_0342", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "152", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the first fill", "drained twice", "correct", "forgot the drain"], "solution_steps": ["first fill: 15 x 4 = 60 litres", "second fill: 3 x 9 = 27 litres", "before draining: 120 + 60 + 27 = 207", "after draining: 207 - 55 = 152"], "option_values": [92, 97, 152, 207], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 343, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:06 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:06 a.m. for 50 minutes. The booking ended at", "endings": [" 7:56 a.m.", " 9:56 a.m.", " 8:56 a.m.", " 9:26 a.m."], "source_id": "deeparithmark_v1_time_depth2_0343", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "536", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["forgot the last full hour", "added an extra hour", "correct", "ran half an hour long"], "solution_steps": ["convert the start: 486 minutes after midnight", "add the duration: 486 + 50 = 536 minutes"], "option_values": [476, 596, 536, 566], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 344, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $1.79.", " $2.27.", " $1.92.", " $2.55."], "source_id": "deeparithmark_v1_money_percent_depth2_0344", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "227", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "correct", "forgot the fee", "read the percentage as a flat number of cents"], "solution_steps": ["take 20% of 240 off: 240 - 48 = 192", "add the 35-cent fee: 192 + 35 = 227"], "option_values": [179, 227, 192, 255], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 345, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.20 was split between two teams in the ratio 5:1 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.20 was split between two teams in the ratio 5:1 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.35.", " $0.64.", " $0.52.", " $0.42."], "source_id": "deeparithmark_v1_ratio_depth5_0345", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "35", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "forgot to deduct the fee", "split the whole prize among one team", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 620 - 200 = 420", "one ratio part: 420 / 6 = 70", "larger share: 5 x 70 = 350", "after charity: 350 - 70 = 280", "per player: 280 / 8 = 35"], "option_values": [35, 64, 52, 42], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 346, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Samir baked 135 muffins. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Samir baked 135 muffins. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "endings": [" 18 muffins.", " 11 muffins.", " 22 muffins.", " 27 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0346", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "18", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["correct", "gave away a half and split among one more child", "split all the cookies among one more child", "split all the cookies, not the rest"], "solution_steps": ["one third given away: 135 / 3 = 45", "rest kept: 135 - 45 = 90", "split among 5: 90 / 5 = 18"], "option_values": [18, 11, 22, 27], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 347, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 9 litres per minute for 6 minutes, then 7 litres per minute for 7 minutes. A drain then removed 25 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 9 litres per minute for 6 minutes, then 7 litres per minute for 7 minutes. A drain then removed 25 litres. The tank then held", "endings": [" 149 litres.", " 173 litres.", " 212 litres.", " 198 litres."], "source_id": "deeparithmark_v1_rate_depth4_0347", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "198", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the second fill", "drained twice", "used the first rate for both stages", "correct"], "solution_steps": ["first fill: 9 x 6 = 54 litres", "second fill: 7 x 7 = 49 litres", "before draining: 120 + 54 + 49 = 223", "after draining: 223 - 25 = 198"], "option_values": [149, 173, 212, 198], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 348, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $9.00 an hour, and then 2 hours at $12.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $9.00 an hour, and then 2 hours at $12.00 an hour. He earned", "endings": [" $36.00.", " $24.00.", " $78.00.", " $168.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0348", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "7800", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid the slower rate for the whole day", "forgot the first stretch", "correct", "added the rates together"], "solution_steps": ["first stretch: 6 x 900 = 5400", "second stretch: 2 x 1200 = 2400", "total pay: 5400 + 2400 = 7800"], "option_values": [3600, 2400, 7800, 16800], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 349, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $0.95 each and 4 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $0.95 each and 4 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $1.53.", " $1.58.", " $1.85.", " $2.05."], "source_id": "deeparithmark_v1_money_depth4_0349", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "205", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among one more person", "forgot the erasers", "swapped the two unit prices", "correct"], "solution_steps": ["markers: 5 x 95 = 475", "erasers: 4 x 35 = 140", "total cost: 475 + 140 = 615", "split between 3 people: 615 / 3 = 205"], "option_values": [153, 158, 185, 205], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 350, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 40 km at 20 km/h, rested 25 minutes, then walked 8 km at 4 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 40 km at 20 km/h, rested 25 minutes, then walked 8 km at 4 km/h. Her total time, in minutes, was", "endings": [" 85 minutes.", " 145 minutes.", " 169 minutes.", " 265 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0350", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "265", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["divided by the speed twice", "forgot the walking leg", "used the cycling speed for both legs", "correct"], "solution_steps": ["cycling time: 60 x 40 / 20 = 120 minutes", "walking time: 60 x 8 / 4 = 120 minutes", "add the rest: 120 + 25 + 120 = 265 minutes"], "option_values": [85, 145, 169, 265], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 351, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.60 was split between two teams in the ratio 3:1 after a $4.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.60 was split between two teams in the ratio 3:1 after a $4.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.06.", " $0.45.", " $0.24.", " $0.18."], "source_id": "deeparithmark_v1_ratio_depth5_0351", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "18", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "divided between the teams instead of the players", "forgot the charity cut", "correct"], "solution_steps": ["after the fee: 560 - 400 = 160", "one ratio part: 160 / 4 = 40", "larger share: 3 x 40 = 120", "after charity: 120 - 30 = 90", "per player: 90 / 5 = 18"], "option_values": [6, 45, 24, 18], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 352, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $4.43.", " $5.44.", " $5.72.", " $5.79."], "source_id": "deeparithmark_v1_money_percent_depth2_0352", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "579", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "forgot the fee", "took the discount off the fee as well", "correct"], "solution_steps": ["take 20% of 680 off: 680 - 136 = 544", "add the 35-cent fee: 544 + 35 = 579"], "option_values": [443, 544, 572, 579], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 353, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:34 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:34 a.m. for 110 minutes. The booking ended at", "endings": [" 9:24 a.m.", " 8:24 a.m.", " 8:54 a.m.", " 9:54 a.m."], "source_id": "deeparithmark_v1_time_depth2_0353", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "504", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added an extra hour", "correct", "ran half an hour long", "ran an hour and a half long"], "solution_steps": ["convert the start: 394 minutes after midnight", "add the duration: 394 + 110 = 504 minutes"], "option_values": [564, 504, 534, 594], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 354, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:14 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:14 a.m. for 50 minutes. The booking ended at", "endings": [" 7:04 a.m.", " 6:49 a.m.", " 5:24 a.m.", " 6:04 a.m."], "source_id": "deeparithmark_v1_time_depth2_0354", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "424", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "stopped a quarter of an hour early", "subtracted the duration instead of adding it", "dropped the hour carry"], "solution_steps": ["convert the start: 374 minutes after midnight", "add the duration: 374 + 50 = 424 minutes"], "option_values": [424, 409, 324, 364], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 355, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.60 was split between two teams in the ratio 5:3 after a $2.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.60 was split between two teams in the ratio 5:3 after a $2.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.37.", " $0.63.", " $0.95.", " $1.12."], "source_id": "deeparithmark_v1_ratio_depth5_0355", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "63", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "correct", "forgot to deduct the fee", "split the whole prize among one team"], "solution_steps": ["after the fee: 760 - 200 = 560", "one ratio part: 560 / 8 = 70", "larger share: 5 x 70 = 350", "after charity: 350 - 35 = 315", "per player: 315 / 5 = 63"], "option_values": [37, 63, 95, 112], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 356, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $7.97.", " $7.56.", " $8.01.", " $7.17."], "source_id": "deeparithmark_v1_money_percent_depth2_0356", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "801", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "forgot the fee", "correct", "took the percentage off twice"], "solution_steps": ["take 10% of 840 off: 840 - 84 = 756", "add the 45-cent fee: 756 + 45 = 801"], "option_values": [797, 756, 801, 717], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 357, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $0.60 each and 3 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $0.60 each and 3 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.11.", " $1.36.", " $1.12.", " $1.38."], "source_id": "deeparithmark_v1_money_depth4_0357", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "111", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "bought one extra of each item", "added the unit prices instead of multiplying", "split only between the friends"], "solution_steps": ["markers: 6 x 60 = 360", "erasers: 3 x 65 = 195", "total cost: 360 + 195 = 555", "split between 5 people: 555 / 5 = 111"], "option_values": [111, 136, 112, 138], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 358, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $16.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $16.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $905.00.", " $596.00.", " $591.00.", " $543.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0358", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "54300", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["added the tax instead of withholding it", "taxed only the regular pay", "paid overtime at double rate", "correct"], "solution_steps": ["regular pay: 32 x 1600 = 51200", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 8 x 2400 = 19200", "gross with bonus: 51200 + 19200 + 2000 = 72400", "take-home: 72400 - 18100 = 54300"], "option_values": [90500, 59600, 59100, 54300], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 359, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Priya baked 180 biscuits. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Priya baked 180 biscuits. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "endings": [" 13 biscuits.", " 36 biscuits.", " 24 biscuits.", " 25 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0359", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "24", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away a third twice and split among one more child", "split all the cookies, not the rest", "correct", "split all the cookies among two more children"], "solution_steps": ["one third given away: 180 / 3 = 60", "rest kept: 180 - 60 = 120", "split among 5: 120 / 5 = 24"], "option_values": [13, 36, 24, 25], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 360, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 54 pallets.", " 28 pallets.", " 52 pallets.", " 49 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0360", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "54", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "took both percentages twice", "took both percentages off the original stock", "stacked on larger pallets"], "solution_steps": ["Monday: 25% of 800 = 200", "left after Monday: 800 - 200 = 600", "Tuesday: 10% of 600 = 60", "left after Tuesday: 600 - 60 = 540", "full pallets: 540 / 10 = 54"], "option_values": [54, 28, 52, 49], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 361, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $12.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $12.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $465.80.", " $469.20.", " $506.60.", " $486.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0361", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "48620", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at the normal rate", "forgot the bonus", "paid overtime at double rate", "correct"], "solution_steps": ["regular pay: 40 x 1200 = 48000", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 4 x 1800 = 7200", "gross with bonus: 48000 + 7200 + 2000 = 57200", "take-home: 57200 - 8580 = 48620"], "option_values": [46580, 46920, 50660, 48620], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 362, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 5 hours at $15.00 an hour, and then 2 hours at $18.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 5 hours at $15.00 an hour, and then 2 hours at $18.00 an hour. He earned", "endings": [" $111.00.", " $36.00.", " $75.00.", " $105.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0362", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "11100", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["correct", "forgot the first stretch", "forgot the second stretch", "paid every hour at the first rate"], "solution_steps": ["first stretch: 5 x 1500 = 7500", "second stretch: 2 x 1800 = 3600", "total pay: 7500 + 3600 = 11100"], "option_values": [11100, 3600, 7500, 10500], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 363, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 3 metres and 47 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 3 metres and 47 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 302 centimetres.", " 392 centimetres.", " 349 centimetres.", " 312 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0363", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "302", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["correct", "added the cut instead of removing it", "counted the extra centimetres twice", "stopped ten centimetres short of the cut"], "solution_steps": ["convert metres: 3 x 100 = 300 cm", "add the extra centimetres: 300 + 47 = 347 cm", "subtract the cut: 347 - 45 = 302 cm"], "option_values": [302, 392, 349, 312], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 364, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 280 shirts. It sold 30% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 280 shirts. It sold 30% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "endings": [" 12 boxes.", " 15 boxes.", " 21 boxes.", " 22 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0364", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "21", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold twice as many", "took the percentage off the remainder again", "correct", "rounded the box count up"], "solution_steps": ["sold: 30% of 280 = 84", "left over: 280 - 84 = 196", "full boxes: 196 / 9 = 21 (remainder 7)"], "option_values": [12, 15, 21, 22], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 365, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:07 a.m.. The first session lasted 45 minutes, the break lasted 20 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:07 a.m.. The first session lasted 45 minutes, the break lasted 20 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 8:32 a.m.", " 8:52 a.m.", " 8:12 a.m.", " 9:12 a.m."], "source_id": "deeparithmark_v1_time_depth3_0365", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "532", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the break", "correct", "forgot the second session", "counted the break twice"], "solution_steps": ["after the first session: 427 + 45 = 472 minutes after midnight", "after the break: 472 + 20 = 492", "after the second session: 492 + 40 = 532"], "option_values": [512, 532, 492, 552], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 366, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $430.10.", " $429.80.", " $521.90.", " $491.30."], "source_id": "deeparithmark_v1_money_rate_depth5_0366", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "52190", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the overtime", "taxed twice", "correct", "paid overtime at the normal rate"], "solution_steps": ["regular pay: 38 x 1200 = 45600", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 6 x 1800 = 10800", "gross with bonus: 45600 + 10800 + 5000 = 61400", "take-home: 61400 - 9210 = 52190"], "option_values": [43010, 42980, 52190, 49130], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 367, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 6 metres and 47 centimetres long. A worker cut off 115 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 6 metres and 47 centimetres long. A worker cut off 115 centimetres. The board left was", "endings": [" 432 centimetres.", " 485 centimetres.", " 579 centimetres.", " 532 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0367", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "532", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["cut a whole metre off as well", "forgot the extra centimetres", "counted the extra centimetres twice", "correct"], "solution_steps": ["convert metres: 6 x 100 = 600 cm", "add the extra centimetres: 600 + 47 = 647 cm", "subtract the cut: 647 - 115 = 532 cm"], "option_values": [432, 485, 579, 532], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 368, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $12.50 an hour, and then 2 hours at $17.50 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $12.50 an hour, and then 2 hours at $17.50 an hour. He earned", "endings": [" $130.00.", " $240.00.", " $110.00.", " $140.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0368", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "11000", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["swapped the two rates", "added the rates together", "correct", "paid every hour at the second rate"], "solution_steps": ["first stretch: 6 x 1250 = 7500", "second stretch: 2 x 1750 = 3500", "total pay: 7500 + 3500 = 11000"], "option_values": [13000, 24000, 11000, 14000], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 369, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:57 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:57 a.m. for 50 minutes. The booking ended at", "endings": [" 8:17 a.m.", " 9:17 a.m.", " 8:47 a.m.", " 7:47 a.m."], "source_id": "deeparithmark_v1_time_depth2_0369", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "467", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran half an hour long", "ran an hour and a half long", "added an extra hour", "correct"], "solution_steps": ["convert the start: 417 minutes after midnight", "add the duration: 417 + 50 = 467 minutes"], "option_values": [497, 557, 527, 467], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 370, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 15 litres per minute for 6 minutes, then 3 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 15 litres per minute for 6 minutes, then 3 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 395 litres.", " 335 litres.", " 475 litres.", " 428 litres."], "source_id": "deeparithmark_v1_rate_depth4_0370", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "335", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["used the first rate for both stages", "correct", "added the drain instead of removing it", "added the rates and multiplied once"], "solution_steps": ["first fill: 15 x 6 = 90 litres", "second fill: 3 x 5 = 15 litres", "before draining: 300 + 90 + 15 = 405", "after draining: 405 - 70 = 335"], "option_values": [395, 335, 475, 428], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 371, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.50 was split between two teams in the ratio 4:1 after a $5.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.50 was split between two teams in the ratio 4:1 after a $5.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.50.", " $0.30.", " $1.20.", " $0.40."], "source_id": "deeparithmark_v1_ratio_depth5_0371", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "30", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split the whole prize among one team", "correct", "forgot to deduct the fee", "forgot the charity cut"], "solution_steps": ["after the fee: 750 - 500 = 250", "one ratio part: 250 / 5 = 50", "larger share: 4 x 50 = 200", "after charity: 200 - 50 = 150", "per player: 150 / 5 = 30"], "option_values": [50, 30, 120, 40], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 372, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 99 pallets.", " 98 pallets.", " 142 pallets.", " 131 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0372", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "98", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["counted the loose sacks as a pallet", "correct", "forgot Monday", "forgot Tuesday"], "solution_steps": ["Monday: 25% of 1400 = 350", "left after Monday: 1400 - 350 = 1050", "Tuesday: 25% of 1050 = 262", "left after Tuesday: 1050 - 262 = 788", "full pallets: 788 / 8 = 98"], "option_values": [99, 98, 142, 131], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 373, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 12 litres per minute for 4 minutes, then 3 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 12 litres per minute for 4 minutes, then 3 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 305 litres.", " 233 litres.", " 278 litres.", " 373 litres."], "source_id": "deeparithmark_v1_rate_depth4_0373", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "233", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["added the rates and multiplied once", "correct", "used the first rate for both stages", "added the drain instead of removing it"], "solution_steps": ["first fill: 12 x 4 = 48 litres", "second fill: 3 x 5 = 15 litres", "before draining: 240 + 48 + 15 = 303", "after draining: 303 - 70 = 233"], "option_values": [305, 233, 278, 373], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 374, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $5.40. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $5.40. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $5.31.", " $5.27.", " $4.77.", " $4.86."], "source_id": "deeparithmark_v1_money_percent_depth2_0374", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "531", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the discount off the fee as well", "took the percentage off twice", "forgot the fee"], "solution_steps": ["take 10% of 540 off: 540 - 54 = 486", "add the 45-cent fee: 486 + 45 = 531"], "option_values": [531, 527, 477, 486], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 375, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $0.45 each and 5 erasers at $0.50 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $0.45 each and 5 erasers at $0.50 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $0.63.", " $1.13.", " $0.94.", " $1.08."], "source_id": "deeparithmark_v1_money_depth4_0375", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "113", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["forgot the erasers", "correct", "split among one more person", "charged the marker price for everything"], "solution_steps": ["markers: 7 x 45 = 315", "erasers: 5 x 50 = 250", "total cost: 315 + 250 = 565", "split between 5 people: 565 / 5 = 113"], "option_values": [63, 113, 94, 108], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 376, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $498.00.", " $471.00.", " $785.00.", " $628.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0376", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "47100", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at double rate", "correct", "added the tax instead of withholding it", "forgot the tax"], "solution_steps": ["regular pay: 40 x 1200 = 48000", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 6 x 1800 = 10800", "gross with bonus: 48000 + 10800 + 4000 = 62800", "take-home: 62800 - 15700 = 47100"], "option_values": [49800, 47100, 78500, 62800], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 377, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 25% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 25% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 44 pallets.", " 16 pallets.", " 48 pallets.", " 45 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0377", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "48", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "took both percentages twice", "correct", "stacked on larger pallets"], "solution_steps": ["Monday: 25% of 1200 = 300", "left after Monday: 1200 - 300 = 900", "Tuesday: 20% of 900 = 180", "left after Tuesday: 900 - 180 = 720", "full pallets: 720 / 15 = 48"], "option_values": [44, 16, 48, 45], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 378, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.90 was split between two teams in the ratio 4:3 after a $3.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.90 was split between two teams in the ratio 4:3 after a $3.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.28.", " $1.22.", " $0.35.", " $0.61."], "source_id": "deeparithmark_v1_ratio_depth5_0378", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "35", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "split the whole prize among one team", "correct", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 790 - 300 = 490", "one ratio part: 490 / 7 = 70", "larger share: 4 x 70 = 280", "after charity: 280 - 140 = 140", "per player: 140 / 4 = 35"], "option_values": [28, 122, 35, 61], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 379, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $1.20 each and 6 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $1.20 each and 6 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $2.10.", " $2.80.", " $5.20.", " $3.50."], "source_id": "deeparithmark_v1_money_depth4_0379", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "350", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among two more people", "forgot the erasers", "charged the marker price for everything", "correct"], "solution_steps": ["markers: 7 x 120 = 840", "erasers: 6 x 35 = 210", "total cost: 840 + 210 = 1050", "split between 3 people: 1050 / 3 = 350"], "option_values": [210, 280, 520, 350], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 380, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $2.56.", " $2.71.", " $3.35.", " $2.86."], "source_id": "deeparithmark_v1_money_percent_depth2_0380", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "271", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "correct", "forgot the discount", "charged the handling fee twice"], "solution_steps": ["take 20% of 320 off: 320 - 64 = 256", "add the 15-cent fee: 256 + 15 = 271"], "option_values": [256, 271, 335, 286], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 381, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 400 shirts. It sold 15% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 400 shirts. It sold 15% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "endings": [" 66 boxes.", " 85 boxes.", " 56 boxes.", " 57 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0381", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "56", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the whole stock, not the rest", "divided by the number of boxes left over", "correct", "rounded the box count up"], "solution_steps": ["sold: 15% of 400 = 60", "left over: 400 - 60 = 340", "full boxes: 340 / 6 = 56 (remainder 4)"], "option_values": [66, 85, 56, 57], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 382, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:25 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:25 a.m. for 50 minutes. The booking ended at", "endings": [" 7:15 a.m.", " 5:35 a.m.", " 6:15 a.m.", " 8:45 a.m."], "source_id": "deeparithmark_v1_time_depth2_0382", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "435", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "subtracted the duration instead of adding it", "dropped the hour carry", "ran an hour and a half long"], "solution_steps": ["convert the start: 385 minutes after midnight", "add the duration: 385 + 50 = 435 minutes"], "option_values": [435, 335, 375, 525], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 383, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:16 a.m.. The first session lasted 70 minutes, the break lasted 20 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:16 a.m.. The first session lasted 70 minutes, the break lasted 20 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 9:36 a.m.", " 8:46 a.m.", " 9:16 a.m.", " 8:26 a.m."], "source_id": "deeparithmark_v1_time_depth3_0383", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "506", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["counted the first session twice", "counted the break twice", "finished half an hour late on top of the break", "correct"], "solution_steps": ["after the first session: 376 + 70 = 446 minutes after midnight", "after the break: 446 + 20 = 466", "after the second session: 466 + 40 = 506"], "option_values": [576, 526, 556, 506], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 384, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $8.40.", " $5.60.", " $6.20.", " $10.60."], "source_id": "deeparithmark_v1_percent_money_depth4_0384", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "840", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "split the total among one more person", "applied the discount twice", "forgot the discount"], "solution_steps": ["discount: 2000 - 400 = 1600", "tax on the discounted price: 1600 + 160 = 1760", "coupon: 1760 - 80 = 1680", "split 2 ways: 1680 / 2 = 840"], "option_values": [840, 560, 620, 1060], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 385, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 15 litres per minute for 10 minutes, then 5 litres per minute for 7 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 15 litres per minute for 10 minutes, then 5 litres per minute for 7 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 355 litres.", " 205 litres.", " 495 litres.", " 425 litres."], "source_id": "deeparithmark_v1_rate_depth4_0385", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "355", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "forgot the first fill", "added the drain instead of removing it", "forgot the drain"], "solution_steps": ["first fill: 15 x 10 = 150 litres", "second fill: 5 x 7 = 35 litres", "before draining: 240 + 150 + 35 = 425", "after draining: 425 - 70 = 355"], "option_values": [355, 205, 495, 425], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 386, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 6 metres and 25 centimetres long. A worker cut off 90 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 6 metres and 25 centimetres long. A worker cut off 90 centimetres. The board left was", "endings": [" 435 centimetres.", " 815 centimetres.", " 715 centimetres.", " 535 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0386", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "535", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["cut a whole metre off as well", "added the cut and a whole metre", "added the cut instead of removing it", "correct"], "solution_steps": ["convert metres: 6 x 100 = 600 cm", "add the extra centimetres: 600 + 25 = 625 cm", "subtract the cut: 625 - 90 = 535 cm"], "option_values": [435, 815, 715, 535], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 387, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:06 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:06 a.m. for 80 minutes. The booking ended at", "endings": [" 5:46 a.m.", " 7:26 a.m.", " 8:26 a.m.", " 9:26 a.m."], "source_id": "deeparithmark_v1_time_depth2_0387", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "506", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "dropped the hour carry", "correct", "added an extra hour"], "solution_steps": ["convert the start: 426 minutes after midnight", "add the duration: 426 + 80 = 506 minutes"], "option_values": [346, 446, 506, 566], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 388, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $3.54.", " $3.29.", " $4.05.", " $4.81."], "source_id": "deeparithmark_v1_money_percent_depth2_0388", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "329", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["charged the handling fee twice", "correct", "forgot the discount", "added the discount instead of removing it"], "solution_steps": ["take 20% of 380 off: 380 - 76 = 304", "add the 25-cent fee: 304 + 25 = 329"], "option_values": [354, 329, 405, 481], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 389, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 700 units. A delivery added 240, then 90 units were shipped out, and 32 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 700 units. A delivery added 240, then 90 units were shipped out, and 32 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 62 crates.", " 17 crates.", " 73 crates.", " 68 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0389", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "68", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed into larger crates", "packed the arriving units only", "added the damaged units", "correct"], "solution_steps": ["after delivery: 700 + 240 = 940", "after shipping: 940 - 90 = 850", "good units: 850 - 32 = 818", "full crates: 818 / 12 = 68 (remainder 2)"], "option_values": [62, 17, 73, 68], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 390, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 4 markers at $1.20 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 4 markers at $1.20 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.17.", " $0.96.", " $1.68.", " $1.18."], "source_id": "deeparithmark_v1_money_depth4_0390", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "117", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "forgot the erasers", "charged the marker price for everything", "added the unit prices instead of multiplying"], "solution_steps": ["markers: 4 x 120 = 480", "erasers: 3 x 35 = 105", "total cost: 480 + 105 = 585", "split between 5 people: 585 / 5 = 117"], "option_values": [117, 96, 168, 118], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 391, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $2.76.", " $2.17.", " $2.81.", " $2.56."], "source_id": "deeparithmark_v1_money_percent_depth2_0391", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "281", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "took the percentage off twice", "correct", "forgot the fee"], "solution_steps": ["take 20% of 320 off: 320 - 64 = 256", "add the 25-cent fee: 256 + 25 = 281"], "option_values": [276, 217, 281, 256], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 392, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $0.45 each and 5 erasers at $0.30 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $0.45 each and 5 erasers at $0.30 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $1.55.", " $0.93.", " $1.16.", " $1.59."], "source_id": "deeparithmark_v1_money_depth4_0392", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "155", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "split among two more people", "split among one more person", "added the unit prices instead of multiplying"], "solution_steps": ["markers: 7 x 45 = 315", "erasers: 5 x 30 = 150", "total cost: 315 + 150 = 465", "split between 3 people: 465 / 3 = 155"], "option_values": [155, 93, 116, 159], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 393, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:39 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:39 a.m. for 110 minutes. The booking ended at", "endings": [" 7:29 a.m.", " 8:14 a.m.", " 6:29 a.m.", " 8:29 a.m."], "source_id": "deeparithmark_v1_time_depth2_0393", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "509", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added the minutes without the hours", "stopped a quarter of an hour early", "dropped the hour carry", "correct"], "solution_steps": ["convert the start: 399 minutes after midnight", "add the duration: 399 + 110 = 509 minutes"], "option_values": [449, 494, 389, 509], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 394, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 320 shirts. It sold 30% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 320 shirts. It sold 30% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 12 boxes.", " 16 boxes.", " 28 boxes.", " 19 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0394", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "28", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the sold shirts", "sold twice as many", "correct", "took the percentage off the remainder again"], "solution_steps": ["sold: 30% of 320 = 96", "left over: 320 - 96 = 224", "full boxes: 224 / 8 = 28 (remainder 0)"], "option_values": [12, 16, 28, 19], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 395, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Dara baked 90 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Dara baked 90 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 15 muffins.", " 7 muffins.", " 6 muffins.", " 18 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0395", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "15", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["correct", "split the given-away cookies too", "gave away two thirds and split among one more child", "split all the cookies among one more child"], "solution_steps": ["one third given away: 90 / 3 = 30", "rest kept: 90 - 30 = 60", "split among 4: 60 / 4 = 15"], "option_values": [15, 7, 6, 18], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 396, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $12.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $12.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $11.48.", " $2.87.", " $2.97.", " $3.82."], "source_id": "deeparithmark_v1_percent_money_depth4_0396", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "287", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["did not split the cost at all", "correct", "forgot the coupon", "split the total among one fewer person"], "solution_steps": ["discount: 1200 - 120 = 1080", "tax on the discounted price: 1080 + 108 = 1188", "coupon: 1188 - 40 = 1148", "split 4 ways: 1148 / 4 = 287"], "option_values": [1148, 287, 297, 382], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 397, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 9 litres per minute for 10 minutes, then 3 litres per minute for 7 minutes. A drain then removed 25 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 9 litres per minute for 10 minutes, then 3 litres per minute for 7 minutes. A drain then removed 25 litres. The tank then held", "endings": [" 305 litres.", " 376 litres.", " 368 litres.", " 326 litres."], "source_id": "deeparithmark_v1_rate_depth4_0397", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "326", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the second fill", "added the drain instead of removing it", "used the first rate for both stages", "correct"], "solution_steps": ["first fill: 9 x 10 = 90 litres", "second fill: 3 x 7 = 21 litres", "before draining: 240 + 90 + 21 = 351", "after draining: 351 - 25 = 326"], "option_values": [305, 376, 368, 326], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 398, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 25% discount came off it, then 5% tax was added to the discounted price, and a $0.80 coupon was applied last. 5 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 25% discount came off it, then 5% tax was added to the discounted price, and a $0.80 coupon was applied last. 5 people split the final cost equally. Each paid", "endings": [" $5.51.", " $5.35.", " $5.67.", " $6.88."], "source_id": "deeparithmark_v1_percent_money_depth4_0398", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "551", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "used the coupon twice", "forgot the coupon", "split the total among one fewer person"], "solution_steps": ["discount: 3600 - 900 = 2700", "tax on the discounted price: 2700 + 135 = 2835", "coupon: 2835 - 80 = 2755", "split 5 ways: 2755 / 5 = 551"], "option_values": [551, 535, 567, 688], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 399, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Ben baked 144 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Ben baked 144 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 24 muffins.", " 28 muffins.", " 36 muffins.", " 96 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0399", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "24", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["correct", "split all the cookies among one more child", "split all the cookies, not the rest", "stopped after giving the third away"], "solution_steps": ["one third given away: 144 / 3 = 48", "rest kept: 144 - 48 = 96", "split among 4: 96 / 4 = 24"], "option_values": [24, 28, 36, 96], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 400, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 480 units. A delivery added 310, then 210 units were shipped out, and 24 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 480 units. A delivery added 310, then 210 units were shipped out, and 24 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 85 crates.", " 61 crates.", " 64 crates.", " 62 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0400", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "61", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the shipping", "correct", "forgot the damaged units", "counted the loose units as a crate"], "solution_steps": ["after delivery: 480 + 310 = 790", "after shipping: 790 - 210 = 580", "good units: 580 - 24 = 556", "full crates: 556 / 9 = 61 (remainder 7)"], "option_values": [85, 61, 64, 62], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 401, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $16.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $16.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $630.40.", " $672.80.", " $681.60.", " $945.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0401", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "63040", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "taxed only the regular pay", "paid overtime at double rate", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 36 x 1600 = 57600", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 8 x 2400 = 19200", "gross with bonus: 57600 + 19200 + 2000 = 78800", "take-home: 78800 - 15760 = 63040"], "option_values": [63040, 67280, 68160, 94560], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 402, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $12.00. A 30% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $12.00. A 30% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $2.04.", " $3.42.", " $4.02.", " $5.22."], "source_id": "deeparithmark_v1_percent_money_depth4_0402", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "402", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "used the coupon twice", "correct", "added the coupon instead of subtracting it"], "solution_steps": ["discount: 1200 - 360 = 840", "tax on the discounted price: 840 + 84 = 924", "coupon: 924 - 120 = 804", "split 2 ways: 804 / 2 = 402"], "option_values": [204, 342, 402, 522], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 403, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $9.20 was split between two teams in the ratio 5:1 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $9.20 was split between two teams in the ratio 5:1 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.52.", " $0.63.", " $1.57.", " $0.84."], "source_id": "deeparithmark_v1_ratio_depth5_0403", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "63", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "correct", "divided between the teams instead of the players", "split the whole prize among one team"], "solution_steps": ["after the fee: 920 - 500 = 420", "one ratio part: 420 / 6 = 70", "larger share: 5 x 70 = 350", "after charity: 350 - 35 = 315", "per player: 315 / 5 = 63"], "option_values": [52, 63, 157, 84], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 404, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Quinn baked 108 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Quinn baked 108 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 18 muffins.", " 13 muffins.", " 7 muffins.", " 12 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0404", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "18", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["correct", "gave away a half instead of a third", "gave away two thirds and split among one more child", "gave away a third twice"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 4: 72 / 4 = 18"], "option_values": [18, 13, 7, 12], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 405, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $569.50.", " $705.50.", " $841.50.", " $773.50."], "source_id": "deeparithmark_v1_money_rate_depth5_0405", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "77350", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the overtime", "paid overtime at the normal rate", "paid overtime at double rate", "correct"], "solution_steps": ["regular pay: 32 x 2000 = 64000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 8 x 3000 = 24000", "gross with bonus: 64000 + 24000 + 3000 = 91000", "take-home: 91000 - 13650 = 77350"], "option_values": [56950, 70550, 84150, 77350], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 406, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 15 litres per minute for 8 minutes, then 3 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 15 litres per minute for 8 minutes, then 3 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 335 litres.", " 295 litres.", " 395 litres.", " 415 litres."], "source_id": "deeparithmark_v1_rate_depth4_0406", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "335", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "drained twice", "used the first rate for both stages", "added the drain instead of removing it"], "solution_steps": ["first fill: 15 x 8 = 120 litres", "second fill: 3 x 5 = 15 litres", "before draining: 240 + 120 + 15 = 375", "after draining: 375 - 40 = 335"], "option_values": [335, 295, 395, 415], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 407, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $376.80.", " $473.60.", " $470.40.", " $502.40."], "source_id": "deeparithmark_v1_money_rate_depth5_0407", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "50240", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "paid overtime at the normal rate", "forgot the bonus", "correct"], "solution_steps": ["regular pay: 40 x 1200 = 48000", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 6 x 1800 = 10800", "gross with bonus: 48000 + 10800 + 4000 = 62800", "take-home: 62800 - 12560 = 50240"], "option_values": [37680, 47360, 47040, 50240], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 408, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $14.00 an hour and 4 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $14.00 an hour and 4 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $478.80.", " $489.60.", " $457.60.", " $514.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0408", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "51480", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "paid overtime at the normal rate", "taxed twice", "correct"], "solution_steps": ["regular pay: 32 x 1400 = 44800", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 4 x 2100 = 8400", "gross with bonus: 44800 + 8400 + 4000 = 57200", "take-home: 57200 - 5720 = 51480"], "option_values": [47880, 48960, 45760, 51480], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 409, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 560 units. A delivery added 260, then 140 units were shipped out, and 18 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 560 units. A delivery added 260, then 140 units were shipped out, and 18 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 73 crates.", " 56 crates.", " 89 crates.", " 77 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0409", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "73", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "shipped twice and damaged twice", "forgot the shipping", "added the damaged units"], "solution_steps": ["after delivery: 560 + 260 = 820", "after shipping: 820 - 140 = 680", "good units: 680 - 18 = 662", "full crates: 662 / 9 = 73 (remainder 5)"], "option_values": [73, 56, 89, 77], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 410, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 60 km at 20 km/h, rested 12 minutes, then walked 5 km at 5 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 60 km at 20 km/h, rested 12 minutes, then walked 5 km at 5 km/h. Her total time, in minutes, was", "endings": [" 192 minutes.", " 264 minutes.", " 252 minutes.", " 792 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0410", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "252", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "counted the rest twice", "correct", "used the walking speed for both legs"], "solution_steps": ["cycling time: 60 x 60 / 20 = 180 minutes", "walking time: 60 x 5 / 5 = 60 minutes", "add the rest: 180 + 12 + 60 = 252 minutes"], "option_values": [192, 264, 252, 792], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 411, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $4.40 was split between two teams in the ratio 4:2 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $4.40 was split between two teams in the ratio 4:2 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.58.", " $0.32.", " $0.16.", " $0.24."], "source_id": "deeparithmark_v1_ratio_depth5_0411", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "16", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot to deduct the fee", "forgot the charity cut", "correct", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 440 - 200 = 240", "one ratio part: 240 / 6 = 40", "larger share: 4 x 40 = 160", "after charity: 160 - 80 = 80", "per player: 80 / 5 = 16"], "option_values": [58, 32, 16, 24], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 412, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $6.21.", " $7.45.", " $6.66.", " $9.09."], "source_id": "deeparithmark_v1_money_percent_depth2_0412", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "621", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "read the percentage as a flat number of cents", "charged the handling fee twice", "added the discount instead of removing it"], "solution_steps": ["take 20% of 720 off: 720 - 144 = 576", "add the 45-cent fee: 576 + 45 = 621"], "option_values": [621, 745, 666, 909], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 413, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $6.87.", " $7.56.", " $7.71.", " $8.45."], "source_id": "deeparithmark_v1_money_percent_depth2_0413", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "771", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "forgot the fee", "correct", "read the percentage as a flat number of cents"], "solution_steps": ["take 10% of 840 off: 840 - 84 = 756", "add the 15-cent fee: 756 + 15 = 771"], "option_values": [687, 756, 771, 845], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 414, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:06 a.m.. The first session lasted 45 minutes, the break lasted 25 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:06 a.m.. The first session lasted 45 minutes, the break lasted 25 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "endings": [" 7:01 a.m.", " 8:01 a.m.", " 6:51 a.m.", " 7:36 a.m."], "source_id": "deeparithmark_v1_time_depth3_0414", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "481", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["added the minutes but not the hours", "correct", "forgot the last session and the break", "forgot the break"], "solution_steps": ["after the first session: 366 + 45 = 411 minutes after midnight", "after the break: 411 + 25 = 436", "after the second session: 436 + 45 = 481"], "option_values": [421, 481, 411, 456], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 415, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 9 litres per minute for 8 minutes, then 7 litres per minute for 9 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 9 litres per minute for 8 minutes, then 7 litres per minute for 9 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 355 litres.", " 395 litres.", " 332 litres.", " 323 litres."], "source_id": "deeparithmark_v1_rate_depth4_0415", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "395", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "correct", "forgot the second fill", "forgot the first fill"], "solution_steps": ["first fill: 9 x 8 = 72 litres", "second fill: 7 x 9 = 63 litres", "before draining: 300 + 72 + 63 = 435", "after draining: 435 - 40 = 395"], "option_values": [355, 395, 332, 323], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 416, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 320 shirts. It sold 30% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 320 shirts. It sold 30% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "endings": [" 32 boxes.", " 18 boxes.", " 13 boxes.", " 22 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0416", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "32", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "sold twice as many", "packed the sold shirts", "took the percentage off the remainder again"], "solution_steps": ["sold: 30% of 320 = 96", "left over: 320 - 96 = 224", "full boxes: 224 / 7 = 32 (remainder 0)"], "option_values": [32, 18, 13, 22], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 417, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $4.80.", " $5.10.", " $5.40.", " $9.70."], "source_id": "deeparithmark_v1_money_percent_depth2_0417", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "540", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "took the discount off the fee as well", "correct", "read the percentage as a flat number of cents"], "solution_steps": ["take 50% of 960 off: 960 - 480 = 480", "add the 60-cent fee: 480 + 60 = 540"], "option_values": [480, 510, 540, 970], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 418, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $543.20.", " $567.80.", " $642.60.", " $659.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0418", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "65960", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "forgot the overtime", "forgot the bonus", "correct"], "solution_steps": ["regular pay: 36 x 1800 = 64800", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 4 x 2700 = 10800", "gross with bonus: 64800 + 10800 + 2000 = 77600", "take-home: 77600 - 11640 = 65960"], "option_values": [54320, 56780, 64260, 65960], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 419, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $3.19.", " $4.71.", " $3.34.", " $3.75."], "source_id": "deeparithmark_v1_money_percent_depth2_0419", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "319", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "added the discount instead of removing it", "charged the handling fee twice", "read the percentage as a flat number of cents"], "solution_steps": ["take 20% of 380 off: 380 - 76 = 304", "add the 15-cent fee: 304 + 15 = 319"], "option_values": [319, 471, 334, 375], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 420, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $730.80.", " $633.60.", " $649.60.", " $712.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0420", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "73080", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "forgot the overtime", "taxed twice", "forgot the bonus"], "solution_steps": ["regular pay: 38 x 1800 = 68400", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 4 x 2700 = 10800", "gross with bonus: 68400 + 10800 + 2000 = 81200", "take-home: 81200 - 8120 = 73080"], "option_values": [73080, 63360, 64960, 71280], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 421, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $15.00 an hour, and then 2 hours at $19.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $15.00 an hour, and then 2 hours at $19.00 an hour. He earned", "endings": [" $98.00.", " $64.00.", " $38.00.", " $114.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0421", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "9800", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["correct", "worked one hour less in each stretch", "forgot the first stretch", "paid every hour at the second rate"], "solution_steps": ["first stretch: 4 x 1500 = 6000", "second stretch: 2 x 1900 = 3800", "total pay: 6000 + 3800 = 9800"], "option_values": [9800, 6400, 3800, 11400], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 422, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $8.90 was split between two teams in the ratio 4:3 after a $4.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $8.90 was split between two teams in the ratio 4:3 after a $4.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.28.", " $0.35.", " $0.52.", " $1.22."], "source_id": "deeparithmark_v1_ratio_depth5_0422", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "35", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "correct", "gave the larger share to the smaller ratio", "split the whole prize among one team"], "solution_steps": ["after the fee: 890 - 400 = 490", "one ratio part: 490 / 7 = 70", "larger share: 4 x 70 = 280", "after charity: 280 - 140 = 140", "per player: 140 / 4 = 35"], "option_values": [28, 35, 52, 122], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 423, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Hana baked 72 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Hana baked 72 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 12 biscuits.", " 48 biscuits.", " 14 biscuits.", " 18 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0423", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "12", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["correct", "stopped after giving the third away", "split all the cookies among one more child", "split all the cookies, not the rest"], "solution_steps": ["one third given away: 72 / 3 = 24", "rest kept: 72 - 24 = 48", "split among 4: 48 / 4 = 12"], "option_values": [12, 48, 14, 18], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 424, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 4 metres and 68 centimetres long. A worker cut off 130 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 4 metres and 68 centimetres long. A worker cut off 130 centimetres. The board left was", "endings": [" 238 centimetres.", " 698 centimetres.", " 338 centimetres.", " 598 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0424", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "338", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["cut a whole metre off as well", "added the cut and a whole metre", "correct", "added the cut instead of removing it"], "solution_steps": ["convert metres: 4 x 100 = 400 cm", "add the extra centimetres: 400 + 68 = 468 cm", "subtract the cut: 468 - 130 = 338 cm"], "option_values": [238, 698, 338, 598], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 425, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 25% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 25% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $5.85.", " $4.05.", " $7.65.", " $9.45."], "source_id": "deeparithmark_v1_money_percent_depth2_0425", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "585", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the percentage off twice", "forgot the discount", "added the discount instead of removing it"], "solution_steps": ["take 25% of 720 off: 720 - 180 = 540", "add the 45-cent fee: 540 + 45 = 585"], "option_values": [585, 405, 765, 945], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 426, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 440 shirts. It sold 40% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 440 shirts. It sold 40% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "endings": [" 24 boxes.", " 44 boxes.", " 29 boxes.", " 48 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0426", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "29", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold half the stock regardless of the percentage", "sold only a tenth of the stock", "correct", "packed the whole stock, not the rest"], "solution_steps": ["sold: 40% of 440 = 176", "left over: 440 - 176 = 264", "full boxes: 264 / 9 = 29 (remainder 3)"], "option_values": [24, 44, 29, 48], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 427, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 400 shirts. It sold 30% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 400 shirts. It sold 30% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "endings": [" 13 boxes.", " 31 boxes.", " 17 boxes.", " 22 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0427", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "31", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the sold shirts", "correct", "sold twice as many", "sold half the stock regardless of the percentage"], "solution_steps": ["sold: 30% of 400 = 120", "left over: 400 - 120 = 280", "full boxes: 280 / 9 = 31 (remainder 1)"], "option_values": [13, 31, 17, 22], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 428, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $14.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $14.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $471.60.", " $529.20.", " $668.80.", " $547.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0428", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "54720", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the overtime", "forgot the bonus", "added the tax instead of withholding it", "correct"], "solution_steps": ["regular pay: 36 x 1400 = 50400", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 4 x 2100 = 8400", "gross with bonus: 50400 + 8400 + 2000 = 60800", "take-home: 60800 - 6080 = 54720"], "option_values": [47160, 52920, 66880, 54720], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 429, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 480 shirts. It sold 15% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 480 shirts. It sold 15% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "endings": [" 37 boxes.", " 46 boxes.", " 48 boxes.", " 45 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0429", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "45", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold twice as many", "rounded the box count up", "sold only a tenth of the stock", "correct"], "solution_steps": ["sold: 15% of 480 = 72", "left over: 480 - 72 = 408", "full boxes: 408 / 9 = 45 (remainder 3)"], "option_values": [37, 46, 48, 45], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 430, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 15 litres per minute for 8 minutes, then 7 litres per minute for 7 minutes. A drain then removed 25 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 15 litres per minute for 8 minutes, then 7 litres per minute for 7 minutes. A drain then removed 25 litres. The tank then held", "endings": [" 419 litres.", " 395 litres.", " 324 litres.", " 444 litres."], "source_id": "deeparithmark_v1_rate_depth4_0430", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "444", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "forgot the second fill", "forgot the first fill", "correct"], "solution_steps": ["first fill: 15 x 8 = 120 litres", "second fill: 7 x 7 = 49 litres", "before draining: 300 + 120 + 49 = 469", "after draining: 469 - 25 = 444"], "option_values": [419, 395, 324, 444], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 431, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 700 units. A delivery added 180, then 250 units were shipped out, and 24 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 700 units. A delivery added 180, then 250 units were shipped out, and 24 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "endings": [" 23 crates.", " 43 crates.", " 25 crates.", " 11 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0431", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "43", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped twice and damaged twice", "correct", "shipped out twice", "packed the arriving units only"], "solution_steps": ["after delivery: 700 + 180 = 880", "after shipping: 880 - 250 = 630", "good units: 630 - 24 = 606", "full crates: 606 / 14 = 43 (remainder 4)"], "option_values": [23, 43, 25, 11], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 432, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 240, then 140 units were shipped out, and 40 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 240, then 140 units were shipped out, and 40 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 75 crates.", " 64 crates.", " 82 crates.", " 91 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0432", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "91", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped out twice", "forgot the delivery", "packed into larger crates", "correct"], "solution_steps": ["after delivery: 760 + 240 = 1000", "after shipping: 1000 - 140 = 860", "good units: 860 - 40 = 820", "full crates: 820 / 9 = 91 (remainder 1)"], "option_values": [75, 64, 82, 91], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 433, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 310, then 210 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 310, then 210 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 64 crates.", " 51 crates.", " 55 crates.", " 52 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0433", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "51", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the shipping", "correct", "added the damaged units", "counted the loose units as a crate"], "solution_steps": ["after delivery: 760 + 310 = 1070", "after shipping: 1070 - 210 = 860", "good units: 860 - 32 = 828", "full crates: 828 / 16 = 51 (remainder 12)"], "option_values": [64, 51, 55, 52], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 434, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:46 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:46 a.m. for 65 minutes. The booking ended at", "endings": [" 6:51 a.m.", " 5:41 a.m.", " 7:51 a.m.", " 8:21 a.m."], "source_id": "deeparithmark_v1_time_depth2_0434", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "471", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "subtracted the duration instead of adding it", "correct", "ran half an hour long"], "solution_steps": ["convert the start: 406 minutes after midnight", "add the duration: 406 + 65 = 471 minutes"], "option_values": [411, 341, 471, 501], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 435, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:09 a.m.. The first session lasted 60 minutes, the break lasted 10 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:09 a.m.. The first session lasted 60 minutes, the break lasted 10 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 10:09 a.m.", " 9:59 a.m.", " 9:19 a.m.", " 8:09 a.m."], "source_id": "deeparithmark_v1_time_depth3_0435", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "609", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["correct", "forgot the break", "forgot the second session", "dropped the hour carry"], "solution_steps": ["after the first session: 489 + 60 = 549 minutes after midnight", "after the break: 549 + 10 = 559", "after the second session: 559 + 50 = 609"], "option_values": [609, 599, 559, 489], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 436, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $28.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $28.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $12.02.", " $8.94.", " $12.32.", " $12.62."], "source_id": "deeparithmark_v1_percent_money_depth4_0436", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "1202", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "applied the discount twice", "forgot the coupon", "added the coupon instead of subtracting it"], "solution_steps": ["discount: 2800 - 560 = 2240", "tax on the discounted price: 2240 + 224 = 2464", "coupon: 2464 - 60 = 2404", "split 2 ways: 2404 / 2 = 1202"], "option_values": [1202, 894, 1232, 1262], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 437, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 72 pallets.", " 67 pallets.", " 98 pallets.", " 73 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0437", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "72", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "stacked on larger pallets", "forgot Monday", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 25% of 1600 = 400", "left after Monday: 1600 - 400 = 1200", "Tuesday: 10% of 1200 = 120", "left after Tuesday: 1200 - 120 = 1080", "full pallets: 1080 / 15 = 72"], "option_values": [72, 67, 98, 73], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 438, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Priya baked 144 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Priya baked 144 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 19 biscuits.", " 14 biscuits.", " 18 biscuits.", " 24 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0438", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "24", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split the rest among one more child", "gave away a half and split among one more child", "gave away a half instead of a third", "correct"], "solution_steps": ["one third given away: 144 / 3 = 48", "rest kept: 144 - 48 = 96", "split among 4: 96 / 4 = 24"], "option_values": [19, 14, 18, 24], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 439, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 50% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 50% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $7.05.", " $6.55.", " $3.65.", " $10.45."], "source_id": "deeparithmark_v1_money_percent_depth2_0439", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "365", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the discount", "read the percentage as a flat number of cents", "correct", "added the discount instead of removing it"], "solution_steps": ["take 50% of 680 off: 680 - 340 = 340", "add the 25-cent fee: 340 + 25 = 365"], "option_values": [705, 655, 365, 1045], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 440, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $28.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $28.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $5.76.", " $4.76.", " $5.96.", " $7.94."], "source_id": "deeparithmark_v1_percent_money_depth4_0440", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "596", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["used the coupon twice", "split the total among one more person", "correct", "split the total among one fewer person"], "solution_steps": ["discount: 2800 - 560 = 2240", "tax on the discounted price: 2240 + 224 = 2464", "coupon: 2464 - 80 = 2384", "split 4 ways: 2384 / 4 = 596"], "option_values": [576, 476, 596, 794], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 441, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $7.56.", " $7.32.", " $9.84.", " $8.16."], "source_id": "deeparithmark_v1_money_percent_depth2_0441", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "816", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "took the percentage off twice", "added the discount instead of removing it", "correct"], "solution_steps": ["take 10% of 840 off: 840 - 84 = 756", "add the 60-cent fee: 756 + 60 = 816"], "option_values": [756, 732, 984, 816], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 442, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 18 km at 18 km/h, rested 25 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 18 km at 18 km/h, rested 25 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "endings": [" 55 minutes.", " 85 minutes.", " 125 minutes.", " 205 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0442", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "205", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["divided by the speed twice", "forgot the walking leg", "used the cycling speed for both legs", "correct"], "solution_steps": ["cycling time: 60 x 18 / 18 = 60 minutes", "walking time: 60 x 12 / 6 = 120 minutes", "add the rest: 60 + 25 + 120 = 205 minutes"], "option_values": [55, 85, 125, 205], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 443, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 280 shirts. It sold 15% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 280 shirts. It sold 15% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "endings": [" 26 boxes.", " 21 boxes.", " 15 boxes.", " 31 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0443", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "26", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "sold twice as many", "sold half the stock regardless of the percentage", "packed the whole stock, not the rest"], "solution_steps": ["sold: 15% of 280 = 42", "left over: 280 - 42 = 238", "full boxes: 238 / 9 = 26 (remainder 4)"], "option_values": [26, 21, 15, 31], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 444, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:35 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:35 a.m. for 110 minutes. The booking ended at", "endings": [" 8:25 a.m.", " 10:25 a.m.", " 11:25 a.m.", " 10:55 a.m."], "source_id": "deeparithmark_v1_time_depth2_0444", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "625", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "correct", "added an extra hour", "ran half an hour long"], "solution_steps": ["convert the start: 515 minutes after midnight", "add the duration: 515 + 110 = 625 minutes"], "option_values": [505, 625, 685, 655], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 445, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 4 metres and 68 centimetres long. A worker cut off 75 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 4 metres and 68 centimetres long. A worker cut off 75 centimetres. The board left was", "endings": [" 325 centimetres.", " 393 centimetres.", " 543 centimetres.", " 643 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0445", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "393", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["forgot the extra centimetres", "correct", "added the cut instead of removing it", "added the cut and a whole metre"], "solution_steps": ["convert metres: 4 x 100 = 400 cm", "add the extra centimetres: 400 + 68 = 468 cm", "subtract the cut: 468 - 75 = 393 cm"], "option_values": [325, 393, 543, 643], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 446, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 360 shirts. It sold 25% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 360 shirts. It sold 25% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 25 boxes.", " 33 boxes.", " 45 boxes.", " 34 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0446", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "33", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["took the percentage off the remainder again", "correct", "packed the whole stock, not the rest", "rounded the box count up"], "solution_steps": ["sold: 25% of 360 = 90", "left over: 360 - 90 = 270", "full boxes: 270 / 8 = 33 (remainder 6)"], "option_values": [25, 33, 45, 34], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 447, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Ivo baked 72 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Ivo baked 72 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 4 biscuits.", " 9 biscuits.", " 8 biscuits.", " 12 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0447", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "12", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away two thirds and split among one more child", "gave away a half instead of a third", "gave away a third twice", "correct"], "solution_steps": ["one third given away: 72 / 3 = 24", "rest kept: 72 - 24 = 48", "split among 4: 48 / 4 = 12"], "option_values": [4, 9, 8, 12], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 448, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Tara baked 135 muffins. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Tara baked 135 muffins. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "endings": [" 18 muffins.", " 15 muffins.", " 27 muffins.", " 19 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0448", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "18", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["correct", "split the rest among one more child", "split all the cookies, not the rest", "split all the cookies among two more children"], "solution_steps": ["one third given away: 135 / 3 = 45", "rest kept: 135 - 45 = 90", "split among 5: 90 / 5 = 18"], "option_values": [18, 15, 27, 19], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 449, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 840 units. A delivery added 130, then 170 units were shipped out, and 12 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 840 units. A delivery added 130, then 170 units were shipped out, and 12 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 38 crates.", " 37 crates.", " 49 crates.", " 46 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0449", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "49", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped out twice", "shipped twice and damaged twice", "correct", "packed into larger crates"], "solution_steps": ["after delivery: 840 + 130 = 970", "after shipping: 970 - 170 = 800", "good units: 800 - 12 = 788", "full crates: 788 / 16 = 49 (remainder 4)"], "option_values": [38, 37, 49, 46], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 450, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $4.14.", " $5.05.", " $4.59.", " $4.95."], "source_id": "deeparithmark_v1_money_percent_depth2_0450", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "459", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "forgot the discount", "correct", "read the percentage as a flat number of cents"], "solution_steps": ["take 10% of 460 off: 460 - 46 = 414", "add the 45-cent fee: 414 + 45 = 459"], "option_values": [414, 505, 459, 495], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 451, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.50 was split between two teams in the ratio 4:1 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.50 was split between two teams in the ratio 4:1 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.17.", " $0.56.", " $0.43.", " $0.14."], "source_id": "deeparithmark_v1_ratio_depth5_0451", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "56", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["gave the larger share to the smaller ratio", "correct", "forgot the fee and the charity cut", "swapped the ratio parts"], "solution_steps": ["after the fee: 550 - 200 = 350", "one ratio part: 350 / 5 = 70", "larger share: 4 x 70 = 280", "after charity: 280 - 56 = 224", "per player: 224 / 4 = 56"], "option_values": [17, 56, 43, 14], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 452, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 440 shirts. It sold 25% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 440 shirts. It sold 25% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "endings": [" 27 boxes.", " 33 boxes.", " 28 boxes.", " 55 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0452", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "27", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "sold only a tenth of the stock", "rounded the box count up", "divided by the number of boxes left over"], "solution_steps": ["sold: 25% of 440 = 110", "left over: 440 - 110 = 330", "full boxes: 330 / 12 = 27 (remainder 6)"], "option_values": [27, 33, 28, 55], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 453, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 4 markers at $0.45 each and 3 erasers at $0.65 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 4 markers at $0.45 each and 3 erasers at $0.65 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $1.05.", " $0.93.", " $1.25.", " $0.75."], "source_id": "deeparithmark_v1_money_depth4_0453", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "125", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["charged the marker price for everything", "split among one more person", "correct", "split among two more people"], "solution_steps": ["markers: 4 x 45 = 180", "erasers: 3 x 65 = 195", "total cost: 180 + 195 = 375", "split between 3 people: 375 / 3 = 125"], "option_values": [105, 93, 125, 75], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 454, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:29 a.m.. The first session lasted 70 minutes, the break lasted 15 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:29 a.m.. The first session lasted 70 minutes, the break lasted 15 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 7:44 a.m.", " 9:59 a.m.", " 10:54 a.m.", " 9:44 a.m."], "source_id": "deeparithmark_v1_time_depth3_0454", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "584", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["dropped the hour carry", "counted the break twice", "counted the first session twice", "correct"], "solution_steps": ["after the first session: 449 + 70 = 519 minutes after midnight", "after the break: 519 + 15 = 534", "after the second session: 534 + 50 = 584"], "option_values": [464, 599, 654, 584], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 455, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 440 shirts. It sold 55% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 440 shirts. It sold 55% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "endings": [" 36 boxes.", " 33 boxes.", " 66 boxes.", " 34 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0455", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "33", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold half the stock regardless of the percentage", "correct", "sold only a tenth of the stock", "counted the loose shirts as a box"], "solution_steps": ["sold: 55% of 440 = 242", "left over: 440 - 242 = 198", "full boxes: 198 / 6 = 33 (remainder 0)"], "option_values": [36, 33, 66, 34], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 456, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Chen baked 108 buns. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Chen baked 108 buns. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "endings": [" 8 buns.", " 9 buns.", " 12 buns.", " 6 buns."], "source_id": "deeparithmark_v1_fractions_depth3_0456", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "12", "unit": "buns", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away a third twice", "gave away a half instead of a third", "correct", "split the given-away cookies too"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 6: 72 / 6 = 12"], "option_values": [8, 9, 12, 6], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 457, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 19 pallets.", " 21 pallets.", " 22 pallets.", " 33 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0457", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "21", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "correct", "counted the loose sacks as a pallet", "forgot Monday"], "solution_steps": ["Monday: 30% of 600 = 180", "left after Monday: 600 - 180 = 420", "Tuesday: 25% of 420 = 105", "left after Tuesday: 420 - 105 = 315", "full pallets: 315 / 15 = 21"], "option_values": [19, 21, 22, 33], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 458, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:28 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:28 a.m. for 80 minutes. The booking ended at", "endings": [" 8:48 a.m.", " 9:48 a.m.", " 9:33 a.m.", " 11:18 a.m."], "source_id": "deeparithmark_v1_time_depth2_0458", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "588", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "correct", "stopped a quarter of an hour early", "ran an hour and a half long"], "solution_steps": ["convert the start: 508 minutes after midnight", "add the duration: 508 + 80 = 588 minutes"], "option_values": [528, 588, 573, 678], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 459, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:47 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:47 a.m. for 50 minutes. The booking ended at", "endings": [" 7:37 a.m.", " 7:22 a.m.", " 8:07 a.m.", " 8:37 a.m."], "source_id": "deeparithmark_v1_time_depth2_0459", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "457", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "stopped a quarter of an hour early", "ran half an hour long", "added an extra hour"], "solution_steps": ["convert the start: 407 minutes after midnight", "add the duration: 407 + 50 = 457 minutes"], "option_values": [457, 442, 487, 517], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 460, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 48 pallets.", " 29 pallets.", " 46 pallets.", " 44 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0460", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "48", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "took both percentages twice", "took both percentages off the original stock", "stacked on larger pallets"], "solution_steps": ["Monday: 10% of 800 = 80", "left after Monday: 800 - 80 = 720", "Tuesday: 20% of 720 = 144", "left after Tuesday: 720 - 144 = 576", "full pallets: 576 / 12 = 48"], "option_values": [48, 29, 46, 44], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 461, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:56 a.m.. The first session lasted 45 minutes, the break lasted 10 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:56 a.m.. The first session lasted 45 minutes, the break lasted 10 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 8:31 a.m.", " 8:41 a.m.", " 7:51 a.m.", " 9:21 a.m."], "source_id": "deeparithmark_v1_time_depth3_0461", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "521", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the break", "correct", "forgot the second session", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 416 + 45 = 461 minutes after midnight", "after the break: 461 + 10 = 471", "after the second session: 471 + 50 = 521"], "option_values": [511, 521, 471, 561], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 462, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Hana baked 90 biscuits. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Hana baked 90 biscuits. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "endings": [" 7 biscuits.", " 18 biscuits.", " 15 biscuits.", " 12 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0462", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "12", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away a half and split among one more child", "split all the cookies, not the rest", "split all the cookies among one more child", "correct"], "solution_steps": ["one third given away: 90 / 3 = 30", "rest kept: 90 - 30 = 60", "split among 5: 60 / 5 = 12"], "option_values": [7, 18, 15, 12], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 463, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $0.45 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $0.45 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.47.", " $1.05.", " $1.22.", " $1.52."], "source_id": "deeparithmark_v1_money_depth4_0463", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "147", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "split among two more people", "split among one more person", "swapped the two unit prices"], "solution_steps": ["markers: 7 x 45 = 315", "erasers: 6 x 70 = 420", "total cost: 315 + 420 = 735", "split between 5 people: 735 / 5 = 147"], "option_values": [147, 105, 122, 152], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 464, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.50 was split between two teams in the ratio 5:2 after a $4.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.50 was split between two teams in the ratio 5:2 after a $4.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.18.", " $0.37.", " $0.47.", " $0.25."], "source_id": "deeparithmark_v1_ratio_depth5_0464", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "47", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "split among one more player", "correct", "gave the larger share to the smaller ratio"], "solution_steps": ["after the fee: 750 - 400 = 350", "one ratio part: 350 / 7 = 50", "larger share: 5 x 50 = 250", "after charity: 250 - 62 = 188", "per player: 188 / 4 = 47"], "option_values": [18, 37, 47, 25], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 465, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $3.80 was split between two teams in the ratio 4:2 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $3.80 was split between two teams in the ratio 4:2 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.15.", " $0.18.", " $0.24.", " $0.12."], "source_id": "deeparithmark_v1_ratio_depth5_0465", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "24", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["gave the larger share to the smaller ratio", "gave twice the share away to charity", "correct", "swapped the ratio parts"], "solution_steps": ["after the fee: 380 - 200 = 180", "one ratio part: 180 / 6 = 30", "larger share: 4 x 30 = 120", "after charity: 120 - 24 = 96", "per player: 96 / 4 = 24"], "option_values": [15, 18, 24, 12], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 466, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $8.20 was split between two teams in the ratio 5:2 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $8.20 was split between two teams in the ratio 5:2 after a $4.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.45.", " $0.42.", " $0.54.", " $0.24."], "source_id": "deeparithmark_v1_ratio_depth5_0466", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "54", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "forgot the fee and the charity cut", "correct", "gave the larger share to the smaller ratio"], "solution_steps": ["after the fee: 820 - 400 = 420", "one ratio part: 420 / 7 = 60", "larger share: 5 x 60 = 300", "after charity: 300 - 30 = 270", "per player: 270 / 5 = 54"], "option_values": [45, 42, 54, 24], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 467, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $16.00. A 10% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $16.00. A 10% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $3.15.", " $3.94.", " $3.48.", " $3.74."], "source_id": "deeparithmark_v1_percent_money_depth4_0467", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "394", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["split the total among one more person", "correct", "applied the discount twice", "used the coupon twice"], "solution_steps": ["discount: 1600 - 160 = 1440", "tax on the discounted price: 1440 + 216 = 1656", "coupon: 1656 - 80 = 1576", "split 4 ways: 1576 / 4 = 394"], "option_values": [315, 394, 348, 374], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 468, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $8.60 was split between two teams in the ratio 4:2 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $8.60 was split between two teams in the ratio 4:2 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.48.", " $0.38.", " $0.72.", " $1.43."], "source_id": "deeparithmark_v1_ratio_depth5_0468", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "48", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "split among one more player", "took the charity cut off the whole prize", "forgot to deduct the fee"], "solution_steps": ["after the fee: 860 - 500 = 360", "one ratio part: 360 / 6 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 48 = 192", "per player: 192 / 4 = 48"], "option_values": [48, 38, 72, 143], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 469, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $14.00 an hour, and then 3 hours at $17.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $14.00 an hour, and then 3 hours at $17.00 an hour. He earned", "endings": [" $107.00.", " $49.00.", " $56.00.", " $51.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0469", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "10700", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["correct", "paid the slower rate for the whole day", "forgot the second stretch", "forgot the first stretch"], "solution_steps": ["first stretch: 4 x 1400 = 5600", "second stretch: 3 x 1700 = 5100", "total pay: 5600 + 5100 = 10700"], "option_values": [10700, 4900, 5600, 5100], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 470, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:05 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:05 a.m. for 80 minutes. The booking ended at", "endings": [" 7:25 a.m.", " 4:45 a.m.", " 8:25 a.m.", " 8:55 a.m."], "source_id": "deeparithmark_v1_time_depth2_0470", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "445", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "subtracted the duration instead of adding it", "added an extra hour", "ran an hour and a half long"], "solution_steps": ["convert the start: 365 minutes after midnight", "add the duration: 365 + 80 = 445 minutes"], "option_values": [445, 285, 505, 535], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 471, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 840 units. A delivery added 240, then 250 units were shipped out, and 12 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 840 units. A delivery added 240, then 250 units were shipped out, and 12 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 72 crates.", " 102 crates.", " 28 crates.", " 133 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0471", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "102", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the delivery", "correct", "packed the arriving units only", "forgot the shipping"], "solution_steps": ["after delivery: 840 + 240 = 1080", "after shipping: 1080 - 250 = 830", "good units: 830 - 12 = 818", "full crates: 818 / 8 = 102 (remainder 2)"], "option_values": [72, 102, 28, 133], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 472, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $12.50 an hour, and then 2 hours at $15.50 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $12.50 an hour, and then 2 hours at $15.50 an hour. He earned", "endings": [" $75.00.", " $53.00.", " $81.00.", " $31.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0472", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "8100", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid every hour at the first rate", "worked one hour less in each stretch", "correct", "forgot the first stretch"], "solution_steps": ["first stretch: 4 x 1250 = 5000", "second stretch: 2 x 1550 = 3100", "total pay: 5000 + 3100 = 8100"], "option_values": [7500, 5300, 8100, 3100], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 473, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:17 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:17 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 11:07 a.m.", " 10:37 a.m.", " 11:22 a.m.", " 10:22 a.m."], "source_id": "deeparithmark_v1_time_depth3_0473", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "622", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["finished half an hour late on top of the break", "counted the break twice", "counted the first session twice", "correct"], "solution_steps": ["after the first session: 497 + 60 = 557 minutes after midnight", "after the break: 557 + 15 = 572", "after the second session: 572 + 50 = 622"], "option_values": [667, 637, 682, 622], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 474, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 25% discount came off it, then 5% tax was added to the discounted price, and a $1.20 coupon was applied last. 3 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 25% discount came off it, then 5% tax was added to the discounted price, and a $1.20 coupon was applied last. 3 people split the final cost equally. Each paid", "endings": [" $27.15.", " $9.45.", " $13.57.", " $9.05."], "source_id": "deeparithmark_v1_percent_money_depth4_0474", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "905", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["did not split the cost at all", "forgot the coupon", "split the total among one fewer person", "correct"], "solution_steps": ["discount: 3600 - 900 = 2700", "tax on the discounted price: 2700 + 135 = 2835", "coupon: 2835 - 120 = 2715", "split 3 ways: 2715 / 3 = 905"], "option_values": [2715, 945, 1357, 905], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 475, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $2.51.", " $2.99.", " $2.75.", " $2.86."], "source_id": "deeparithmark_v1_money_percent_depth2_0475", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "251", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "added the discount instead of removing it", "forgot the discount", "charged the handling fee twice"], "solution_steps": ["take 10% of 240 off: 240 - 24 = 216", "add the 35-cent fee: 216 + 35 = 251"], "option_values": [251, 299, 275, 286], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 476, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 12 litres per minute for 6 minutes, then 5 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 12 litres per minute for 6 minutes, then 5 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "endings": [" 257 litres.", " 247 litres.", " 302 litres.", " 365 litres."], "source_id": "deeparithmark_v1_rate_depth4_0476", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "302", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the second fill", "drained twice", "correct", "used the first rate for both stages"], "solution_steps": ["first fill: 12 x 6 = 72 litres", "second fill: 5 x 9 = 45 litres", "before draining: 240 + 72 + 45 = 357", "after draining: 357 - 55 = 302"], "option_values": [257, 247, 302, 365], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 477, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 5 metres and 12 centimetres long. A worker cut off 75 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 5 metres and 12 centimetres long. A worker cut off 75 centimetres. The board left was", "endings": [" 687 centimetres.", " 447 centimetres.", " 437 centimetres.", " 449 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0477", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "437", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["added the cut and a whole metre", "stopped ten centimetres short of the cut", "correct", "counted the extra centimetres twice"], "solution_steps": ["convert metres: 5 x 100 = 500 cm", "add the extra centimetres: 500 + 12 = 512 cm", "subtract the cut: 512 - 75 = 437 cm"], "option_values": [687, 447, 437, 449], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 478, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $14.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $14.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $550.40.", " $449.60.", " $526.40.", " $825.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0478", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "55040", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "forgot the overtime", "forgot the bonus", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 38 x 1400 = 53200", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 6 x 2100 = 12600", "gross with bonus: 53200 + 12600 + 3000 = 68800", "take-home: 68800 - 13760 = 55040"], "option_values": [55040, 44960, 52640, 82560], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 479, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 260, then 250 units were shipped out, and 32 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 260, then 250 units were shipped out, and 32 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 57 crates.", " 92 crates.", " 61 crates.", " 59 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0479", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "92", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped twice and damaged twice", "correct", "shipped out twice", "forgot the delivery"], "solution_steps": ["after delivery: 760 + 260 = 1020", "after shipping: 1020 - 250 = 770", "good units: 770 - 32 = 738", "full crates: 738 / 8 = 92 (remainder 2)"], "option_values": [57, 92, 61, 59], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 480, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 60 km at 20 km/h, rested 12 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 60 km at 20 km/h, rested 12 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "endings": [" 237 minutes.", " 912 minutes.", " 384 minutes.", " 372 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0480", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "372", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["used the cycling speed for both legs", "used the walking speed for both legs", "counted the rest twice", "correct"], "solution_steps": ["cycling time: 60 x 60 / 20 = 180 minutes", "walking time: 60 x 15 / 5 = 180 minutes", "add the rest: 180 + 12 + 180 = 372 minutes"], "option_values": [237, 912, 384, 372], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 481, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:56 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:56 a.m. for 80 minutes. The booking ended at", "endings": [" 7:16 a.m.", " 8:16 a.m.", " 9:16 a.m.", " 8:46 a.m."], "source_id": "deeparithmark_v1_time_depth2_0481", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "496", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added the minutes without the hours", "correct", "added an extra hour", "ran half an hour long"], "solution_steps": ["convert the start: 416 minutes after midnight", "add the duration: 416 + 80 = 496 minutes"], "option_values": [436, 496, 556, 526], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 482, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $4.70.", " $5.50.", " $16.40.", " $4.10."], "source_id": "deeparithmark_v1_percent_money_depth4_0482", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "410", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["added the coupon instead of subtracting it", "forgot the discount and the coupon", "did not split the cost at all", "correct"], "solution_steps": ["discount: 2000 - 400 = 1600", "tax on the discounted price: 1600 + 160 = 1760", "coupon: 1760 - 120 = 1640", "split 4 ways: 1640 / 4 = 410"], "option_values": [470, 550, 1640, 410], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 483, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:02 a.m.. The first session lasted 50 minutes, the break lasted 25 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:02 a.m.. The first session lasted 50 minutes, the break lasted 25 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 9:17 a.m.", " 9:42 a.m.", " 8:07 a.m.", " 10:07 a.m."], "source_id": "deeparithmark_v1_time_depth3_0483", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "607", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the second session", "forgot the break", "dropped the hour carry", "correct"], "solution_steps": ["after the first session: 482 + 50 = 532 minutes after midnight", "after the break: 532 + 25 = 557", "after the second session: 557 + 50 = 607"], "option_values": [557, 582, 487, 607], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 484, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $8.20 was split between two teams in the ratio 5:1 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $8.20 was split between two teams in the ratio 5:1 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.43.", " $0.35.", " $0.42.", " $0.52."], "source_id": "deeparithmark_v1_ratio_depth5_0484", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "35", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the charity cut", "correct", "took the charity cut off the whole prize", "split the whole prize among one team"], "solution_steps": ["after the fee: 820 - 400 = 420", "one ratio part: 420 / 6 = 70", "larger share: 5 x 70 = 350", "after charity: 350 - 70 = 280", "per player: 280 / 8 = 35"], "option_values": [43, 35, 42, 52], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 485, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:14 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:14 a.m. for 65 minutes. The booking ended at", "endings": [" 6:19 a.m.", " 7:19 a.m.", " 7:04 a.m.", " 5:09 a.m."], "source_id": "deeparithmark_v1_time_depth2_0485", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "439", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "correct", "stopped a quarter of an hour early", "subtracted the duration instead of adding it"], "solution_steps": ["convert the start: 374 minutes after midnight", "add the duration: 374 + 65 = 439 minutes"], "option_values": [379, 439, 424, 309], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 486, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 56 pallets.", " 74 pallets.", " 57 pallets.", " 88 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0486", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "56", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "forgot Tuesday", "counted the loose sacks as a pallet", "forgot Monday"], "solution_steps": ["Monday: 30% of 1600 = 480", "left after Monday: 1600 - 480 = 1120", "Tuesday: 25% of 1120 = 280", "left after Tuesday: 1120 - 280 = 840", "full pallets: 840 / 15 = 56"], "option_values": [56, 74, 57, 88], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 487, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Ben baked 72 cookies. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Ben baked 72 cookies. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 14 cookies.", " 48 cookies.", " 12 cookies.", " 18 cookies."], "source_id": "deeparithmark_v1_fractions_depth3_0487", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "12", "unit": "cookies", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split all the cookies among one more child", "stopped after giving the third away", "correct", "split all the cookies, not the rest"], "solution_steps": ["one third given away: 72 / 3 = 24", "rest kept: 72 - 24 = 48", "split among 4: 48 / 4 = 12"], "option_values": [14, 48, 12, 18], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 488, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 420 units. A delivery added 260, then 140 units were shipped out, and 18 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 420 units. A delivery added 260, then 140 units were shipped out, and 18 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 31 crates.", " 21 crates.", " 45 crates.", " 43 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0488", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "43", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped out twice", "forgot the delivery", "forgot the damaged units", "correct"], "solution_steps": ["after delivery: 420 + 260 = 680", "after shipping: 680 - 140 = 540", "good units: 540 - 18 = 522", "full crates: 522 / 12 = 43 (remainder 6)"], "option_values": [31, 21, 45, 43], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 489, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:33 a.m.. The first session lasted 55 minutes, the break lasted 15 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:33 a.m.. The first session lasted 55 minutes, the break lasted 15 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "endings": [" 6:28 a.m.", " 7:43 a.m.", " 9:13 a.m.", " 8:28 a.m."], "source_id": "deeparithmark_v1_time_depth3_0489", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "508", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["dropped the hour carry", "forgot the second session", "finished half an hour late on top of the break", "correct"], "solution_steps": ["after the first session: 393 + 55 = 448 minutes after midnight", "after the break: 448 + 15 = 463", "after the second session: 463 + 45 = 508"], "option_values": [388, 463, 553, 508], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 490, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.40 was split between two teams in the ratio 3:1 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.40 was split between two teams in the ratio 3:1 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.06.", " $0.22.", " $0.72.", " $0.18."], "source_id": "deeparithmark_v1_ratio_depth5_0490", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "18", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "forgot the charity cut", "divided between the teams instead of the players", "correct"], "solution_steps": ["after the fee: 640 - 400 = 240", "one ratio part: 240 / 4 = 60", "larger share: 3 x 60 = 180", "after charity: 180 - 36 = 144", "per player: 144 / 8 = 18"], "option_values": [6, 22, 72, 18], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 491, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 9 litres per minute for 6 minutes, then 3 litres per minute for 9 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 9 litres per minute for 6 minutes, then 3 litres per minute for 9 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 221 litres.", " 194 litres.", " 301 litres.", " 261 litres."], "source_id": "deeparithmark_v1_rate_depth4_0491", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "221", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "forgot the second fill", "added the drain instead of removing it", "forgot the drain"], "solution_steps": ["first fill: 9 x 6 = 54 litres", "second fill: 3 x 9 = 27 litres", "before draining: 180 + 54 + 27 = 261", "after draining: 261 - 40 = 221"], "option_values": [221, 194, 301, 261], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 492, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $7.62.", " $7.77.", " $7.92.", " $31.08."], "source_id": "deeparithmark_v1_percent_money_depth4_0492", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "777", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["used the coupon twice", "correct", "forgot the coupon", "did not split the cost at all"], "solution_steps": ["discount: 3600 - 720 = 2880", "tax on the discounted price: 2880 + 288 = 3168", "coupon: 3168 - 60 = 3108", "split 4 ways: 3108 / 4 = 777"], "option_values": [762, 777, 792, 3108], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 493, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:03 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:03 a.m. for 95 minutes. The booking ended at", "endings": [" 5:28 a.m.", " 8:38 a.m.", " 7:38 a.m.", " 8:23 a.m."], "source_id": "deeparithmark_v1_time_depth2_0493", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "518", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "correct", "dropped the hour carry", "stopped a quarter of an hour early"], "solution_steps": ["convert the start: 423 minutes after midnight", "add the duration: 423 + 95 = 518 minutes"], "option_values": [328, 518, 458, 503], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 494, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.60 was split between two teams in the ratio 4:2 after a $2.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.60 was split between two teams in the ratio 4:2 after a $2.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.24.", " $0.46.", " $0.27.", " $0.45."], "source_id": "deeparithmark_v1_ratio_depth5_0494", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "27", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "forgot to deduct the fee", "correct", "split the whole prize among one team"], "solution_steps": ["after the fee: 560 - 200 = 360", "one ratio part: 360 / 6 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 24 = 216", "per player: 216 / 8 = 27"], "option_values": [24, 46, 27, 45], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 495, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:08 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:08 a.m. for 80 minutes. The booking ended at", "endings": [" 9:58 a.m.", " 10:28 a.m.", " 10:58 a.m.", " 9:28 a.m."], "source_id": "deeparithmark_v1_time_depth2_0495", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "568", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran half an hour long", "added an extra hour", "ran an hour and a half long", "correct"], "solution_steps": ["convert the start: 488 minutes after midnight", "add the duration: 488 + 80 = 568 minutes"], "option_values": [598, 628, 658, 568], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 496, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 10% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 10% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 58 pallets.", " 63 pallets.", " 74 pallets.", " 64 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0496", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "63", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "correct", "forgot Monday", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 10% of 1400 = 140", "left after Monday: 1400 - 140 = 1260", "Tuesday: 40% of 1260 = 504", "left after Tuesday: 1260 - 504 = 756", "full pallets: 756 / 12 = 63"], "option_values": [58, 63, 74, 64], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 497, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:03 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:03 a.m. for 110 minutes. The booking ended at", "endings": [" 4:13 a.m.", " 7:53 a.m.", " 8:23 a.m.", " 9:23 a.m."], "source_id": "deeparithmark_v1_time_depth2_0497", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "473", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "correct", "ran half an hour long", "ran an hour and a half long"], "solution_steps": ["convert the start: 363 minutes after midnight", "add the duration: 363 + 110 = 473 minutes"], "option_values": [253, 473, 503, 563], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 498, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:17 a.m.. The first session lasted 60 minutes, the break lasted 25 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:17 a.m.. The first session lasted 60 minutes, the break lasted 25 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "endings": [" 8:17 a.m.", " 6:17 a.m.", " 8:42 a.m.", " 9:12 a.m."], "source_id": "deeparithmark_v1_time_depth3_0498", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "497", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["correct", "dropped the hour carry", "counted the break twice", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 377 + 60 = 437 minutes after midnight", "after the break: 437 + 25 = 462", "after the second session: 462 + 35 = 497"], "option_values": [497, 377, 522, 552], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 499, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $604.80.", " $680.40.", " $662.40.", " $831.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0499", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "68040", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "correct", "forgot the bonus", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 40 x 1600 = 64000", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 4 x 2400 = 9600", "gross with bonus: 64000 + 9600 + 2000 = 75600", "take-home: 75600 - 7560 = 68040"], "option_values": [60480, 68040, 66240, 83160], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 500, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:40 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:40 a.m. for 80 minutes. The booking ended at", "endings": [" 5:20 a.m.", " 6:00 a.m.", " 9:00 a.m.", " 8:00 a.m."], "source_id": "deeparithmark_v1_time_depth2_0500", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "480", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "dropped the hour carry", "added an extra hour", "correct"], "solution_steps": ["convert the start: 400 minutes after midnight", "add the duration: 400 + 80 = 480 minutes"], "option_values": [320, 360, 540, 480], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 501, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 20% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 20% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 38 pallets.", " 32 pallets.", " 39 pallets.", " 64 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0501", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "38", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "took both percentages off the original stock", "counted the loose sacks as a pallet", "forgot Tuesday"], "solution_steps": ["Monday: 20% of 800 = 160", "left after Monday: 800 - 160 = 640", "Tuesday: 40% of 640 = 256", "left after Tuesday: 640 - 256 = 384", "full pallets: 384 / 10 = 38"], "option_values": [38, 32, 39, 64], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 502, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $9.20 was split between two teams in the ratio 4:2 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $9.20 was split between two teams in the ratio 4:2 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.52.", " $0.63.", " $0.35.", " $0.94."], "source_id": "deeparithmark_v1_ratio_depth5_0502", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "63", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the fee and the charity cut", "correct", "gave the larger share to the smaller ratio", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 920 - 500 = 420", "one ratio part: 420 / 6 = 70", "larger share: 4 x 70 = 280", "after charity: 280 - 28 = 252", "per player: 252 / 4 = 63"], "option_values": [52, 63, 35, 94], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 503, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 700 units. A delivery added 310, then 90 units were shipped out, and 32 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 700 units. A delivery added 310, then 90 units were shipped out, and 32 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 112 crates.", " 111 crates.", " 115 crates.", " 122 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0503", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "111", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["counted the loose units as a crate", "correct", "forgot the damaged units", "forgot the shipping"], "solution_steps": ["after delivery: 700 + 310 = 1010", "after shipping: 1010 - 90 = 920", "good units: 920 - 32 = 888", "full crates: 888 / 8 = 111 (remainder 0)"], "option_values": [112, 111, 115, 122], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 504, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $16.00. A 20% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $16.00. A 20% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $6.96.", " $5.12.", " $4.64.", " $7.36."], "source_id": "deeparithmark_v1_percent_money_depth4_0504", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "696", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "applied the discount twice", "split the total among one more person", "forgot the coupon"], "solution_steps": ["discount: 1600 - 320 = 1280", "tax on the discounted price: 1280 + 192 = 1472", "coupon: 1472 - 80 = 1392", "split 2 ways: 1392 / 2 = 696"], "option_values": [696, 512, 464, 736], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 505, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 560 units. A delivery added 240, then 170 units were shipped out, and 18 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 560 units. A delivery added 240, then 170 units were shipped out, and 18 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 31 crates.", " 51 crates.", " 18 crates.", " 36 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0505", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "51", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the delivery", "correct", "packed the arriving units only", "shipped out twice"], "solution_steps": ["after delivery: 560 + 240 = 800", "after shipping: 800 - 170 = 630", "good units: 630 - 18 = 612", "full crates: 612 / 12 = 51 (remainder 0)"], "option_values": [31, 51, 18, 36], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 506, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:06 a.m.. The first session lasted 45 minutes, the break lasted 25 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:06 a.m.. The first session lasted 45 minutes, the break lasted 25 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 9:31 a.m.", " 9:51 a.m.", " 9:06 a.m.", " 10:01 a.m."], "source_id": "deeparithmark_v1_time_depth3_0506", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "546", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["counted the break twice", "counted the first session twice", "correct", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 426 + 45 = 471 minutes after midnight", "after the break: 471 + 25 = 496", "after the second session: 496 + 50 = 546"], "option_values": [571, 591, 546, 601], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 507, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Amara baked 108 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Amara baked 108 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 21 muffins.", " 72 muffins.", " 27 muffins.", " 18 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0507", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "18", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split all the cookies among one more child", "stopped after giving the third away", "split all the cookies, not the rest", "correct"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 4: 72 / 4 = 18"], "option_values": [21, 72, 27, 18], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 508, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 36 km at 18 km/h, rested 12 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 36 km at 18 km/h, rested 12 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "endings": [" 252 minutes.", " 132 minutes.", " 492 minutes.", " 264 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0508", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "252", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["correct", "forgot the walking leg", "used the walking speed for both legs", "counted the rest twice"], "solution_steps": ["cycling time: 60 x 36 / 18 = 120 minutes", "walking time: 60 x 12 / 6 = 120 minutes", "add the rest: 120 + 12 + 120 = 252 minutes"], "option_values": [252, 132, 492, 264], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 509, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $3.87.", " $3.42.", " $3.49.", " $3.83."], "source_id": "deeparithmark_v1_money_percent_depth2_0509", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "387", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "forgot the fee", "took the percentage off twice", "took the discount off the fee as well"], "solution_steps": ["take 10% of 380 off: 380 - 38 = 342", "add the 45-cent fee: 342 + 45 = 387"], "option_values": [387, 342, 349, 383], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 510, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:13 a.m.. The first session lasted 60 minutes, the break lasted 20 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:13 a.m.. The first session lasted 60 minutes, the break lasted 20 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "endings": [" 9:08 a.m.", " 11:08 a.m.", " 10:08 a.m.", " 10:28 a.m."], "source_id": "deeparithmark_v1_time_depth3_0510", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "608", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["added the minutes but not the hours", "counted the first session twice", "correct", "counted the break twice"], "solution_steps": ["after the first session: 493 + 60 = 553 minutes after midnight", "after the break: 553 + 20 = 573", "after the second session: 573 + 35 = 608"], "option_values": [548, 668, 608, 628], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 511, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 3 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 3 people split the final cost equally. Each paid", "endings": [" $18.60.", " $6.60.", " $6.20.", " $9.30."], "source_id": "deeparithmark_v1_percent_money_depth4_0511", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "620", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["did not split the cost at all", "forgot the coupon", "correct", "split the total among one fewer person"], "solution_steps": ["discount: 2000 - 200 = 1800", "tax on the discounted price: 1800 + 180 = 1980", "coupon: 1980 - 120 = 1860", "split 3 ways: 1860 / 3 = 620"], "option_values": [1860, 660, 620, 930], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 512, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $8.00 was split between two teams in the ratio 4:1 after a $5.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $8.00 was split between two teams in the ratio 4:1 after a $5.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.37.", " $0.15.", " $0.45.", " $0.56."], "source_id": "deeparithmark_v1_ratio_depth5_0512", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "45", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the fee and the charity cut", "gave the larger share to the smaller ratio", "correct", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 800 - 500 = 300", "one ratio part: 300 / 5 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 60 = 180", "per player: 180 / 4 = 45"], "option_values": [37, 15, 45, 56], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 513, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 36 km at 12 km/h, rested 12 minutes, then walked 18 km at 6 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 36 km at 12 km/h, rested 12 minutes, then walked 18 km at 6 km/h. Her total time, in minutes, was", "endings": [" 192 minutes.", " 372 minutes.", " 552 minutes.", " 384 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0513", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "372", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "correct", "used the walking speed for both legs", "counted the rest twice"], "solution_steps": ["cycling time: 60 x 36 / 12 = 180 minutes", "walking time: 60 x 18 / 6 = 180 minutes", "add the rest: 180 + 12 + 180 = 372 minutes"], "option_values": [192, 372, 552, 384], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 514, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 480 shirts. It sold 25% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 480 shirts. It sold 25% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "endings": [" 20 boxes.", " 30 boxes.", " 10 boxes.", " 40 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0514", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "30", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold twice as many", "correct", "packed the sold shirts", "packed the whole stock, not the rest"], "solution_steps": ["sold: 25% of 480 = 120", "left over: 480 - 120 = 360", "full boxes: 360 / 12 = 30 (remainder 0)"], "option_values": [20, 30, 10, 40], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 515, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:35 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:35 a.m. for 65 minutes. The booking ended at", "endings": [" 5:30 a.m.", " 8:40 a.m.", " 7:40 a.m.", " 9:10 a.m."], "source_id": "deeparithmark_v1_time_depth2_0515", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "460", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "added an extra hour", "correct", "ran an hour and a half long"], "solution_steps": ["convert the start: 395 minutes after midnight", "add the duration: 395 + 65 = 460 minutes"], "option_values": [330, 520, 460, 550], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 516, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $1.20 each and 3 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $1.20 each and 3 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $2.88.", " $2.33.", " $2.31.", " $2.68."], "source_id": "deeparithmark_v1_money_depth4_0516", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "231", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split only between the friends", "added the unit prices instead of multiplying", "correct", "bought one extra of each item"], "solution_steps": ["markers: 8 x 120 = 960", "erasers: 3 x 65 = 195", "total cost: 960 + 195 = 1155", "split between 5 people: 1155 / 5 = 231"], "option_values": [288, 233, 231, 268], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 517, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $0.75 each and 3 erasers at $0.70 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $0.75 each and 3 erasers at $0.70 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $1.95.", " $1.46.", " $1.91.", " $1.25."], "source_id": "deeparithmark_v1_money_depth4_0517", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "195", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "split among one more person", "swapped the two unit prices", "forgot the erasers"], "solution_steps": ["markers: 5 x 75 = 375", "erasers: 3 x 70 = 210", "total cost: 375 + 210 = 585", "split between 3 people: 585 / 3 = 195"], "option_values": [195, 146, 191, 125], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 518, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $1.20 each and 3 erasers at $0.30 each. She split the total cost equally between herself and 5 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $1.20 each and 3 erasers at $0.30 each. She split the total cost equally between herself and 5 friends. Each person paid", "endings": [" $1.55.", " $1.16.", " $1.32.", " $1.56."], "source_id": "deeparithmark_v1_money_depth4_0518", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "155", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "split among two more people", "split among one more person", "added the unit prices instead of multiplying"], "solution_steps": ["markers: 7 x 120 = 840", "erasers: 3 x 30 = 90", "total cost: 840 + 90 = 930", "split between 6 people: 930 / 6 = 155"], "option_values": [155, 116, 132, 156], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 519, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 420 units. A delivery added 130, then 170 units were shipped out, and 40 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 420 units. A delivery added 130, then 170 units were shipped out, and 40 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "endings": [" 22 crates.", " 25 crates.", " 36 crates.", " 24 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0519", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "24", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed into larger crates", "counted the loose units as a crate", "forgot the shipping", "correct"], "solution_steps": ["after delivery: 420 + 130 = 550", "after shipping: 550 - 170 = 380", "good units: 380 - 40 = 340", "full crates: 340 / 14 = 24 (remainder 4)"], "option_values": [22, 25, 36, 24], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 520, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:52 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:52 a.m. for 50 minutes. The booking ended at", "endings": [" 8:27 a.m.", " 7:02 a.m.", " 8:42 a.m.", " 7:42 a.m."], "source_id": "deeparithmark_v1_time_depth2_0520", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "522", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "subtracted the duration instead of adding it", "correct", "dropped the hour carry"], "solution_steps": ["convert the start: 472 minutes after midnight", "add the duration: 472 + 50 = 522 minutes"], "option_values": [507, 422, 522, 462], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 521, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $6.57.", " $5.89.", " $6.12.", " $6.53."], "source_id": "deeparithmark_v1_money_percent_depth2_0521", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "657", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the percentage off twice", "forgot the fee", "took the discount off the fee as well"], "solution_steps": ["take 10% of 680 off: 680 - 68 = 612", "add the 45-cent fee: 612 + 45 = 657"], "option_values": [657, 589, 612, 653], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 522, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $20.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $20.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $570.00.", " $720.00.", " $760.00.", " $1140.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0522", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "76000", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "forgot the bonus", "correct", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 36 x 2000 = 72000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 6 x 3000 = 18000", "gross with bonus: 72000 + 18000 + 5000 = 95000", "take-home: 95000 - 19000 = 76000"], "option_values": [57000, 72000, 76000, 114000], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 523, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $561.00.", " $544.00.", " $442.00.", " $595.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0523", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "59500", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "paid overtime at the normal rate", "forgot the overtime", "correct"], "solution_steps": ["regular pay: 40 x 1200 = 48000", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 10 x 1800 = 18000", "gross with bonus: 48000 + 18000 + 4000 = 70000", "take-home: 70000 - 10500 = 59500"], "option_values": [56100, 54400, 44200, 59500], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 524, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:48 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:48 a.m. for 110 minutes. The booking ended at", "endings": [" 8:38 a.m.", " 9:38 a.m.", " 10:08 a.m.", " 9:08 a.m."], "source_id": "deeparithmark_v1_time_depth2_0524", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "518", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "added an extra hour", "ran an hour and a half long", "ran half an hour long"], "solution_steps": ["convert the start: 408 minutes after midnight", "add the duration: 408 + 110 = 518 minutes"], "option_values": [518, 578, 608, 548], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 525, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 25% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 25% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 33 pallets.", " 12 pallets.", " 37 pallets.", " 36 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0525", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "36", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "took both percentages twice", "counted the loose sacks as a pallet", "correct"], "solution_steps": ["Monday: 25% of 600 = 150", "left after Monday: 600 - 150 = 450", "Tuesday: 20% of 450 = 90", "left after Tuesday: 450 - 90 = 360", "full pallets: 360 / 10 = 36"], "option_values": [33, 12, 37, 36], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 526, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $14.00 an hour and 6 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $14.00 an hour and 6 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $597.60.", " $776.60.", " $673.20.", " $635.40."], "source_id": "deeparithmark_v1_money_rate_depth5_0526", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "63540", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at the normal rate", "added the tax instead of withholding it", "paid overtime at double rate", "correct"], "solution_steps": ["regular pay: 40 x 1400 = 56000", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 6 x 2100 = 12600", "gross with bonus: 56000 + 12600 + 2000 = 70600", "take-home: 70600 - 7060 = 63540"], "option_values": [59760, 77660, 67320, 63540], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 527, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 9 litres per minute for 10 minutes, then 5 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 9 litres per minute for 10 minutes, then 5 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 335 litres.", " 375 litres.", " 415 litres.", " 455 litres."], "source_id": "deeparithmark_v1_rate_depth4_0527", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "375", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "correct", "forgot the drain", "added the drain instead of removing it"], "solution_steps": ["first fill: 9 x 10 = 90 litres", "second fill: 5 x 5 = 25 litres", "before draining: 300 + 90 + 25 = 415", "after draining: 415 - 40 = 375"], "option_values": [335, 375, 415, 455], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 528, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $784.00.", " $656.00.", " $848.00.", " $832.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0528", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "84800", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at the normal rate", "forgot the overtime", "correct", "forgot the bonus"], "solution_steps": ["regular pay: 40 x 2000 = 80000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 8 x 3000 = 24000", "gross with bonus: 80000 + 24000 + 2000 = 106000", "take-home: 106000 - 21200 = 84800"], "option_values": [78400, 65600, 84800, 83200], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 529, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 6 metres and 47 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 6 metres and 47 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 502 centimetres.", " 792 centimetres.", " 692 centimetres.", " 602 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0529", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "602", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["cut a whole metre off as well", "added the cut and a whole metre", "added the cut instead of removing it", "correct"], "solution_steps": ["convert metres: 6 x 100 = 600 cm", "add the extra centimetres: 600 + 47 = 647 cm", "subtract the cut: 647 - 45 = 602 cm"], "option_values": [502, 792, 692, 602], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 530, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 560 units. A delivery added 240, then 140 units were shipped out, and 40 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 560 units. A delivery added 240, then 140 units were shipped out, and 40 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "endings": [" 45 crates.", " 44 crates.", " 47 crates.", " 54 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0530", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "44", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["counted the loose units as a crate", "correct", "forgot the damaged units", "forgot the shipping"], "solution_steps": ["after delivery: 560 + 240 = 800", "after shipping: 800 - 140 = 660", "good units: 660 - 40 = 620", "full crates: 620 / 14 = 44 (remainder 4)"], "option_values": [45, 44, 47, 54], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 531, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Vera baked 135 cookies. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Vera baked 135 cookies. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "endings": [" 18 cookies.", " 22 cookies.", " 27 cookies.", " 19 cookies."], "source_id": "deeparithmark_v1_fractions_depth3_0531", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "18", "unit": "cookies", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["correct", "split all the cookies among one more child", "split all the cookies, not the rest", "split all the cookies among two more children"], "solution_steps": ["one third given away: 135 / 3 = 45", "rest kept: 135 - 45 = 90", "split among 5: 90 / 5 = 18"], "option_values": [18, 22, 27, 19], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 532, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 60 km at 20 km/h, rested 12 minutes, then walked 8 km at 4 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 60 km at 20 km/h, rested 12 minutes, then walked 8 km at 4 km/h. Her total time, in minutes, was", "endings": [" 192 minutes.", " 216 minutes.", " 324 minutes.", " 312 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0532", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "312", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "used the cycling speed for both legs", "counted the rest twice", "correct"], "solution_steps": ["cycling time: 60 x 60 / 20 = 180 minutes", "walking time: 60 x 8 / 4 = 120 minutes", "add the rest: 180 + 12 + 120 = 312 minutes"], "option_values": [192, 216, 324, 312], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 533, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $12.00. A 30% discount came off it, then 5% tax was added to the discounted price, and a $0.40 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $12.00. A 30% discount came off it, then 5% tax was added to the discounted price, and a $0.40 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $2.32.", " $8.42.", " $4.21.", " $4.41."], "source_id": "deeparithmark_v1_percent_money_depth4_0533", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "421", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "split the total among one fewer person", "correct", "forgot the coupon"], "solution_steps": ["discount: 1200 - 360 = 840", "tax on the discounted price: 840 + 42 = 882", "coupon: 882 - 40 = 842", "split 2 ways: 842 / 2 = 421"], "option_values": [232, 842, 421, 441], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 534, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 4 markers at $0.45 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 4 markers at $0.45 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $1.05.", " $2.85.", " $0.97.", " $0.95."], "source_id": "deeparithmark_v1_money_depth4_0534", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "95", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["charged the marker price for everything", "did not split the total at all", "added the unit prices instead of multiplying", "correct"], "solution_steps": ["markers: 4 x 45 = 180", "erasers: 3 x 35 = 105", "total cost: 180 + 105 = 285", "split between 3 people: 285 / 3 = 95"], "option_values": [105, 285, 97, 95], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 535, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Ivo baked 108 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Ivo baked 108 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 13 biscuits.", " 12 biscuits.", " 18 biscuits.", " 21 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0535", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "18", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away a half instead of a third", "gave away a third twice", "correct", "split all the cookies among one more child"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 4: 72 / 4 = 18"], "option_values": [13, 12, 18, 21], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 536, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Hana baked 216 buns. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Hana baked 216 buns. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "endings": [" 12 buns.", " 24 buns.", " 16 buns.", " 27 buns."], "source_id": "deeparithmark_v1_fractions_depth3_0536", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "24", "unit": "buns", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split the given-away cookies too", "correct", "gave away a third twice", "split all the cookies among two more children"], "solution_steps": ["one third given away: 216 / 3 = 72", "rest kept: 216 - 72 = 144", "split among 6: 144 / 6 = 24"], "option_values": [12, 24, 16, 27], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 537, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $584.00.", " $544.00.", " $816.00.", " $592.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0537", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "54400", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed only the regular pay", "correct", "added the tax instead of withholding it", "paid overtime at double rate"], "solution_steps": ["regular pay: 40 x 1200 = 48000", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 10 x 1800 = 18000", "gross with bonus: 48000 + 18000 + 2000 = 68000", "take-home: 68000 - 13600 = 54400"], "option_values": [58400, 54400, 81600, 59200], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 538, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $4.50 was split between two teams in the ratio 2:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $4.50 was split between two teams in the ratio 2:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.10.", " $0.20.", " $0.40.", " $0.30."], "source_id": "deeparithmark_v1_ratio_depth5_0538", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "20", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "correct", "divided between the teams instead of the players", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 450 - 300 = 150", "one ratio part: 150 / 3 = 50", "larger share: 2 x 50 = 100", "after charity: 100 - 20 = 80", "per player: 80 / 4 = 20"], "option_values": [10, 20, 40, 30], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 539, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $12.50 an hour, and then 3 hours at $17.50 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $12.50 an hour, and then 3 hours at $17.50 an hour. He earned", "endings": [" $102.50.", " $52.50.", " $87.50.", " $72.50."], "source_id": "deeparithmark_v1_rate_pay_depth3_0539", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "10250", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["correct", "forgot the first stretch", "paid every hour at the first rate", "worked one hour less in each stretch"], "solution_steps": ["first stretch: 4 x 1250 = 5000", "second stretch: 3 x 1750 = 5250", "total pay: 5000 + 5250 = 10250"], "option_values": [10250, 5250, 8750, 7250], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 540, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $631.80.", " $604.80.", " $561.60.", " $545.40."], "source_id": "deeparithmark_v1_money_rate_depth5_0540", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "63180", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "forgot the bonus", "taxed twice", "forgot the overtime"], "solution_steps": ["regular pay: 36 x 1600 = 57600", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 4 x 2400 = 9600", "gross with bonus: 57600 + 9600 + 3000 = 70200", "take-home: 70200 - 7020 = 63180"], "option_values": [63180, 60480, 56160, 54540], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 541, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 3 metres and 47 centimetres long. A worker cut off 130 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 3 metres and 47 centimetres long. A worker cut off 130 centimetres. The board left was", "endings": [" 477 centimetres.", " 217 centimetres.", " 264 centimetres.", " 227 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0541", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "217", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["added the cut instead of removing it", "correct", "counted the extra centimetres twice", "stopped ten centimetres short of the cut"], "solution_steps": ["convert metres: 3 x 100 = 300 cm", "add the extra centimetres: 300 + 47 = 347 cm", "subtract the cut: 347 - 130 = 217 cm"], "option_values": [477, 217, 264, 227], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 542, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 10% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 10% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 126 pallets.", " 141 pallets.", " 108 pallets.", " 159 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0542", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "141", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "correct", "took both percentages twice", "forgot Monday"], "solution_steps": ["Monday: 10% of 1400 = 140", "left after Monday: 1400 - 140 = 1260", "Tuesday: 10% of 1260 = 126", "left after Tuesday: 1260 - 126 = 1134", "full pallets: 1134 / 8 = 141"], "option_values": [126, 141, 108, 159], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 543, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 12 litres per minute for 8 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 12 litres per minute for 8 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 281 litres.", " 351 litres.", " 255 litres.", " 326 litres."], "source_id": "deeparithmark_v1_rate_depth4_0543", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "351", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "correct", "forgot the first fill", "forgot the second fill"], "solution_steps": ["first fill: 12 x 8 = 96 litres", "second fill: 5 x 5 = 25 litres", "before draining: 300 + 96 + 25 = 421", "after draining: 421 - 70 = 351"], "option_values": [281, 351, 255, 326], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 544, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1000 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1000 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 58 pallets.", " 43 pallets.", " 44 pallets.", " 68 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0544", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "43", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["forgot Tuesday", "correct", "counted the loose sacks as a pallet", "forgot Monday"], "solution_steps": ["Monday: 30% of 1000 = 300", "left after Monday: 1000 - 300 = 700", "Tuesday: 25% of 700 = 175", "left after Tuesday: 700 - 175 = 525", "full pallets: 525 / 12 = 43"], "option_values": [58, 43, 44, 68], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 545, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $9.00 an hour, and then 2 hours at $14.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $9.00 an hour, and then 2 hours at $14.00 an hour. He earned", "endings": [" $82.00.", " $72.00.", " $73.00.", " $102.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0545", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "8200", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["correct", "paid every hour at the first rate", "worked one hour less in the first stretch", "swapped the two rates"], "solution_steps": ["first stretch: 6 x 900 = 5400", "second stretch: 2 x 1400 = 2800", "total pay: 5400 + 2800 = 8200"], "option_values": [8200, 7200, 7300, 10200], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 546, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.50 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.50 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.08.", " $0.25.", " $0.32.", " $0.88."], "source_id": "deeparithmark_v1_ratio_depth5_0546", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "32", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "forgot the fee and the charity cut", "correct", "forgot to deduct the fee"], "solution_steps": ["after the fee: 550 - 300 = 250", "one ratio part: 250 / 5 = 50", "larger share: 4 x 50 = 200", "after charity: 200 - 40 = 160", "per player: 160 / 5 = 32"], "option_values": [8, 25, 32, 88], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 547, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $0.75 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 3 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $0.75 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 3 friends. Each person paid", "endings": [" $1.60.", " $4.80.", " $1.50.", " $1.20."], "source_id": "deeparithmark_v1_money_depth4_0547", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "120", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split only between the friends", "did not split the total at all", "charged the marker price for everything", "correct"], "solution_steps": ["markers: 5 x 75 = 375", "erasers: 3 x 35 = 105", "total cost: 375 + 105 = 480", "split between 4 people: 480 / 4 = 120"], "option_values": [160, 480, 150, 120], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 548, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $9.65.", " $7.93.", " $8.18.", " $9.85."], "source_id": "deeparithmark_v1_money_percent_depth2_0548", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "793", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["read the percentage as a flat number of cents", "correct", "charged the handling fee twice", "forgot the discount"], "solution_steps": ["take 20% of 960 off: 960 - 192 = 768", "add the 25-cent fee: 768 + 25 = 793"], "option_values": [965, 793, 818, 985], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 549, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $0.75 each and 6 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $0.75 each and 6 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.52.", " $1.81.", " $1.83.", " $1.05."], "source_id": "deeparithmark_v1_money_depth4_0549", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "183", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among one more person", "swapped the two unit prices", "correct", "forgot the erasers"], "solution_steps": ["markers: 7 x 75 = 525", "erasers: 6 x 65 = 390", "total cost: 525 + 390 = 915", "split between 5 people: 915 / 5 = 183"], "option_values": [152, 181, 183, 105], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 550, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $6.01.", " $4.57.", " $5.96.", " $5.76."], "source_id": "deeparithmark_v1_money_percent_depth2_0550", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "601", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the percentage off twice", "took the discount off the fee as well", "forgot the fee"], "solution_steps": ["take 20% of 720 off: 720 - 144 = 576", "add the 25-cent fee: 576 + 25 = 601"], "option_values": [601, 457, 596, 576], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 551, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:04 a.m.. The first session lasted 55 minutes, the break lasted 10 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:04 a.m.. The first session lasted 55 minutes, the break lasted 10 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 10:44 a.m.", " 9:49 a.m.", " 9:59 a.m.", " 10:29 a.m."], "source_id": "deeparithmark_v1_time_depth3_0551", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "589", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["counted the first session twice", "correct", "counted the break twice", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 484 + 55 = 539 minutes after midnight", "after the break: 539 + 10 = 549", "after the second session: 549 + 40 = 589"], "option_values": [644, 589, 599, 629], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 552, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 400 shirts. It sold 25% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 400 shirts. It sold 25% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 25 boxes.", " 12 boxes.", " 45 boxes.", " 37 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0552", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "37", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold twice as many", "packed the sold shirts", "sold only a tenth of the stock", "correct"], "solution_steps": ["sold: 25% of 400 = 100", "left over: 400 - 100 = 300", "full boxes: 300 / 8 = 37 (remainder 4)"], "option_values": [25, 12, 45, 37], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 553, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 30% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 30% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 94 pallets.", " 105 pallets.", " 95 pallets.", " 139 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0553", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "94", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "forgot Tuesday", "counted the loose sacks as a pallet", "forgot Monday"], "solution_steps": ["Monday: 30% of 1200 = 360", "left after Monday: 1200 - 360 = 840", "Tuesday: 10% of 840 = 84", "left after Tuesday: 840 - 84 = 756", "full pallets: 756 / 8 = 94"], "option_values": [94, 105, 95, 139], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 554, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 9 litres per minute for 4 minutes, then 3 litres per minute for 7 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 9 litres per minute for 4 minutes, then 3 litres per minute for 7 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 182 litres.", " 177 litres.", " 107 litres.", " 247 litres."], "source_id": "deeparithmark_v1_rate_depth4_0554", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "107", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["added the rates and multiplied once", "forgot the drain", "correct", "added the drain instead of removing it"], "solution_steps": ["first fill: 9 x 4 = 36 litres", "second fill: 3 x 7 = 21 litres", "before draining: 120 + 36 + 21 = 177", "after draining: 177 - 70 = 107"], "option_values": [182, 177, 107, 247], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 555, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 10% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 10% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 67 pallets.", " 62 pallets.", " 65 pallets.", " 35 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0555", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "67", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "stacked on larger pallets", "took both percentages off the original stock", "took both percentages twice"], "solution_steps": ["Monday: 10% of 1200 = 120", "left after Monday: 1200 - 120 = 1080", "Tuesday: 25% of 1080 = 270", "left after Tuesday: 1080 - 270 = 810", "full pallets: 810 / 12 = 67"], "option_values": [67, 62, 65, 35], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 556, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:56 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:56 a.m. for 125 minutes. The booking ended at", "endings": [" 10:01 a.m.", " 11:01 a.m.", " 10:31 a.m.", " 11:31 a.m."], "source_id": "deeparithmark_v1_time_depth2_0556", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "601", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "added an extra hour", "ran half an hour long", "ran an hour and a half long"], "solution_steps": ["convert the start: 476 minutes after midnight", "add the duration: 476 + 125 = 601 minutes"], "option_values": [601, 661, 631, 691], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 557, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $4.33.", " $5.69.", " $5.44.", " $6.85."], "source_id": "deeparithmark_v1_money_percent_depth2_0557", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "569", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "correct", "forgot the fee", "read the percentage as a flat number of cents"], "solution_steps": ["take 20% of 680 off: 680 - 136 = 544", "add the 25-cent fee: 544 + 25 = 569"], "option_values": [433, 569, 544, 685], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 558, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 420 units. A delivery added 180, then 250 units were shipped out, and 12 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 420 units. A delivery added 180, then 250 units were shipped out, and 12 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 73 crates.", " 43 crates.", " 45 crates.", " 42 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0558", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "42", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the shipping", "forgot the damaged units", "added the damaged units", "correct"], "solution_steps": ["after delivery: 420 + 180 = 600", "after shipping: 600 - 250 = 350", "good units: 350 - 12 = 338", "full crates: 338 / 8 = 42 (remainder 2)"], "option_values": [73, 43, 45, 42], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 559, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $728.00.", " $952.00.", " $926.00.", " $884.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0559", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "88400", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "paid overtime at double rate", "taxed only the regular pay", "correct"], "solution_steps": ["regular pay: 38 x 2000 = 76000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 8 x 3000 = 24000", "gross with bonus: 76000 + 24000 + 4000 = 104000", "take-home: 104000 - 15600 = 88400"], "option_values": [72800, 95200, 92600, 88400], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 560, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 840 units. A delivery added 240, then 140 units were shipped out, and 24 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 840 units. A delivery added 240, then 140 units were shipped out, and 24 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "endings": [" 61 crates.", " 55 crates.", " 53 crates.", " 65 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0560", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "65", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed into larger crates", "shipped out twice", "shipped twice and damaged twice", "correct"], "solution_steps": ["after delivery: 840 + 240 = 1080", "after shipping: 1080 - 140 = 940", "good units: 940 - 24 = 916", "full crates: 916 / 14 = 65 (remainder 6)"], "option_values": [61, 55, 53, 65], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 561, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 4 metres and 55 centimetres long. A worker cut off 115 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 4 metres and 55 centimetres long. A worker cut off 115 centimetres. The board left was", "endings": [" 350 centimetres.", " 570 centimetres.", " 670 centimetres.", " 340 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0561", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "340", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["stopped ten centimetres short of the cut", "added the cut instead of removing it", "added the cut and a whole metre", "correct"], "solution_steps": ["convert metres: 4 x 100 = 400 cm", "add the extra centimetres: 400 + 55 = 455 cm", "subtract the cut: 455 - 115 = 340 cm"], "option_values": [350, 570, 670, 340], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 562, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 20% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 20% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 33 pallets.", " 12 pallets.", " 32 pallets.", " 36 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0562", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "36", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "took both percentages twice", "stacked on larger pallets", "correct"], "solution_steps": ["Monday: 20% of 600 = 120", "left after Monday: 600 - 120 = 480", "Tuesday: 25% of 480 = 120", "left after Tuesday: 480 - 120 = 360", "full pallets: 360 / 10 = 36"], "option_values": [33, 12, 32, 36], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 563, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 69 pallets.", " 75 pallets.", " 66 pallets.", " 108 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0563", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "75", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "correct", "took both percentages off the original stock", "forgot Monday"], "solution_steps": ["Monday: 25% of 1600 = 400", "left after Monday: 1600 - 400 = 1200", "Tuesday: 25% of 1200 = 300", "left after Tuesday: 1200 - 300 = 900", "full pallets: 900 / 12 = 75"], "option_values": [69, 75, 66, 108], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 564, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 4 metres and 68 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 4 metres and 68 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 423 centimetres.", " 355 centimetres.", " 323 centimetres.", " 513 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0564", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "423", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["correct", "forgot the extra centimetres", "cut a whole metre off as well", "added the cut instead of removing it"], "solution_steps": ["convert metres: 4 x 100 = 400 cm", "add the extra centimetres: 400 + 68 = 468 cm", "subtract the cut: 468 - 45 = 423 cm"], "option_values": [423, 355, 323, 513], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 565, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $14.00 an hour, and then 2 hours at $19.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $14.00 an hour, and then 2 hours at $19.00 an hour. He earned", "endings": [" $122.00.", " $142.00.", " $152.00.", " $264.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0565", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "12200", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["correct", "swapped the two rates", "paid every hour at the second rate", "added the rates together"], "solution_steps": ["first stretch: 6 x 1400 = 8400", "second stretch: 2 x 1900 = 3800", "total pay: 8400 + 3800 = 12200"], "option_values": [12200, 14200, 15200, 26400], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 566, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 10% discount came off it, then 5% tax was added to the discounted price, and a $0.60 coupon was applied last. 3 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 10% discount came off it, then 5% tax was added to the discounted price, and a $0.60 coupon was applied last. 3 people split the final cost equally. Each paid", "endings": [" $5.40.", " $5.90.", " $18.30.", " $6.10."], "source_id": "deeparithmark_v1_percent_money_depth4_0566", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "610", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "used the coupon twice", "did not split the cost at all", "correct"], "solution_steps": ["discount: 2000 - 200 = 1800", "tax on the discounted price: 1800 + 90 = 1890", "coupon: 1890 - 60 = 1830", "split 3 ways: 1830 / 3 = 610"], "option_values": [540, 590, 1830, 610], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 567, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 5 hours at $15.00 an hour, and then 2 hours at $17.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 5 hours at $15.00 an hour, and then 2 hours at $17.00 an hour. He earned", "endings": [" $34.00.", " $109.00.", " $94.00.", " $105.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0567", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "10900", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["forgot the first stretch", "correct", "worked one hour less in the first stretch", "paid every hour at the first rate"], "solution_steps": ["first stretch: 5 x 1500 = 7500", "second stretch: 2 x 1700 = 3400", "total pay: 7500 + 3400 = 10900"], "option_values": [3400, 10900, 9400, 10500], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 568, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $1.20 each and 4 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $1.20 each and 4 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $2.24.", " $1.68.", " $1.86.", " $1.94."], "source_id": "deeparithmark_v1_money_depth4_0568", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "224", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "forgot the erasers", "split among one more person", "swapped the two unit prices"], "solution_steps": ["markers: 7 x 120 = 840", "erasers: 4 x 70 = 280", "total cost: 840 + 280 = 1120", "split between 5 people: 1120 / 5 = 224"], "option_values": [224, 168, 186, 194], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 569, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $20.00 an hour and 4 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $20.00 an hour and 4 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $744.00.", " $837.00.", " $873.00.", " $1023.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0569", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "83700", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "correct", "paid overtime at double rate", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 38 x 2000 = 76000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 4 x 3000 = 12000", "gross with bonus: 76000 + 12000 + 5000 = 93000", "take-home: 93000 - 9300 = 83700"], "option_values": [74400, 83700, 87300, 102300], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 570, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $16.00 an hour and 6 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $16.00 an hour and 6 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $579.00.", " $471.00.", " $965.00.", " $772.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0570", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "57900", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "forgot the overtime", "added the tax instead of withholding it", "forgot the tax"], "solution_steps": ["regular pay: 38 x 1600 = 60800", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 6 x 2400 = 14400", "gross with bonus: 60800 + 14400 + 2000 = 77200", "take-home: 77200 - 19300 = 57900"], "option_values": [57900, 47100, 96500, 77200], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 571, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 20% discount came off it, then 10% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $8.80.", " $8.20.", " $9.40.", " $16.40."], "source_id": "deeparithmark_v1_percent_money_depth4_0571", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "820", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["forgot the coupon", "correct", "added the coupon instead of subtracting it", "split the total among one fewer person"], "solution_steps": ["discount: 2000 - 400 = 1600", "tax on the discounted price: 1600 + 160 = 1760", "coupon: 1760 - 120 = 1640", "split 2 ways: 1640 / 2 = 820"], "option_values": [880, 820, 940, 1640], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 572, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $0.95 each and 4 erasers at $0.50 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $0.95 each and 4 erasers at $0.50 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.35.", " $1.36.", " $1.64.", " $1.68."], "source_id": "deeparithmark_v1_money_depth4_0572", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "135", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "added the unit prices instead of multiplying", "bought one extra of each item", "split only between the friends"], "solution_steps": ["markers: 5 x 95 = 475", "erasers: 4 x 50 = 200", "total cost: 475 + 200 = 675", "split between 5 people: 675 / 5 = 135"], "option_values": [135, 136, 164, 168], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 573, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $12.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $12.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $515.20.", " $715.20.", " $476.80.", " $509.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0573", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "47680", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at double rate", "added the tax instead of withholding it", "correct", "taxed only the regular pay"], "solution_steps": ["regular pay: 36 x 1200 = 43200", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 8 x 1800 = 14400", "gross with bonus: 43200 + 14400 + 2000 = 59600", "take-home: 59600 - 11920 = 47680"], "option_values": [51520, 71520, 47680, 50960], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 574, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:14 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:14 a.m. for 110 minutes. The booking ended at", "endings": [" 7:49 a.m.", " 8:04 a.m.", " 8:34 a.m.", " 9:04 a.m."], "source_id": "deeparithmark_v1_time_depth2_0574", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "484", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "correct", "ran half an hour long", "added an extra hour"], "solution_steps": ["convert the start: 374 minutes after midnight", "add the duration: 374 + 110 = 484 minutes"], "option_values": [469, 484, 514, 544], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 575, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 30% discount came off it, then 8% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 30% discount came off it, then 8% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $3.58.", " $2.06.", " $14.72.", " $3.68."], "source_id": "deeparithmark_v1_percent_money_depth4_0575", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "368", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["used the coupon twice", "applied the discount twice", "did not split the cost at all", "correct"], "solution_steps": ["discount: 2000 - 600 = 1400", "tax on the discounted price: 1400 + 112 = 1512", "coupon: 1512 - 40 = 1472", "split 4 ways: 1472 / 4 = 368"], "option_values": [358, 206, 1472, 368], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 576, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:06 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:06 a.m. for 125 minutes. The booking ended at", "endings": [" 8:41 a.m.", " 9:41 a.m.", " 9:11 a.m.", " 8:11 a.m."], "source_id": "deeparithmark_v1_time_depth2_0576", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "491", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran half an hour long", "ran an hour and a half long", "added an extra hour", "correct"], "solution_steps": ["convert the start: 366 minutes after midnight", "add the duration: 366 + 125 = 491 minutes"], "option_values": [521, 581, 551, 491], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 577, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 280 shirts. It sold 40% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 280 shirts. It sold 40% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "endings": [" 15 boxes.", " 21 boxes.", " 23 boxes.", " 14 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0577", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "14", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["counted the loose shirts as a box", "sold only a tenth of the stock", "packed the whole stock, not the rest", "correct"], "solution_steps": ["sold: 40% of 280 = 112", "left over: 280 - 112 = 168", "full boxes: 168 / 12 = 14 (remainder 0)"], "option_values": [15, 21, 23, 14], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 578, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 440 shirts. It sold 40% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 440 shirts. It sold 40% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 22 boxes.", " 11 boxes.", " 27 boxes.", " 33 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0578", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "33", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the sold shirts", "sold twice as many", "sold half the stock regardless of the percentage", "correct"], "solution_steps": ["sold: 40% of 440 = 176", "left over: 440 - 176 = 264", "full boxes: 264 / 8 = 33 (remainder 0)"], "option_values": [22, 11, 27, 33], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 579, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 310, then 90 units were shipped out, and 24 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 310, then 90 units were shipped out, and 24 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 96 crates.", " 93 crates.", " 95 crates.", " 106 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0579", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "106", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped out twice", "shipped twice and damaged twice", "packed into larger crates", "correct"], "solution_steps": ["after delivery: 760 + 310 = 1070", "after shipping: 1070 - 90 = 980", "good units: 980 - 24 = 956", "full crates: 956 / 9 = 106 (remainder 2)"], "option_values": [96, 93, 95, 106], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 580, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $4.40 was split between two teams in the ratio 5:3 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $4.40 was split between two teams in the ratio 5:3 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.09.", " $0.12.", " $0.15.", " $0.55."], "source_id": "deeparithmark_v1_ratio_depth5_0580", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "15", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "split among one more player", "correct", "forgot to deduct the fee"], "solution_steps": ["after the fee: 440 - 200 = 240", "one ratio part: 240 / 8 = 30", "larger share: 5 x 30 = 150", "after charity: 150 - 75 = 75", "per player: 75 / 5 = 15"], "option_values": [9, 12, 15, 55], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 581, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.00 was split between two teams in the ratio 3:2 after a $3.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.00 was split between two teams in the ratio 3:2 after a $3.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.08.", " $0.24.", " $0.12.", " $0.16."], "source_id": "deeparithmark_v1_ratio_depth5_0581", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "12", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "forgot the charity cut", "correct", "gave the larger share to the smaller ratio"], "solution_steps": ["after the fee: 500 - 300 = 200", "one ratio part: 200 / 5 = 40", "larger share: 3 x 40 = 120", "after charity: 120 - 60 = 60", "per player: 60 / 5 = 12"], "option_values": [8, 24, 12, 16], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 582, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 840 units. A delivery added 240, then 140 units were shipped out, and 12 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 840 units. A delivery added 240, then 140 units were shipped out, and 12 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 103 crates.", " 97 crates.", " 116 crates.", " 86 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0582", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "116", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed into larger crates", "shipped twice and damaged twice", "correct", "forgot the delivery"], "solution_steps": ["after delivery: 840 + 240 = 1080", "after shipping: 1080 - 140 = 940", "good units: 940 - 12 = 928", "full crates: 928 / 8 = 116 (remainder 0)"], "option_values": [103, 97, 116, 86], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 583, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 112 pallets.", " 131 pallets.", " 115 pallets.", " 116 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0583", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "115", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "forgot Monday", "correct", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 10% of 1600 = 160", "left after Monday: 1600 - 160 = 1440", "Tuesday: 20% of 1440 = 288", "left after Tuesday: 1440 - 288 = 1152", "full pallets: 1152 / 10 = 115"], "option_values": [112, 131, 115, 116], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 584, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 20% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $1.92.", " $1.69.", " $2.17.", " $2.12."], "source_id": "deeparithmark_v1_money_percent_depth2_0584", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "217", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "took the percentage off twice", "correct", "took the discount off the fee as well"], "solution_steps": ["take 20% of 240 off: 240 - 48 = 192", "add the 25-cent fee: 192 + 25 = 217"], "option_values": [192, 169, 217, 212], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 585, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 6 litres per minute for 8 minutes, then 7 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 6 litres per minute for 8 minutes, then 7 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 343 litres.", " 303 litres.", " 338 litres.", " 308 litres."], "source_id": "deeparithmark_v1_rate_depth4_0585", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "343", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "drained twice", "used the first rate for both stages", "forgot the second fill"], "solution_steps": ["first fill: 6 x 8 = 48 litres", "second fill: 7 x 5 = 35 litres", "before draining: 300 + 48 + 35 = 383", "after draining: 383 - 40 = 343"], "option_values": [343, 303, 338, 308], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 586, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:43 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:43 a.m. for 95 minutes. The booking ended at", "endings": [" 11:48 a.m.", " 10:18 a.m.", " 10:48 a.m.", " 11:18 a.m."], "source_id": "deeparithmark_v1_time_depth2_0586", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "618", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran an hour and a half long", "correct", "ran half an hour long", "added an extra hour"], "solution_steps": ["convert the start: 523 minutes after midnight", "add the duration: 523 + 95 = 618 minutes"], "option_values": [708, 618, 648, 678], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 587, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:33 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:33 a.m. for 65 minutes. The booking ended at", "endings": [" 9:23 a.m.", " 8:38 a.m.", " 11:08 a.m.", " 9:38 a.m."], "source_id": "deeparithmark_v1_time_depth2_0587", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "578", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "dropped the hour carry", "ran an hour and a half long", "correct"], "solution_steps": ["convert the start: 513 minutes after midnight", "add the duration: 513 + 65 = 578 minutes"], "option_values": [563, 518, 668, 578], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 588, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 15 litres per minute for 4 minutes, then 7 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 15 litres per minute for 4 minutes, then 7 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 309 litres.", " 249 litres.", " 269 litres.", " 365 litres."], "source_id": "deeparithmark_v1_rate_depth4_0588", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "309", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "forgot the first fill", "drained twice", "used the first rate for both stages"], "solution_steps": ["first fill: 15 x 4 = 60 litres", "second fill: 7 x 7 = 49 litres", "before draining: 240 + 60 + 49 = 349", "after draining: 349 - 40 = 309"], "option_values": [309, 249, 269, 365], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 589, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $12.00. A 10% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $12.00. A 10% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $6.21.", " $5.81.", " $6.61.", " $11.62."], "source_id": "deeparithmark_v1_percent_money_depth4_0589", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "581", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["forgot the coupon", "correct", "added the coupon instead of subtracting it", "split the total among one fewer person"], "solution_steps": ["discount: 1200 - 120 = 1080", "tax on the discounted price: 1080 + 162 = 1242", "coupon: 1242 - 80 = 1162", "split 2 ways: 1162 / 2 = 581"], "option_values": [621, 581, 661, 1162], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 590, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:01 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:01 a.m. for 65 minutes. The booking ended at", "endings": [" 8:51 a.m.", " 9:36 a.m.", " 10:06 a.m.", " 9:06 a.m."], "source_id": "deeparithmark_v1_time_depth2_0590", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "546", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "ran half an hour long", "added an extra hour", "correct"], "solution_steps": ["convert the start: 481 minutes after midnight", "add the duration: 481 + 65 = 546 minutes"], "option_values": [531, 576, 606, 546], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 591, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 5 metres and 74 centimetres long. A worker cut off 60 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 5 metres and 74 centimetres long. A worker cut off 60 centimetres. The board left was", "endings": [" 634 centimetres.", " 514 centimetres.", " 734 centimetres.", " 524 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0591", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "514", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["added the cut instead of removing it", "correct", "added the cut and a whole metre", "stopped ten centimetres short of the cut"], "solution_steps": ["convert metres: 5 x 100 = 500 cm", "add the extra centimetres: 500 + 74 = 574 cm", "subtract the cut: 574 - 60 = 514 cm"], "option_values": [634, 514, 734, 524], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 592, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 280 shirts. It sold 25% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 280 shirts. It sold 25% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "endings": [" 5 boxes.", " 13 boxes.", " 17 boxes.", " 11 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0592", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "17", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the sold shirts", "took the percentage off the remainder again", "correct", "sold twice as many"], "solution_steps": ["sold: 25% of 280 = 70", "left over: 280 - 70 = 210", "full boxes: 210 / 12 = 17 (remainder 6)"], "option_values": [5, 13, 17, 11], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 593, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:18 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:18 a.m. for 65 minutes. The booking ended at", "endings": [" 7:23 a.m.", " 7:08 a.m.", " 6:23 a.m.", " 7:53 a.m."], "source_id": "deeparithmark_v1_time_depth2_0593", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "443", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "stopped a quarter of an hour early", "dropped the hour carry", "ran half an hour long"], "solution_steps": ["convert the start: 378 minutes after midnight", "add the duration: 378 + 65 = 443 minutes"], "option_values": [443, 428, 383, 473], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 594, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.00 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.00 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.24.", " $0.07.", " $0.18.", " $0.27."], "source_id": "deeparithmark_v1_ratio_depth5_0594", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "27", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "gave the larger share to the smaller ratio", "forgot the fee and the charity cut", "correct"], "solution_steps": ["after the fee: 600 - 300 = 300", "one ratio part: 300 / 5 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 24 = 216", "per player: 216 / 8 = 27"], "option_values": [24, 7, 18, 27], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 595, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 6 litres per minute for 4 minutes, then 7 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 6 litres per minute for 4 minutes, then 7 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 139 litres.", " 104 litres.", " 99 litres.", " 179 litres."], "source_id": "deeparithmark_v1_rate_depth4_0595", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "139", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "forgot the second fill", "drained twice", "forgot the drain"], "solution_steps": ["first fill: 6 x 4 = 24 litres", "second fill: 7 x 5 = 35 litres", "before draining: 120 + 24 + 35 = 179", "after draining: 179 - 40 = 139"], "option_values": [139, 104, 99, 179], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 596, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:13 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:13 a.m. for 80 minutes. The booking ended at", "endings": [" 7:18 a.m.", " 7:33 a.m.", " 6:33 a.m.", " 4:53 a.m."], "source_id": "deeparithmark_v1_time_depth2_0596", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "453", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "correct", "dropped the hour carry", "subtracted the duration instead of adding it"], "solution_steps": ["convert the start: 373 minutes after midnight", "add the duration: 373 + 80 = 453 minutes"], "option_values": [438, 453, 393, 293], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 597, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 25% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 25% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $5.55.", " $3.75.", " $5.52.", " $7.35."], "source_id": "deeparithmark_v1_money_percent_depth2_0597", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "555", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the percentage off twice", "took the discount off the fee as well", "forgot the discount"], "solution_steps": ["take 25% of 720 off: 720 - 180 = 540", "add the 15-cent fee: 540 + 15 = 555"], "option_values": [555, 375, 552, 735], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 598, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 3 hours at $15.00 an hour, and then 3 hours at $17.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 3 hours at $15.00 an hour, and then 3 hours at $17.00 an hour. He earned", "endings": [" $64.00.", " $96.00.", " $45.00.", " $102.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0598", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "9600", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["worked one hour less in each stretch", "correct", "forgot the second stretch", "paid every hour at the second rate"], "solution_steps": ["first stretch: 3 x 1500 = 4500", "second stretch: 3 x 1700 = 5100", "total pay: 4500 + 5100 = 9600"], "option_values": [6400, 9600, 4500, 10200], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 599, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $0.45 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $0.45 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $1.38.", " $0.93.", " $1.16.", " $1.55."], "source_id": "deeparithmark_v1_money_depth4_0599", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "155", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["swapped the two unit prices", "split among two more people", "split among one more person", "correct"], "solution_steps": ["markers: 8 x 45 = 360", "erasers: 3 x 35 = 105", "total cost: 360 + 105 = 465", "split between 3 people: 465 / 3 = 155"], "option_values": [138, 93, 116, 155], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 600, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $0.75 each and 6 erasers at $0.50 each. She split the total cost equally between herself and 5 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $0.75 each and 6 erasers at $0.50 each. She split the total cost equally between herself and 5 friends. Each person paid", "endings": [" $1.07.", " $1.25.", " $0.75.", " $0.93."], "source_id": "deeparithmark_v1_money_depth4_0600", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "125", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among one more person", "correct", "forgot the erasers", "split among two more people"], "solution_steps": ["markers: 6 x 75 = 450", "erasers: 6 x 50 = 300", "total cost: 450 + 300 = 750", "split between 6 people: 750 / 6 = 125"], "option_values": [107, 125, 75, 93], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 601, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 10% discount came off it, then 15% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 10% discount came off it, then 15% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $18.03.", " $18.33.", " $12.22.", " $36.66."], "source_id": "deeparithmark_v1_percent_money_depth4_0601", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "1833", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["used the coupon twice", "correct", "split the total among one more person", "split the total among one fewer person"], "solution_steps": ["discount: 3600 - 360 = 3240", "tax on the discounted price: 3240 + 486 = 3726", "coupon: 3726 - 60 = 3666", "split 2 ways: 3666 / 2 = 1833"], "option_values": [1803, 1833, 1222, 3666], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 602, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 20 km at 20 km/h, rested 30 minutes, then walked 4 km at 4 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 20 km at 20 km/h, rested 30 minutes, then walked 4 km at 4 km/h. Her total time, in minutes, was", "endings": [" 90 minutes.", " 60 minutes.", " 150 minutes.", " 180 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0602", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "150", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "divided by the speed twice", "correct", "counted the rest twice"], "solution_steps": ["cycling time: 60 x 20 / 20 = 60 minutes", "walking time: 60 x 4 / 4 = 60 minutes", "add the rest: 60 + 30 + 60 = 150 minutes"], "option_values": [90, 60, 150, 180], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 603, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:02 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:02 a.m. for 65 minutes. The booking ended at", "endings": [" 9:37 a.m.", " 9:07 a.m.", " 8:37 a.m.", " 8:07 a.m."], "source_id": "deeparithmark_v1_time_depth2_0603", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "487", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran an hour and a half long", "added an extra hour", "ran half an hour long", "correct"], "solution_steps": ["convert the start: 422 minutes after midnight", "add the duration: 422 + 65 = 487 minutes"], "option_values": [577, 547, 517, 487], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 604, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.00 was split between two teams in the ratio 4:2 after a $3.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.00 was split between two teams in the ratio 4:2 after a $3.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.25.", " $0.12.", " $0.37.", " $0.75."], "source_id": "deeparithmark_v1_ratio_depth5_0604", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "25", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "swapped the ratio parts", "took the charity cut off the whole prize", "split the whole prize among one team"], "solution_steps": ["after the fee: 600 - 300 = 300", "one ratio part: 300 / 6 = 50", "larger share: 4 x 50 = 200", "after charity: 200 - 100 = 100", "per player: 100 / 4 = 25"], "option_values": [25, 12, 37, 75], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 605, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $7.68.", " $6.11.", " $8.03.", " $11.87."], "source_id": "deeparithmark_v1_money_percent_depth2_0605", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "803", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "took the percentage off twice", "correct", "added the discount instead of removing it"], "solution_steps": ["take 20% of 960 off: 960 - 192 = 768", "add the 35-cent fee: 768 + 35 = 803"], "option_values": [768, 611, 803, 1187], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 606, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:02 a.m.. The first session lasted 50 minutes, the break lasted 20 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:02 a.m.. The first session lasted 50 minutes, the break lasted 20 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "endings": [" 7:27 a.m.", " 7:47 a.m.", " 7:12 a.m.", " 6:52 a.m."], "source_id": "deeparithmark_v1_time_depth3_0606", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "467", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the break", "correct", "forgot the second session", "forgot the last session and the break"], "solution_steps": ["after the first session: 362 + 50 = 412 minutes after midnight", "after the break: 412 + 20 = 432", "after the second session: 432 + 35 = 467"], "option_values": [447, 467, 432, 412], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 607, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $5.40. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $5.40. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $4.32.", " $5.75.", " $5.55.", " $4.67."], "source_id": "deeparithmark_v1_money_percent_depth2_0607", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "467", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "forgot the discount", "read the percentage as a flat number of cents", "correct"], "solution_steps": ["take 20% of 540 off: 540 - 108 = 432", "add the 35-cent fee: 432 + 35 = 467"], "option_values": [432, 575, 555, 467], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 608, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $686.00.", " $1127.00.", " $833.00.", " $872.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0608", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "83300", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "added the tax instead of withholding it", "correct", "taxed only the regular pay"], "solution_steps": ["regular pay: 36 x 2000 = 72000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 8 x 3000 = 24000", "gross with bonus: 72000 + 24000 + 2000 = 98000", "take-home: 98000 - 14700 = 83300"], "option_values": [68600, 112700, 83300, 87200], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 609, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:21 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:21 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 8:16 a.m.", " 11:16 a.m.", " 10:16 a.m.", " 11:01 a.m."], "source_id": "deeparithmark_v1_time_depth3_0609", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "616", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["dropped the hour carry", "counted the first session twice", "correct", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 501 + 60 = 561 minutes after midnight", "after the break: 561 + 15 = 576", "after the second session: 576 + 40 = 616"], "option_values": [496, 676, 616, 661], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 610, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 12 litres per minute for 8 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 12 litres per minute for 8 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 206 litres.", " 135 litres.", " 231 litres.", " 161 litres."], "source_id": "deeparithmark_v1_rate_depth4_0610", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "231", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the second fill", "forgot the first fill", "correct", "drained twice"], "solution_steps": ["first fill: 12 x 8 = 96 litres", "second fill: 5 x 5 = 25 litres", "before draining: 180 + 96 + 25 = 301", "after draining: 301 - 70 = 231"], "option_values": [206, 135, 231, 161], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 611, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 560 units. A delivery added 310, then 90 units were shipped out, and 32 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 560 units. A delivery added 310, then 90 units were shipped out, and 32 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 78 crates.", " 97 crates.", " 93 crates.", " 104 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0611", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "93", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped twice and damaged twice", "forgot the damaged units", "correct", "forgot the shipping"], "solution_steps": ["after delivery: 560 + 310 = 870", "after shipping: 870 - 90 = 780", "good units: 780 - 32 = 748", "full crates: 748 / 8 = 93 (remainder 4)"], "option_values": [78, 97, 93, 104], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 612, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.00 was split between two teams in the ratio 4:1 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.00 was split between two teams in the ratio 4:1 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.24.", " $0.06.", " $0.18.", " $0.37."], "source_id": "deeparithmark_v1_ratio_depth5_0612", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "24", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "swapped the ratio parts", "gave twice the share away to charity", "split the whole prize among one team"], "solution_steps": ["after the fee: 500 - 200 = 300", "one ratio part: 300 / 5 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 48 = 192", "per player: 192 / 8 = 24"], "option_values": [24, 6, 18, 37], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 613, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Quinn baked 108 cookies. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Quinn baked 108 cookies. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 7 cookies.", " 9 cookies.", " 72 cookies.", " 18 cookies."], "source_id": "deeparithmark_v1_fractions_depth3_0613", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "18", "unit": "cookies", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away two thirds and split among one more child", "split the given-away cookies too", "stopped after giving the third away", "correct"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 4: 72 / 4 = 18"], "option_values": [7, 9, 72, 18], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 614, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Vera baked 90 cookies. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Vera baked 90 cookies. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "endings": [" 5 cookies.", " 12 cookies.", " 18 cookies.", " 15 cookies."], "source_id": "deeparithmark_v1_fractions_depth3_0614", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "12", "unit": "cookies", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away two thirds and split among one more child", "correct", "split all the cookies, not the rest", "split all the cookies among one more child"], "solution_steps": ["one third given away: 90 / 3 = 30", "rest kept: 90 - 30 = 60", "split among 5: 60 / 5 = 12"], "option_values": [5, 12, 18, 15], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 615, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 10% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 10% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 72 pallets.", " 106 pallets.", " 95 pallets.", " 94 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0615", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "94", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "forgot Monday", "counted the loose sacks as a pallet", "correct"], "solution_steps": ["Monday: 10% of 1400 = 140", "left after Monday: 1400 - 140 = 1260", "Tuesday: 10% of 1260 = 126", "left after Tuesday: 1260 - 126 = 1134", "full pallets: 1134 / 12 = 94"], "option_values": [72, 106, 95, 94], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 616, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 3 hours at $9.00 an hour, and then 4 hours at $14.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 3 hours at $9.00 an hour, and then 4 hours at $14.00 an hour. He earned", "endings": [" $83.00.", " $27.00.", " $161.00.", " $98.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0616", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "8300", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["correct", "forgot the second stretch", "added the rates together", "paid every hour at the second rate"], "solution_steps": ["first stretch: 3 x 900 = 2700", "second stretch: 4 x 1400 = 5600", "total pay: 2700 + 5600 = 8300"], "option_values": [8300, 2700, 16100, 9800], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 617, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 440 shirts. It sold 30% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 440 shirts. It sold 30% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "endings": [" 24 boxes.", " 19 boxes.", " 34 boxes.", " 35 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0617", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "34", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold half the stock regardless of the percentage", "sold twice as many", "correct", "rounded the box count up"], "solution_steps": ["sold: 30% of 440 = 132", "left over: 440 - 132 = 308", "full boxes: 308 / 9 = 34 (remainder 2)"], "option_values": [24, 19, 34, 35], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 618, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $12.00 an hour and 8 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $12.00 an hour and 8 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $475.20.", " $511.20.", " $381.60.", " $454.40."], "source_id": "deeparithmark_v1_money_rate_depth5_0618", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "51120", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "correct", "forgot the overtime", "taxed twice"], "solution_steps": ["regular pay: 32 x 1200 = 38400", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 8 x 1800 = 14400", "gross with bonus: 38400 + 14400 + 4000 = 56800", "take-home: 56800 - 5680 = 51120"], "option_values": [47520, 51120, 38160, 45440], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 619, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 6 litres per minute for 4 minutes, then 3 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 6 litres per minute for 4 minutes, then 3 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "endings": [" 212 litres.", " 263 litres.", " 236 litres.", " 302 litres."], "source_id": "deeparithmark_v1_rate_depth4_0619", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "236", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the first fill", "used the first rate for both stages", "correct", "added the rates and multiplied once"], "solution_steps": ["first fill: 6 x 4 = 24 litres", "second fill: 3 x 9 = 27 litres", "before draining: 240 + 24 + 27 = 291", "after draining: 291 - 55 = 236"], "option_values": [212, 263, 236, 302], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 620, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Greta baked 90 muffins. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Greta baked 90 muffins. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "endings": [" 8 muffins.", " 12 muffins.", " 9 muffins.", " 6 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0620", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "12", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away a third twice", "correct", "gave away a half instead of a third", "split the given-away cookies too"], "solution_steps": ["one third given away: 90 / 3 = 30", "rest kept: 90 - 30 = 60", "split among 5: 60 / 5 = 12"], "option_values": [8, 12, 9, 6], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 621, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.50 was split between two teams in the ratio 3:2 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.50 was split between two teams in the ratio 3:2 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.35.", " $0.42.", " $0.33.", " $0.31."], "source_id": "deeparithmark_v1_ratio_depth5_0621", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "42", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["gave the larger share to the smaller ratio", "correct", "split among one more player", "gave twice the share away to charity"], "solution_steps": ["after the fee: 650 - 300 = 350", "one ratio part: 350 / 5 = 70", "larger share: 3 x 70 = 210", "after charity: 210 - 42 = 168", "per player: 168 / 4 = 42"], "option_values": [35, 42, 33, 31], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 622, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $14.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $14.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $523.60.", " $445.20.", " $540.60.", " $731.40."], "source_id": "deeparithmark_v1_money_rate_depth5_0622", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "54060", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "taxed twice", "correct", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 32 x 1400 = 44800", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 8 x 2100 = 16800", "gross with bonus: 44800 + 16800 + 2000 = 63600", "take-home: 63600 - 9540 = 54060"], "option_values": [52360, 44520, 54060, 73140], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 623, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:37 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:37 a.m. for 125 minutes. The booking ended at", "endings": [" 4:32 a.m.", " 8:42 a.m.", " 7:42 a.m.", " 8:27 a.m."], "source_id": "deeparithmark_v1_time_depth2_0623", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "522", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "correct", "forgot the last full hour", "stopped a quarter of an hour early"], "solution_steps": ["convert the start: 397 minutes after midnight", "add the duration: 397 + 125 = 522 minutes"], "option_values": [272, 522, 462, 507], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 624, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 6 metres and 12 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 6 metres and 12 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 567 centimetres.", " 579 centimetres.", " 657 centimetres.", " 757 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0624", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "567", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["correct", "counted the extra centimetres twice", "added the cut instead of removing it", "added the cut and a whole metre"], "solution_steps": ["convert metres: 6 x 100 = 600 cm", "add the extra centimetres: 600 + 12 = 612 cm", "subtract the cut: 612 - 45 = 567 cm"], "option_values": [567, 579, 657, 757], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 625, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $14.00 an hour and 4 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $14.00 an hour and 4 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $590.40.", " $524.80.", " $615.60.", " $721.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0625", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "59040", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "taxed twice", "paid overtime at double rate", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 38 x 1400 = 53200", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 4 x 2100 = 8400", "gross with bonus: 53200 + 8400 + 4000 = 65600", "take-home: 65600 - 6560 = 59040"], "option_values": [59040, 52480, 61560, 72160], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 626, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:13 a.m.. The first session lasted 70 minutes, the break lasted 15 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:13 a.m.. The first session lasted 70 minutes, the break lasted 15 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 9:38 a.m.", " 9:23 a.m.", " 10:03 a.m.", " 10:18 a.m."], "source_id": "deeparithmark_v1_time_depth3_0626", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "618", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the second session", "forgot the last session and the break", "forgot the break", "correct"], "solution_steps": ["after the first session: 493 + 70 = 563 minutes after midnight", "after the break: 563 + 15 = 578", "after the second session: 578 + 40 = 618"], "option_values": [578, 563, 603, 618], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 627, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:56 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:56 a.m. for 80 minutes. The booking ended at", "endings": [" 7:16 a.m.", " 9:01 a.m.", " 9:46 a.m.", " 9:16 a.m."], "source_id": "deeparithmark_v1_time_depth2_0627", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "556", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "stopped a quarter of an hour early", "ran half an hour long", "correct"], "solution_steps": ["convert the start: 476 minutes after midnight", "add the duration: 476 + 80 = 556 minutes"], "option_values": [436, 541, 586, 556], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 628, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $0.75 each and 5 erasers at $0.50 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $0.75 each and 5 erasers at $0.50 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $0.75.", " $0.89.", " $1.25.", " $1.04."], "source_id": "deeparithmark_v1_money_depth4_0628", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "125", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["forgot the erasers", "split among two more people", "correct", "split among one more person"], "solution_steps": ["markers: 5 x 75 = 375", "erasers: 5 x 50 = 250", "total cost: 375 + 250 = 625", "split between 5 people: 625 / 5 = 125"], "option_values": [75, 89, 125, 104], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 629, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $20.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $20.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $841.50.", " $688.50.", " $892.50.", " $1138.50."], "source_id": "deeparithmark_v1_money_rate_depth5_0629", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "84150", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "forgot the overtime", "paid overtime at double rate", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 38 x 2000 = 76000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 6 x 3000 = 18000", "gross with bonus: 76000 + 18000 + 5000 = 99000", "take-home: 99000 - 14850 = 84150"], "option_values": [84150, 68850, 89250, 113850], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 630, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $16.00. A 30% discount came off it, then 15% tax was added to the discounted price, and a $0.40 coupon was applied last. 3 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $16.00. A 30% discount came off it, then 15% tax was added to the discounted price, and a $0.40 coupon was applied last. 3 people split the final cost equally. Each paid", "endings": [" $4.02.", " $4.16.", " $3.12.", " $6.13."], "source_id": "deeparithmark_v1_percent_money_depth4_0630", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "416", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["used the coupon twice", "correct", "split the total among one more person", "forgot the discount and the coupon"], "solution_steps": ["discount: 1600 - 480 = 1120", "tax on the discounted price: 1120 + 168 = 1288", "coupon: 1288 - 40 = 1248", "split 3 ways: 1248 / 3 = 416"], "option_values": [402, 416, 312, 613], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 631, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $2.75.", " $2.85.", " $2.61.", " $3.09."], "source_id": "deeparithmark_v1_money_percent_depth2_0631", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "261", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["read the percentage as a flat number of cents", "forgot the discount", "correct", "added the discount instead of removing it"], "solution_steps": ["take 10% of 240 off: 240 - 24 = 216", "add the 45-cent fee: 216 + 45 = 261"], "option_values": [275, 285, 261, 309], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 632, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:41 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:41 a.m. for 50 minutes. The booking ended at", "endings": [" 7:31 a.m.", " 5:51 a.m.", " 6:31 a.m.", " 7:16 a.m."], "source_id": "deeparithmark_v1_time_depth2_0632", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "451", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "subtracted the duration instead of adding it", "dropped the hour carry", "stopped a quarter of an hour early"], "solution_steps": ["convert the start: 401 minutes after midnight", "add the duration: 401 + 50 = 451 minutes"], "option_values": [451, 351, 391, 436], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 633, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $7.68.", " $8.88.", " $8.28.", " $12.12."], "source_id": "deeparithmark_v1_money_percent_depth2_0633", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "828", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "charged the handling fee twice", "correct", "added the discount instead of removing it"], "solution_steps": ["take 20% of 960 off: 960 - 192 = 768", "add the 60-cent fee: 768 + 60 = 828"], "option_values": [768, 888, 828, 1212], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 634, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 440 shirts. It sold 30% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 440 shirts. It sold 30% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 27 boxes.", " 49 boxes.", " 38 boxes.", " 55 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0634", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "38", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold half the stock regardless of the percentage", "sold only a tenth of the stock", "correct", "packed the whole stock, not the rest"], "solution_steps": ["sold: 30% of 440 = 132", "left over: 440 - 132 = 308", "full boxes: 308 / 8 = 38 (remainder 4)"], "option_values": [27, 49, 38, 55], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 635, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 280 shirts. It sold 40% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 280 shirts. It sold 40% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "endings": [" 16 boxes.", " 14 boxes.", " 8 boxes.", " 24 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0635", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "24", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the sold shirts", "took the percentage off the remainder again", "sold twice as many", "correct"], "solution_steps": ["sold: 40% of 280 = 112", "left over: 280 - 112 = 168", "full boxes: 168 / 7 = 24 (remainder 0)"], "option_values": [16, 14, 8, 24], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 636, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 2 metres and 74 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 2 metres and 74 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 229 centimetres.", " 155 centimetres.", " 303 centimetres.", " 239 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0636", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "229", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["correct", "forgot the extra centimetres", "counted the extra centimetres twice", "stopped ten centimetres short of the cut"], "solution_steps": ["convert metres: 2 x 100 = 200 cm", "add the extra centimetres: 200 + 74 = 274 cm", "subtract the cut: 274 - 45 = 229 cm"], "option_values": [229, 155, 303, 239], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 637, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 30 km at 15 km/h, rested 30 minutes, then walked 5 km at 5 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 30 km at 15 km/h, rested 30 minutes, then walked 5 km at 5 km/h. Her total time, in minutes, was", "endings": [" 210 minutes.", " 170 minutes.", " 450 minutes.", " 240 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0637", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "210", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["correct", "used the cycling speed for both legs", "used the walking speed for both legs", "counted the rest twice"], "solution_steps": ["cycling time: 60 x 30 / 15 = 120 minutes", "walking time: 60 x 5 / 5 = 60 minutes", "add the rest: 120 + 30 + 60 = 210 minutes"], "option_values": [210, 170, 450, 240], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 638, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 24 km at 12 km/h, rested 25 minutes, then walked 6 km at 6 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 24 km at 12 km/h, rested 25 minutes, then walked 6 km at 6 km/h. Her total time, in minutes, was", "endings": [" 145 minutes.", " 205 minutes.", " 55 minutes.", " 175 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0638", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "205", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "correct", "divided by the speed twice", "used the cycling speed for both legs"], "solution_steps": ["cycling time: 60 x 24 / 12 = 120 minutes", "walking time: 60 x 6 / 6 = 60 minutes", "add the rest: 120 + 25 + 60 = 205 minutes"], "option_values": [145, 205, 55, 175], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 639, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 25% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 25% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $7.54.", " $12.45.", " $7.65.", " $10.05."], "source_id": "deeparithmark_v1_money_percent_depth2_0639", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "765", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "added the discount instead of removing it", "correct", "forgot the discount"], "solution_steps": ["take 25% of 960 off: 960 - 240 = 720", "add the 45-cent fee: 720 + 45 = 765"], "option_values": [754, 1245, 765, 1005], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 640, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $1.20 each and 4 erasers at $0.35 each. She split the total cost equally between herself and 3 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $1.20 each and 4 erasers at $0.35 each. She split the total cost equally between herself and 3 friends. Each person paid", "endings": [" $2.46.", " $2.23.", " $1.85.", " $1.87."], "source_id": "deeparithmark_v1_money_depth4_0640", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "185", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split only between the friends", "bought one extra of each item", "correct", "added the unit prices instead of multiplying"], "solution_steps": ["markers: 5 x 120 = 600", "erasers: 4 x 35 = 140", "total cost: 600 + 140 = 740", "split between 4 people: 740 / 4 = 185"], "option_values": [246, 223, 185, 187], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 641, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.90 was split between two teams in the ratio 4:3 after a $3.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.90 was split between two teams in the ratio 4:3 after a $3.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.49.", " $0.89.", " $0.42.", " $1.05."], "source_id": "deeparithmark_v1_ratio_depth5_0641", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "42", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the fee and the charity cut", "forgot to deduct the fee", "correct", "divided between the teams instead of the players"], "solution_steps": ["after the fee: 790 - 300 = 490", "one ratio part: 490 / 7 = 70", "larger share: 4 x 70 = 280", "after charity: 280 - 70 = 210", "per player: 210 / 5 = 42"], "option_values": [49, 89, 42, 105], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 642, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:43 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:43 a.m. for 65 minutes. The booking ended at", "endings": [" 9:33 a.m.", " 10:18 a.m.", " 11:18 a.m.", " 9:48 a.m."], "source_id": "deeparithmark_v1_time_depth2_0642", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "588", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "ran half an hour long", "ran an hour and a half long", "correct"], "solution_steps": ["convert the start: 523 minutes after midnight", "add the duration: 523 + 65 = 588 minutes"], "option_values": [573, 618, 678, 588], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 643, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:13 a.m.. The first session lasted 70 minutes, the break lasted 25 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:13 a.m.. The first session lasted 70 minutes, the break lasted 25 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 6:38 a.m.", " 7:23 a.m.", " 8:13 a.m.", " 8:38 a.m."], "source_id": "deeparithmark_v1_time_depth3_0643", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "518", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["dropped the hour carry", "forgot the last session and the break", "forgot the break", "correct"], "solution_steps": ["after the first session: 373 + 70 = 443 minutes after midnight", "after the break: 443 + 25 = 468", "after the second session: 468 + 50 = 518"], "option_values": [398, 443, 493, 518], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 644, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.00 was split between two teams in the ratio 4:1 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.00 was split between two teams in the ratio 4:1 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.12.", " $0.22.", " $0.18.", " $0.25."], "source_id": "deeparithmark_v1_ratio_depth5_0644", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "18", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the fee and the charity cut", "took the charity cut off the whole prize", "correct", "split the whole prize among one team"], "solution_steps": ["after the fee: 700 - 500 = 200", "one ratio part: 200 / 5 = 40", "larger share: 4 x 40 = 160", "after charity: 160 - 16 = 144", "per player: 144 / 8 = 18"], "option_values": [12, 22, 18, 25], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 645, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $0.45 each and 5 erasers at $0.30 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $0.45 each and 5 erasers at $0.30 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.05.", " $0.86.", " $0.99.", " $0.84."], "source_id": "deeparithmark_v1_money_depth4_0645", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "84", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split only between the friends", "added the unit prices instead of multiplying", "charged the marker price for everything", "correct"], "solution_steps": ["markers: 6 x 45 = 270", "erasers: 5 x 30 = 150", "total cost: 270 + 150 = 420", "split between 5 people: 420 / 5 = 84"], "option_values": [105, 86, 99, 84], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 646, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $0.75 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $0.75 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $1.89.", " $3.13.", " $3.15.", " $9.45."], "source_id": "deeparithmark_v1_money_depth4_0646", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "315", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among two more people", "swapped the two unit prices", "correct", "did not split the total at all"], "solution_steps": ["markers: 7 x 75 = 525", "erasers: 6 x 70 = 420", "total cost: 525 + 420 = 945", "split between 3 people: 945 / 3 = 315"], "option_values": [189, 313, 315, 945], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 647, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $4.14.", " $4.74.", " $4.68.", " $4.28."], "source_id": "deeparithmark_v1_money_percent_depth2_0647", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "474", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "correct", "took the discount off the fee as well", "took the percentage off twice"], "solution_steps": ["take 10% of 460 off: 460 - 46 = 414", "add the 60-cent fee: 414 + 60 = 474"], "option_values": [414, 474, 468, 428], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 648, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 840 units. A delivery added 240, then 90 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 840 units. A delivery added 240, then 90 units were shipped out, and 32 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 59 crates.", " 63 crates.", " 65 crates.", " 61 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0648", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "59", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "added the damaged units", "forgot the shipping", "forgot the damaged units"], "solution_steps": ["after delivery: 840 + 240 = 1080", "after shipping: 1080 - 90 = 990", "good units: 990 - 32 = 958", "full crates: 958 / 16 = 59 (remainder 14)"], "option_values": [59, 63, 65, 61], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 649, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $493.20.", " $657.60.", " $628.80.", " $685.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0649", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "65760", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "correct", "paid overtime at the normal rate", "taxed only the regular pay"], "solution_steps": ["regular pay: 38 x 1800 = 68400", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 4 x 2700 = 10800", "gross with bonus: 68400 + 10800 + 3000 = 82200", "take-home: 82200 - 16440 = 65760"], "option_values": [49320, 65760, 62880, 68520], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 650, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $24.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $24.00. A 25% discount came off it, then 8% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $9.42.", " $9.12.", " $6.18.", " $6.28."], "source_id": "deeparithmark_v1_percent_money_depth4_0650", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "942", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "used the coupon twice", "applied the discount twice", "split the total among one more person"], "solution_steps": ["discount: 2400 - 600 = 1800", "tax on the discounted price: 1800 + 144 = 1944", "coupon: 1944 - 60 = 1884", "split 2 ways: 1884 / 2 = 942"], "option_values": [942, 912, 618, 628], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 651, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $12.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $12.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $3.48.", " $5.34.", " $9.48.", " $4.74."], "source_id": "deeparithmark_v1_percent_money_depth4_0651", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "474", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "added the coupon instead of subtracting it", "split the total among one fewer person", "correct"], "solution_steps": ["discount: 1200 - 240 = 960", "tax on the discounted price: 960 + 48 = 1008", "coupon: 1008 - 60 = 948", "split 2 ways: 948 / 2 = 474"], "option_values": [348, 534, 948, 474], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 652, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 480 units. A delivery added 130, then 140 units were shipped out, and 32 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 480 units. A delivery added 130, then 140 units were shipped out, and 32 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 41 crates.", " 39 crates.", " 37 crates.", " 36 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0652", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "36", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["added the damaged units", "forgot the damaged units", "counted the loose units as a crate", "correct"], "solution_steps": ["after delivery: 480 + 130 = 610", "after shipping: 610 - 140 = 470", "good units: 470 - 32 = 438", "full crates: 438 / 12 = 36 (remainder 6)"], "option_values": [41, 39, 37, 36], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 653, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $8.87.", " $9.75.", " $8.89.", " $9.85."], "source_id": "deeparithmark_v1_money_percent_depth2_0653", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "889", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "read the percentage as a flat number of cents", "correct", "forgot the discount"], "solution_steps": ["take 10% of 960 off: 960 - 96 = 864", "add the 25-cent fee: 864 + 25 = 889"], "option_values": [887, 975, 889, 985], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 654, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 30% discount came off it, then 8% tax was added to the discounted price, and a $0.60 coupon was applied last. 3 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 30% discount came off it, then 8% tax was added to the discounted price, and a $0.60 coupon was applied last. 3 people split the final cost equally. Each paid", "endings": [" $5.24.", " $5.04.", " $7.26.", " $4.84."], "source_id": "deeparithmark_v1_percent_money_depth4_0654", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "484", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["added the coupon instead of subtracting it", "forgot the coupon", "split the total among one fewer person", "correct"], "solution_steps": ["discount: 2000 - 600 = 1400", "tax on the discounted price: 1400 + 112 = 1512", "coupon: 1512 - 60 = 1452", "split 3 ways: 1452 / 3 = 484"], "option_values": [524, 504, 726, 484], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 655, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 9 litres per minute for 10 minutes, then 3 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 9 litres per minute for 10 minutes, then 3 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 157 litres.", " 297 litres.", " 227 litres.", " 367 litres."], "source_id": "deeparithmark_v1_rate_depth4_0655", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "227", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "forgot the drain", "correct", "added the drain instead of removing it"], "solution_steps": ["first fill: 9 x 10 = 90 litres", "second fill: 3 x 9 = 27 litres", "before draining: 180 + 90 + 27 = 297", "after draining: 297 - 70 = 227"], "option_values": [157, 297, 227, 367], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 656, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 15 litres per minute for 4 minutes, then 5 litres per minute for 5 minutes. A drain then removed 55 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 15 litres per minute for 4 minutes, then 5 litres per minute for 5 minutes. A drain then removed 55 litres. The tank then held", "endings": [" 210 litres.", " 380 litres.", " 320 litres.", " 270 litres."], "source_id": "deeparithmark_v1_rate_depth4_0656", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "270", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the first fill", "added the drain instead of removing it", "used the first rate for both stages", "correct"], "solution_steps": ["first fill: 15 x 4 = 60 litres", "second fill: 5 x 5 = 25 litres", "before draining: 240 + 60 + 25 = 325", "after draining: 325 - 55 = 270"], "option_values": [210, 380, 320, 270], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 657, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $15.00 an hour, and then 3 hours at $19.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $15.00 an hour, and then 3 hours at $19.00 an hour. He earned", "endings": [" $135.00.", " $57.00.", " $159.00.", " $147.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0657", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "14700", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid every hour at the first rate", "forgot the first stretch", "swapped the two rates", "correct"], "solution_steps": ["first stretch: 6 x 1500 = 9000", "second stretch: 3 x 1900 = 5700", "total pay: 9000 + 5700 = 14700"], "option_values": [13500, 5700, 15900, 14700], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 658, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 33 pallets.", " 38 pallets.", " 54 pallets.", " 37 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0658", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "37", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "counted the loose sacks as a pallet", "forgot Monday", "correct"], "solution_steps": ["Monday: 25% of 800 = 200", "left after Monday: 800 - 200 = 600", "Tuesday: 25% of 600 = 150", "left after Tuesday: 600 - 150 = 450", "full pallets: 450 / 12 = 37"], "option_values": [33, 38, 54, 37], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 659, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $615.40.", " $523.60.", " $584.80.", " $506.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0659", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "61540", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "forgot the overtime", "paid overtime at the normal rate", "taxed twice"], "solution_steps": ["regular pay: 32 x 1800 = 57600", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 4 x 2700 = 10800", "gross with bonus: 57600 + 10800 + 4000 = 72400", "take-home: 72400 - 10860 = 61540"], "option_values": [61540, 52360, 58480, 50680], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 660, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:05 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:05 a.m. for 65 minutes. The booking ended at", "endings": [" 10:40 a.m.", " 10:10 a.m.", " 9:10 a.m.", " 9:40 a.m."], "source_id": "deeparithmark_v1_time_depth2_0660", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "550", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran an hour and a half long", "added an extra hour", "correct", "ran half an hour long"], "solution_steps": ["convert the start: 485 minutes after midnight", "add the duration: 485 + 65 = 550 minutes"], "option_values": [640, 610, 550, 580], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 661, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 5 hours at $14.00 an hour, and then 4 hours at $19.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 5 hours at $14.00 an hour, and then 4 hours at $19.00 an hour. He earned", "endings": [" $63.00.", " $146.00.", " $126.00.", " $151.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0661", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "14600", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid the slower rate for the whole day", "correct", "paid every hour at the first rate", "swapped the two rates"], "solution_steps": ["first stretch: 5 x 1400 = 7000", "second stretch: 4 x 1900 = 7600", "total pay: 7000 + 7600 = 14600"], "option_values": [6300, 14600, 12600, 15100], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 662, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 20% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 20% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 25 pallets.", " 21 pallets.", " 24 pallets.", " 36 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0662", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "25", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "took both percentages off the original stock", "stacked on larger pallets", "forgot Monday"], "solution_steps": ["Monday: 20% of 800 = 160", "left after Monday: 800 - 160 = 640", "Tuesday: 40% of 640 = 256", "left after Tuesday: 640 - 256 = 384", "full pallets: 384 / 15 = 25"], "option_values": [25, 21, 24, 36], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 663, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 54 km at 18 km/h, rested 12 minutes, then walked 4 km at 4 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 54 km at 18 km/h, rested 12 minutes, then walked 4 km at 4 km/h. Her total time, in minutes, was", "endings": [" 192 minutes.", " 72 minutes.", " 205 minutes.", " 252 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0663", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "252", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "divided by the speed twice", "used the cycling speed for both legs", "correct"], "solution_steps": ["cycling time: 60 x 54 / 18 = 180 minutes", "walking time: 60 x 4 / 4 = 60 minutes", "add the rest: 180 + 12 + 60 = 252 minutes"], "option_values": [192, 72, 205, 252], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 664, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $28.00. A 30% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $28.00. A 30% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $2.88.", " $6.92.", " $5.19.", " $5.39."], "source_id": "deeparithmark_v1_percent_money_depth4_0664", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "519", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "split the total among one fewer person", "correct", "forgot the coupon"], "solution_steps": ["discount: 2800 - 840 = 1960", "tax on the discounted price: 1960 + 196 = 2156", "coupon: 2156 - 80 = 2076", "split 4 ways: 2076 / 4 = 519"], "option_values": [288, 692, 519, 539], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 665, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 6 litres per minute for 6 minutes, then 5 litres per minute for 9 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 6 litres per minute for 6 minutes, then 5 litres per minute for 9 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 185 litres.", " 221 litres.", " 176 litres.", " 181 litres."], "source_id": "deeparithmark_v1_rate_depth4_0665", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "221", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the first fill", "correct", "forgot the second fill", "drained twice"], "solution_steps": ["first fill: 6 x 6 = 36 litres", "second fill: 5 x 9 = 45 litres", "before draining: 180 + 36 + 45 = 261", "after draining: 261 - 40 = 221"], "option_values": [185, 221, 176, 181], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 666, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 72 pallets.", " 76 pallets.", " 112 pallets.", " 84 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0666", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "84", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "stacked on larger pallets", "forgot Tuesday", "correct"], "solution_steps": ["Monday: 30% of 1600 = 480", "left after Monday: 1600 - 480 = 1120", "Tuesday: 25% of 1120 = 280", "left after Tuesday: 1120 - 280 = 840", "full pallets: 840 / 10 = 84"], "option_values": [72, 76, 112, 84], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 667, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $3.80 was split between two teams in the ratio 5:1 after a $2.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $3.80 was split between two teams in the ratio 5:1 after a $2.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.27.", " $0.32.", " $0.63.", " $0.36."], "source_id": "deeparithmark_v1_ratio_depth5_0667", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "27", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "took the charity cut off the whole prize", "forgot to deduct the fee", "split the whole prize among one team"], "solution_steps": ["after the fee: 380 - 200 = 180", "one ratio part: 180 / 6 = 30", "larger share: 5 x 30 = 150", "after charity: 150 - 15 = 135", "per player: 135 / 5 = 27"], "option_values": [27, 32, 63, 36], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 668, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Milo baked 144 buns. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Milo baked 144 buns. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 19 buns.", " 18 buns.", " 24 buns.", " 12 buns."], "source_id": "deeparithmark_v1_fractions_depth3_0668", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "24", "unit": "buns", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split the rest among one more child", "gave away a half instead of a third", "correct", "split the given-away cookies too"], "solution_steps": ["one third given away: 144 / 3 = 48", "rest kept: 144 - 48 = 96", "split among 4: 96 / 4 = 24"], "option_values": [19, 18, 24, 12], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 669, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1000 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1000 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 28 pallets.", " 65 pallets.", " 84 pallets.", " 64 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0669", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "64", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "counted the loose sacks as a pallet", "forgot Monday", "correct"], "solution_steps": ["Monday: 20% of 1000 = 200", "left after Monday: 1000 - 200 = 800", "Tuesday: 20% of 800 = 160", "left after Tuesday: 800 - 160 = 640", "full pallets: 640 / 10 = 64"], "option_values": [28, 65, 84, 64], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 670, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1000 sacks. It sent out 10% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1000 sacks. It sent out 10% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 75 pallets.", " 56 pallets.", " 64 pallets.", " 57 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0670", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "56", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["forgot Tuesday", "correct", "forgot Monday", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 10% of 1000 = 100", "left after Monday: 1000 - 100 = 900", "Tuesday: 25% of 900 = 225", "left after Tuesday: 900 - 225 = 675", "full pallets: 675 / 12 = 56"], "option_values": [75, 56, 64, 57], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 671, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:03 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:03 a.m. for 80 minutes. The booking ended at", "endings": [" 7:08 a.m.", " 8:23 a.m.", " 8:53 a.m.", " 7:23 a.m."], "source_id": "deeparithmark_v1_time_depth2_0671", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "443", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "added an extra hour", "ran an hour and a half long", "correct"], "solution_steps": ["convert the start: 363 minutes after midnight", "add the duration: 363 + 80 = 443 minutes"], "option_values": [428, 503, 533, 443], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 672, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Ben baked 135 muffins. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Ben baked 135 muffins. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "endings": [" 6 muffins.", " 15 muffins.", " 9 muffins.", " 7 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0672", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "15", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away two thirds and split among one more child", "correct", "gave away a half and split among one more child", "split the given-away cookies too"], "solution_steps": ["one third given away: 135 / 3 = 45", "rest kept: 135 - 45 = 90", "split among 6: 90 / 6 = 15"], "option_values": [6, 15, 9, 7], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 673, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $16.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $16.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $481.20.", " $641.60.", " $680.40.", " $962.40."], "source_id": "deeparithmark_v1_money_rate_depth5_0673", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "64160", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "correct", "taxed only the regular pay", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 38 x 1600 = 60800", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 6 x 2400 = 14400", "gross with bonus: 60800 + 14400 + 5000 = 80200", "take-home: 80200 - 16040 = 64160"], "option_values": [48120, 64160, 68040, 96240], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 674, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 12 km at 12 km/h, rested 12 minutes, then walked 5 km at 5 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 12 km at 12 km/h, rested 12 minutes, then walked 5 km at 5 km/h. Her total time, in minutes, was", "endings": [" 97 minutes.", " 216 minutes.", " 144 minutes.", " 132 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0674", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "132", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["used the cycling speed for both legs", "used the walking speed for both legs", "counted the rest twice", "correct"], "solution_steps": ["cycling time: 60 x 12 / 12 = 60 minutes", "walking time: 60 x 5 / 5 = 60 minutes", "add the rest: 60 + 12 + 60 = 132 minutes"], "option_values": [97, 216, 144, 132], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 675, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:54 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:54 a.m. for 110 minutes. The booking ended at", "endings": [" 9:44 a.m.", " 10:14 a.m.", " 11:14 a.m.", " 10:44 a.m."], "source_id": "deeparithmark_v1_time_depth2_0675", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "584", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "ran half an hour long", "ran an hour and a half long", "added an extra hour"], "solution_steps": ["convert the start: 474 minutes after midnight", "add the duration: 474 + 110 = 584 minutes"], "option_values": [584, 614, 674, 644], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 676, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 50% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 50% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $8.85.", " $4.65.", " $13.05.", " $8.35."], "source_id": "deeparithmark_v1_money_percent_depth2_0676", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "465", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the discount", "correct", "added the discount instead of removing it", "read the percentage as a flat number of cents"], "solution_steps": ["take 50% of 840 off: 840 - 420 = 420", "add the 45-cent fee: 420 + 45 = 465"], "option_values": [885, 465, 1305, 835], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 677, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 20% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $2.27.", " $2.91.", " $4.19.", " $3.35."], "source_id": "deeparithmark_v1_money_percent_depth2_0677", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "291", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "correct", "added the discount instead of removing it", "read the percentage as a flat number of cents"], "solution_steps": ["take 20% of 320 off: 320 - 64 = 256", "add the 35-cent fee: 256 + 35 = 291"], "option_values": [227, 291, 419, 335], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 678, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 25% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 25% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 52 pallets.", " 68 pallets.", " 105 pallets.", " 67 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0678", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "67", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "counted the loose sacks as a pallet", "forgot Monday", "correct"], "solution_steps": ["Monday: 25% of 1200 = 300", "left after Monday: 1200 - 300 = 900", "Tuesday: 40% of 900 = 360", "left after Tuesday: 900 - 360 = 540", "full pallets: 540 / 8 = 67"], "option_values": [52, 68, 105, 67], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 679, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $11.97.", " $10.05.", " $8.13.", " $8.58."], "source_id": "deeparithmark_v1_money_percent_depth2_0679", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "813", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["added the discount instead of removing it", "forgot the discount", "correct", "charged the handling fee twice"], "solution_steps": ["take 20% of 960 off: 960 - 192 = 768", "add the 45-cent fee: 768 + 45 = 813"], "option_values": [1197, 1005, 813, 858], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 680, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 25% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 25% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 57 pallets.", " 98 pallets.", " 63 pallets.", " 64 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0680", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "63", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "forgot Monday", "correct", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 25% of 1400 = 350", "left after Monday: 1400 - 350 = 1050", "Tuesday: 40% of 1050 = 420", "left after Tuesday: 1050 - 420 = 630", "full pallets: 630 / 10 = 63"], "option_values": [57, 98, 63, 64], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 681, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:12 a.m.. The first session lasted 60 minutes, the break lasted 25 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:12 a.m.. The first session lasted 60 minutes, the break lasted 25 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 9:27 a.m.", " 10:27 a.m.", " 10:22 a.m.", " 9:52 a.m."], "source_id": "deeparithmark_v1_time_depth3_0681", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "567", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["correct", "counted the first session twice", "finished half an hour late on top of the break", "counted the break twice"], "solution_steps": ["after the first session: 432 + 60 = 492 minutes after midnight", "after the break: 492 + 25 = 517", "after the second session: 517 + 50 = 567"], "option_values": [567, 627, 622, 592], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 682, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 51 pallets.", " 84 pallets.", " 81 pallets.", " 95 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0682", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "84", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "correct", "took both percentages off the original stock", "forgot Monday"], "solution_steps": ["Monday: 10% of 1400 = 140", "left after Monday: 1400 - 140 = 1260", "Tuesday: 20% of 1260 = 252", "left after Tuesday: 1260 - 252 = 1008", "full pallets: 1008 / 12 = 84"], "option_values": [51, 84, 81, 95], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 683, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 10% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 10% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 86 pallets.", " 85 pallets.", " 81 pallets.", " 66 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0683", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "86", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "took both percentages off the original stock", "stacked on larger pallets", "took both percentages twice"], "solution_steps": ["Monday: 10% of 1600 = 160", "left after Monday: 1600 - 160 = 1440", "Tuesday: 10% of 1440 = 144", "left after Tuesday: 1440 - 144 = 1296", "full pallets: 1296 / 15 = 86"], "option_values": [86, 85, 81, 66], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 684, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:22 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:22 a.m. for 110 minutes. The booking ended at", "endings": [" 9:12 a.m.", " 8:12 a.m.", " 9:42 a.m.", " 8:42 a.m."], "source_id": "deeparithmark_v1_time_depth2_0684", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "492", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added an extra hour", "correct", "ran an hour and a half long", "ran half an hour long"], "solution_steps": ["convert the start: 382 minutes after midnight", "add the duration: 382 + 110 = 492 minutes"], "option_values": [552, 492, 582, 522], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 685, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 33 pallets.", " 36 pallets.", " 37 pallets.", " 46 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0685", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "36", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "correct", "counted the loose sacks as a pallet", "forgot Monday"], "solution_steps": ["Monday: 20% of 600 = 120", "left after Monday: 600 - 120 = 480", "Tuesday: 10% of 480 = 48", "left after Tuesday: 480 - 48 = 432", "full pallets: 432 / 12 = 36"], "option_values": [33, 36, 37, 46], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 686, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Omar baked 108 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Omar baked 108 muffins. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 18 muffins.", " 13 muffins.", " 21 muffins.", " 72 muffins."], "source_id": "deeparithmark_v1_fractions_depth3_0686", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "18", "unit": "muffins", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["correct", "gave away a half instead of a third", "split all the cookies among one more child", "stopped after giving the third away"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 4: 72 / 4 = 18"], "option_values": [18, 13, 21, 72], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 687, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 25% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 25% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $5.35.", " $3.65.", " $5.29.", " $8.75."], "source_id": "deeparithmark_v1_money_percent_depth2_0687", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "535", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the percentage off twice", "took the discount off the fee as well", "added the discount instead of removing it"], "solution_steps": ["take 25% of 680 off: 680 - 170 = 510", "add the 25-cent fee: 510 + 25 = 535"], "option_values": [535, 365, 529, 875], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 688, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:12 a.m.. The first session lasted 50 minutes, the break lasted 20 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:12 a.m.. The first session lasted 50 minutes, the break lasted 20 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "endings": [" 7:02 a.m.", " 8:47 a.m.", " 8:17 a.m.", " 7:57 a.m."], "source_id": "deeparithmark_v1_time_depth3_0688", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "477", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the last session and the break", "counted the first session twice", "counted the break twice", "correct"], "solution_steps": ["after the first session: 372 + 50 = 422 minutes after midnight", "after the break: 422 + 20 = 442", "after the second session: 442 + 35 = 477"], "option_values": [422, 527, 497, 477], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 689, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $507.00.", " $562.00.", " $676.00.", " $845.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0689", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "50700", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "taxed only the regular pay", "forgot the tax", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 38 x 1200 = 45600", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 10 x 1800 = 18000", "gross with bonus: 45600 + 18000 + 4000 = 67600", "take-home: 67600 - 16900 = 50700"], "option_values": [50700, 56200, 67600, 84500], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 690, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:44 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:44 a.m. for 125 minutes. The booking ended at", "endings": [" 6:39 a.m.", " 10:34 a.m.", " 10:49 a.m.", " 11:49 a.m."], "source_id": "deeparithmark_v1_time_depth2_0690", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "649", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "stopped a quarter of an hour early", "correct", "added an extra hour"], "solution_steps": ["convert the start: 524 minutes after midnight", "add the duration: 524 + 125 = 649 minutes"], "option_values": [399, 634, 649, 709], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 691, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Vera baked 108 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Vera baked 108 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 27 biscuits.", " 18 biscuits.", " 72 biscuits.", " 21 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0691", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "18", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split all the cookies, not the rest", "correct", "stopped after giving the third away", "split all the cookies among one more child"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 4: 72 / 4 = 18"], "option_values": [27, 18, 72, 21], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 692, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 56 pallets.", " 66 pallets.", " 42 pallets.", " 43 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0692", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "42", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["forgot Tuesday", "forgot Monday", "correct", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 30% of 1200 = 360", "left after Monday: 1200 - 360 = 840", "Tuesday: 25% of 840 = 210", "left after Tuesday: 840 - 210 = 630", "full pallets: 630 / 15 = 42"], "option_values": [56, 66, 42, 43], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 693, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $9.60 was split between two teams in the ratio 5:3 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $9.60 was split between two teams in the ratio 5:3 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.56.", " $0.33.", " $0.42.", " $0.46."], "source_id": "deeparithmark_v1_ratio_depth5_0693", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "56", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "swapped the ratio parts", "gave the larger share to the smaller ratio", "split among one more player"], "solution_steps": ["after the fee: 960 - 400 = 560", "one ratio part: 560 / 8 = 70", "larger share: 5 x 70 = 350", "after charity: 350 - 70 = 280", "per player: 280 / 5 = 56"], "option_values": [56, 33, 42, 46], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 694, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 15 litres per minute for 10 minutes, then 7 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 15 litres per minute for 10 minutes, then 7 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 225 litres.", " 345 litres.", " 305 litres.", " 265 litres."], "source_id": "deeparithmark_v1_rate_depth4_0694", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "265", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "added the drain instead of removing it", "forgot the drain", "correct"], "solution_steps": ["first fill: 15 x 10 = 150 litres", "second fill: 7 x 5 = 35 litres", "before draining: 120 + 150 + 35 = 305", "after draining: 305 - 40 = 265"], "option_values": [225, 345, 305, 265], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 695, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:46 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:46 a.m. for 80 minutes. The booking ended at", "endings": [" 9:06 a.m.", " 7:06 a.m.", " 6:26 a.m.", " 10:06 a.m."], "source_id": "deeparithmark_v1_time_depth2_0695", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "546", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "dropped the hour carry", "subtracted the duration instead of adding it", "added an extra hour"], "solution_steps": ["convert the start: 466 minutes after midnight", "add the duration: 466 + 80 = 546 minutes"], "option_values": [546, 426, 386, 606], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 696, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 560 units. A delivery added 180, then 140 units were shipped out, and 32 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 560 units. A delivery added 180, then 140 units were shipped out, and 32 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 78 crates.", " 66 crates.", " 64 crates.", " 63 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0696", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "63", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the shipping", "forgot the damaged units", "counted the loose units as a crate", "correct"], "solution_steps": ["after delivery: 560 + 180 = 740", "after shipping: 740 - 140 = 600", "good units: 600 - 32 = 568", "full crates: 568 / 9 = 63 (remainder 1)"], "option_values": [78, 66, 64, 63], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 697, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 30% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 30% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 32 pallets.", " 54 pallets.", " 52 pallets.", " 31 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0697", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "31", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["counted the loose sacks as a pallet", "forgot Monday", "forgot Tuesday", "correct"], "solution_steps": ["Monday: 30% of 600 = 180", "left after Monday: 600 - 180 = 420", "Tuesday: 40% of 420 = 168", "left after Tuesday: 420 - 168 = 252", "full pallets: 252 / 8 = 31"], "option_values": [32, 54, 52, 31], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 698, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 30 km at 15 km/h, rested 12 minutes, then walked 6 km at 6 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 30 km at 15 km/h, rested 12 minutes, then walked 6 km at 6 km/h. Her total time, in minutes, was", "endings": [" 156 minutes.", " 372 minutes.", " 192 minutes.", " 204 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0698", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "192", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["used the cycling speed for both legs", "used the walking speed for both legs", "correct", "counted the rest twice"], "solution_steps": ["cycling time: 60 x 30 / 15 = 120 minutes", "walking time: 60 x 6 / 6 = 60 minutes", "add the rest: 120 + 12 + 60 = 192 minutes"], "option_values": [156, 372, 192, 204], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 699, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $9.09.", " $8.64.", " $8.13.", " $9.05."], "source_id": "deeparithmark_v1_money_percent_depth2_0699", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "909", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "forgot the fee", "took the percentage off twice", "took the discount off the fee as well"], "solution_steps": ["take 10% of 960 off: 960 - 96 = 864", "add the 45-cent fee: 864 + 45 = 909"], "option_values": [909, 864, 813, 905], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 700, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 25% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 25% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $4.95.", " $7.32.", " $7.35.", " $9.75."], "source_id": "deeparithmark_v1_money_percent_depth2_0700", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "735", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "took the discount off the fee as well", "correct", "forgot the discount"], "solution_steps": ["take 25% of 960 off: 960 - 240 = 720", "add the 15-cent fee: 720 + 15 = 735"], "option_values": [495, 732, 735, 975], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 701, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 30% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 30% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 63 pallets.", " 27 pallets.", " 67 pallets.", " 64 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0701", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "67", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "took both percentages twice", "correct", "took both percentages off the original stock"], "solution_steps": ["Monday: 30% of 1600 = 480", "left after Monday: 1600 - 480 = 1120", "Tuesday: 10% of 1120 = 112", "left after Tuesday: 1120 - 112 = 1008", "full pallets: 1008 / 15 = 67"], "option_values": [63, 27, 67, 64], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 702, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $12.00 an hour and 4 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $12.00 an hour and 4 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $443.20.", " $433.80.", " $498.60.", " $510.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0702", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "49860", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "forgot the overtime", "correct", "taxed only the regular pay"], "solution_steps": ["regular pay: 36 x 1200 = 43200", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 4 x 1800 = 7200", "gross with bonus: 43200 + 7200 + 5000 = 55400", "take-home: 55400 - 5540 = 49860"], "option_values": [44320, 43380, 49860, 51080], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 703, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 72 pallets.", " 64 pallets.", " 73 pallets.", " 92 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0703", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "72", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "stacked on larger pallets", "counted the loose sacks as a pallet", "forgot Monday"], "solution_steps": ["Monday: 20% of 800 = 160", "left after Monday: 800 - 160 = 640", "Tuesday: 10% of 640 = 64", "left after Tuesday: 640 - 64 = 576", "full pallets: 576 / 8 = 72"], "option_values": [72, 64, 73, 92], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 704, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 50% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 50% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $3.75.", " $4.25.", " $6.15.", " $2.35."], "source_id": "deeparithmark_v1_money_percent_depth2_0704", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "235", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["read the percentage as a flat number of cents", "forgot the discount", "added the discount instead of removing it", "correct"], "solution_steps": ["take 50% of 380 off: 380 - 190 = 190", "add the 45-cent fee: 190 + 45 = 235"], "option_values": [375, 425, 615, 235], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 705, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 9 litres per minute for 6 minutes, then 7 litres per minute for 7 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 9 litres per minute for 6 minutes, then 7 litres per minute for 7 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 273 litres.", " 224 litres.", " 219 litres.", " 203 litres."], "source_id": "deeparithmark_v1_rate_depth4_0705", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "273", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "forgot the second fill", "forgot the first fill", "drained twice"], "solution_steps": ["first fill: 9 x 6 = 54 litres", "second fill: 7 x 7 = 49 litres", "before draining: 240 + 54 + 49 = 343", "after draining: 343 - 70 = 273"], "option_values": [273, 224, 219, 203], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 706, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 9 litres per minute for 8 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 9 litres per minute for 8 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 195 litres.", " 197 litres.", " 242 litres.", " 267 litres."], "source_id": "deeparithmark_v1_rate_depth4_0706", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "267", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the first fill", "drained twice", "forgot the second fill", "correct"], "solution_steps": ["first fill: 9 x 8 = 72 litres", "second fill: 5 x 5 = 25 litres", "before draining: 240 + 72 + 25 = 337", "after draining: 337 - 70 = 267"], "option_values": [195, 197, 242, 267], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 707, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $14.00 an hour, and then 4 hours at $19.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $14.00 an hour, and then 4 hours at $19.00 an hour. He earned", "endings": [" $99.00.", " $112.00.", " $76.00.", " $132.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0707", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "13200", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["worked one hour less in each stretch", "paid every hour at the first rate", "forgot the first stretch", "correct"], "solution_steps": ["first stretch: 4 x 1400 = 5600", "second stretch: 4 x 1900 = 7600", "total pay: 5600 + 7600 = 13200"], "option_values": [9900, 11200, 7600, 13200], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 708, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 30% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 30% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 46 pallets.", " 52 pallets.", " 53 pallets.", " 65 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0708", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "52", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "correct", "counted the loose sacks as a pallet", "forgot Tuesday"], "solution_steps": ["Monday: 30% of 1400 = 420", "left after Monday: 1400 - 420 = 980", "Tuesday: 20% of 980 = 196", "left after Tuesday: 980 - 196 = 784", "full pallets: 784 / 15 = 52"], "option_values": [46, 52, 53, 65], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 709, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 440 shirts. It sold 40% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 440 shirts. It sold 40% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "endings": [" 31 boxes.", " 37 boxes.", " 38 boxes.", " 62 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0709", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "37", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold half the stock regardless of the percentage", "correct", "rounded the box count up", "packed the whole stock, not the rest"], "solution_steps": ["sold: 40% of 440 = 176", "left over: 440 - 176 = 264", "full boxes: 264 / 7 = 37 (remainder 5)"], "option_values": [31, 37, 38, 62], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 710, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $3.23.", " $3.87.", " $3.45.", " $3.58."], "source_id": "deeparithmark_v1_money_percent_depth2_0710", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "323", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "added the discount instead of removing it", "read the percentage as a flat number of cents", "charged the handling fee twice"], "solution_steps": ["take 10% of 320 off: 320 - 32 = 288", "add the 35-cent fee: 288 + 35 = 323"], "option_values": [323, 387, 345, 358], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 711, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 9 litres per minute for 8 minutes, then 7 litres per minute for 7 minutes. A drain then removed 25 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 9 litres per minute for 8 minutes, then 7 litres per minute for 7 minutes. A drain then removed 25 litres. The tank then held", "endings": [" 251 litres.", " 276 litres.", " 227 litres.", " 301 litres."], "source_id": "deeparithmark_v1_rate_depth4_0711", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "276", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "correct", "forgot the second fill", "forgot the drain"], "solution_steps": ["first fill: 9 x 8 = 72 litres", "second fill: 7 x 7 = 49 litres", "before draining: 180 + 72 + 49 = 301", "after draining: 301 - 25 = 276"], "option_values": [251, 276, 227, 301], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 712, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 40 km at 20 km/h, rested 12 minutes, then walked 4 km at 4 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 40 km at 20 km/h, rested 12 minutes, then walked 4 km at 4 km/h. Her total time, in minutes, was", "endings": [" 132 minutes.", " 192 minutes.", " 57 minutes.", " 144 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0712", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "192", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "correct", "divided by the speed twice", "used the cycling speed for both legs"], "solution_steps": ["cycling time: 60 x 40 / 20 = 120 minutes", "walking time: 60 x 4 / 4 = 60 minutes", "add the rest: 120 + 12 + 60 = 192 minutes"], "option_values": [132, 192, 57, 144], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 713, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 4 markers at $0.45 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 4 markers at $0.45 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $0.73.", " $0.57.", " $0.63.", " $0.58."], "source_id": "deeparithmark_v1_money_depth4_0713", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "57", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["bought one extra of each item", "correct", "charged the marker price for everything", "added the unit prices instead of multiplying"], "solution_steps": ["markers: 4 x 45 = 180", "erasers: 3 x 35 = 105", "total cost: 180 + 105 = 285", "split between 5 people: 285 / 5 = 57"], "option_values": [73, 57, 63, 58], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 714, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $14.00 an hour, and then 2 hours at $19.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $14.00 an hour, and then 2 hours at $19.00 an hour. He earned", "endings": [" $114.00.", " $198.00.", " $94.00.", " $104.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0714", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "9400", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid every hour at the second rate", "added the rates together", "correct", "swapped the two rates"], "solution_steps": ["first stretch: 4 x 1400 = 5600", "second stretch: 2 x 1900 = 3800", "total pay: 5600 + 3800 = 9400"], "option_values": [11400, 19800, 9400, 10400], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 715, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 6 litres per minute for 6 minutes, then 3 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 6 litres per minute for 6 minutes, then 3 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 163 litres.", " 233 litres.", " 305 litres.", " 373 litres."], "source_id": "deeparithmark_v1_rate_depth4_0715", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "233", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "correct", "added the rates and multiplied once", "added the drain instead of removing it"], "solution_steps": ["first fill: 6 x 6 = 36 litres", "second fill: 3 x 9 = 27 litres", "before draining: 240 + 36 + 27 = 303", "after draining: 303 - 70 = 233"], "option_values": [163, 233, 305, 373], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 716, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $5.88.", " $5.91.", " $5.76.", " $4.47."], "source_id": "deeparithmark_v1_money_percent_depth2_0716", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "591", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "correct", "forgot the fee", "took the percentage off twice"], "solution_steps": ["take 20% of 720 off: 720 - 144 = 576", "add the 15-cent fee: 576 + 15 = 591"], "option_values": [588, 591, 576, 447], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 717, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:39 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:39 a.m. for 65 minutes. The booking ended at", "endings": [" 7:29 a.m.", " 6:44 a.m.", " 7:44 a.m.", " 5:34 a.m."], "source_id": "deeparithmark_v1_time_depth2_0717", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "464", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "dropped the hour carry", "correct", "subtracted the duration instead of adding it"], "solution_steps": ["convert the start: 399 minutes after midnight", "add the duration: 399 + 65 = 464 minutes"], "option_values": [449, 404, 464, 334], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 718, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 360 shirts. It sold 30% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 360 shirts. It sold 30% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "endings": [" 15 boxes.", " 36 boxes.", " 25 boxes.", " 37 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0718", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "36", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the sold shirts", "correct", "took the percentage off the remainder again", "counted the loose shirts as a box"], "solution_steps": ["sold: 30% of 360 = 108", "left over: 360 - 108 = 252", "full boxes: 252 / 7 = 36 (remainder 0)"], "option_values": [15, 36, 25, 37], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 719, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.20 was split between two teams in the ratio 2:1 after a $4.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.20 was split between two teams in the ratio 2:1 after a $4.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.12.", " $0.06.", " $0.18.", " $0.24."], "source_id": "deeparithmark_v1_ratio_depth5_0719", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "12", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "swapped the ratio parts", "took the charity cut off the whole prize", "split the whole prize among one team"], "solution_steps": ["after the fee: 520 - 400 = 120", "one ratio part: 120 / 3 = 40", "larger share: 2 x 40 = 80", "after charity: 80 - 20 = 60", "per player: 60 / 5 = 12"], "option_values": [12, 6, 18, 24], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 720, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 620 units. A delivery added 180, then 170 units were shipped out, and 24 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 620 units. A delivery added 180, then 170 units were shipped out, and 24 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 97 crates.", " 81 crates.", " 75 crates.", " 78 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0720", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "75", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the shipping", "added the damaged units", "correct", "forgot the damaged units"], "solution_steps": ["after delivery: 620 + 180 = 800", "after shipping: 800 - 170 = 630", "good units: 630 - 24 = 606", "full crates: 606 / 8 = 75 (remainder 6)"], "option_values": [97, 81, 75, 78], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 721, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 33 pallets.", " 36 pallets.", " 49 pallets.", " 37 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0721", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "36", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "correct", "forgot Monday", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 25% of 800 = 200", "left after Monday: 800 - 200 = 600", "Tuesday: 10% of 600 = 60", "left after Tuesday: 600 - 60 = 540", "full pallets: 540 / 15 = 36"], "option_values": [33, 36, 49, 37], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 722, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 86 pallets.", " 78 pallets.", " 52 pallets.", " 84 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0722", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "86", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "stacked on larger pallets", "took both percentages twice", "took both percentages off the original stock"], "solution_steps": ["Monday: 20% of 1200 = 240", "left after Monday: 1200 - 240 = 960", "Tuesday: 10% of 960 = 96", "left after Tuesday: 960 - 96 = 864", "full pallets: 864 / 10 = 86"], "option_values": [86, 78, 52, 84], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 723, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 360 shirts. It sold 40% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 360 shirts. It sold 40% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "endings": [" 6 boxes.", " 18 boxes.", " 15 boxes.", " 19 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0723", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "18", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold twice as many", "correct", "sold half the stock regardless of the percentage", "counted the loose shirts as a box"], "solution_steps": ["sold: 40% of 360 = 144", "left over: 360 - 144 = 216", "full boxes: 216 / 12 = 18 (remainder 0)"], "option_values": [6, 18, 15, 19], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 724, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 50% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 50% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $3.15.", " $5.25.", " $3.65.", " $2.05."], "source_id": "deeparithmark_v1_money_percent_depth2_0724", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "205", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["read the percentage as a flat number of cents", "added the discount instead of removing it", "forgot the discount", "correct"], "solution_steps": ["take 50% of 320 off: 320 - 160 = 160", "add the 45-cent fee: 160 + 45 = 205"], "option_values": [315, 525, 365, 205], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 725, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $5.64.", " $7.32.", " $6.72.", " $7.92."], "source_id": "deeparithmark_v1_money_percent_depth2_0725", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "732", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "correct", "forgot the fee", "charged the handling fee twice"], "solution_steps": ["take 20% of 840 off: 840 - 168 = 672", "add the 60-cent fee: 672 + 60 = 732"], "option_values": [564, 732, 672, 792], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 726, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Samir baked 72 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Samir baked 72 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 14 biscuits.", " 18 biscuits.", " 12 biscuits.", " 48 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0726", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "12", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split all the cookies among one more child", "split all the cookies, not the rest", "correct", "stopped after giving the third away"], "solution_steps": ["one third given away: 72 / 3 = 24", "rest kept: 72 - 24 = 48", "split among 4: 48 / 4 = 12"], "option_values": [14, 18, 12, 48], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 727, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $6.04.", " $4.68.", " $8.76.", " $6.64."], "source_id": "deeparithmark_v1_money_percent_depth2_0727", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "604", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the percentage off twice", "added the discount instead of removing it", "charged the handling fee twice"], "solution_steps": ["take 20% of 680 off: 680 - 136 = 544", "add the 60-cent fee: 544 + 60 = 604"], "option_values": [604, 468, 876, 664], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 728, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 6 litres per minute for 8 minutes, then 3 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 6 litres per minute for 8 minutes, then 3 litres per minute for 9 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 245 litres.", " 175 litres.", " 218 litres.", " 197 litres."], "source_id": "deeparithmark_v1_rate_depth4_0728", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "245", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "drained twice", "forgot the second fill", "forgot the first fill"], "solution_steps": ["first fill: 6 x 8 = 48 litres", "second fill: 3 x 9 = 27 litres", "before draining: 240 + 48 + 27 = 315", "after draining: 315 - 70 = 245"], "option_values": [245, 175, 218, 197], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 729, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 84 pallets.", " 85 pallets.", " 112 pallets.", " 121 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0729", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "84", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "counted the loose sacks as a pallet", "forgot Tuesday", "forgot Monday"], "solution_steps": ["Monday: 25% of 1200 = 300", "left after Monday: 1200 - 300 = 900", "Tuesday: 25% of 900 = 225", "left after Tuesday: 900 - 225 = 675", "full pallets: 675 / 8 = 84"], "option_values": [84, 85, 112, 121], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 730, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $16.00. A 10% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $16.00. A 10% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $7.88.", " $7.48.", " $5.25.", " $6.96."], "source_id": "deeparithmark_v1_percent_money_depth4_0730", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "788", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "used the coupon twice", "split the total among one more person", "applied the discount twice"], "solution_steps": ["discount: 1600 - 160 = 1440", "tax on the discounted price: 1440 + 216 = 1656", "coupon: 1656 - 80 = 1576", "split 2 ways: 1576 / 2 = 788"], "option_values": [788, 748, 525, 696], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 731, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $0.95 each and 3 erasers at $0.70 each. She split the total cost equally between herself and 3 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $0.95 each and 3 erasers at $0.70 each. She split the total cost equally between herself and 3 friends. Each person paid", "endings": [" $2.13.", " $2.36.", " $1.97.", " $1.95."], "source_id": "deeparithmark_v1_money_depth4_0731", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "195", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["charged the marker price for everything", "bought one extra of each item", "added the unit prices instead of multiplying", "correct"], "solution_steps": ["markers: 6 x 95 = 570", "erasers: 3 x 70 = 210", "total cost: 570 + 210 = 780", "split between 4 people: 780 / 4 = 195"], "option_values": [213, 236, 197, 195], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 732, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $3.45.", " $3.35.", " $3.13.", " $3.38."], "source_id": "deeparithmark_v1_money_percent_depth2_0732", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "313", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the discount", "read the percentage as a flat number of cents", "correct", "charged the handling fee twice"], "solution_steps": ["take 10% of 320 off: 320 - 32 = 288", "add the 25-cent fee: 288 + 25 = 313"], "option_values": [345, 335, 313, 338], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 733, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1000 sacks. It sent out 25% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1000 sacks. It sent out 25% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 25 pallets.", " 66 pallets.", " 75 pallets.", " 68 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0733", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "75", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "stacked on larger pallets", "correct", "took both percentages off the original stock"], "solution_steps": ["Monday: 25% of 1000 = 250", "left after Monday: 1000 - 250 = 750", "Tuesday: 20% of 750 = 150", "left after Tuesday: 750 - 150 = 600", "full pallets: 600 / 8 = 75"], "option_values": [25, 66, 75, 68], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 734, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 60 km at 20 km/h, rested 12 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 60 km at 20 km/h, rested 12 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "endings": [" 192 minutes.", " 324 minutes.", " 732 minutes.", " 312 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0734", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "312", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "counted the rest twice", "used the walking speed for both legs", "correct"], "solution_steps": ["cycling time: 60 x 60 / 20 = 180 minutes", "walking time: 60 x 12 / 6 = 120 minutes", "add the rest: 180 + 12 + 120 = 312 minutes"], "option_values": [192, 324, 732, 312], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 735, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 6 litres per minute for 8 minutes, then 3 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 6 litres per minute for 8 minutes, then 3 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 128 litres.", " 149 litres.", " 101 litres.", " 189 litres."], "source_id": "deeparithmark_v1_rate_depth4_0735", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "149", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the second fill", "correct", "forgot the first fill", "forgot the drain"], "solution_steps": ["first fill: 6 x 8 = 48 litres", "second fill: 3 x 7 = 21 litres", "before draining: 120 + 48 + 21 = 189", "after draining: 189 - 40 = 149"], "option_values": [128, 149, 101, 189], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 736, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:48 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:48 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "endings": [" 8:48 a.m.", " 7:48 a.m.", " 8:33 a.m.", " 8:03 a.m."], "source_id": "deeparithmark_v1_time_depth3_0736", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "528", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["correct", "forgot the last session and the break", "forgot the break", "forgot the second session"], "solution_steps": ["after the first session: 408 + 60 = 468 minutes after midnight", "after the break: 468 + 15 = 483", "after the second session: 483 + 45 = 528"], "option_values": [528, 468, 513, 483], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 737, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 104 pallets.", " 56 pallets.", " 98 pallets.", " 108 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0737", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "108", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "took both percentages twice", "stacked on larger pallets", "correct"], "solution_steps": ["Monday: 25% of 1600 = 400", "left after Monday: 1600 - 400 = 1200", "Tuesday: 10% of 1200 = 120", "left after Tuesday: 1200 - 120 = 1080", "full pallets: 1080 / 10 = 108"], "option_values": [104, 56, 98, 108], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 738, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 480 units. A delivery added 180, then 250 units were shipped out, and 40 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 480 units. A delivery added 180, then 250 units were shipped out, and 40 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 41 crates.", " 15 crates.", " 37 crates.", " 42 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0738", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "41", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "packed the arriving units only", "packed into larger crates", "counted the loose units as a crate"], "solution_steps": ["after delivery: 480 + 180 = 660", "after shipping: 660 - 250 = 410", "good units: 410 - 40 = 370", "full crates: 370 / 9 = 41 (remainder 1)"], "option_values": [41, 15, 37, 42], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 739, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:21 a.m.. The first session lasted 45 minutes, the break lasted 15 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:21 a.m.. The first session lasted 45 minutes, the break lasted 15 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 8:11 a.m.", " 10:11 a.m.", " 9:06 a.m.", " 9:11 a.m."], "source_id": "deeparithmark_v1_time_depth3_0739", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "611", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["dropped the hour carry", "correct", "forgot the last session and the break", "added the minutes but not the hours"], "solution_steps": ["after the first session: 501 + 45 = 546 minutes after midnight", "after the break: 546 + 15 = 561", "after the second session: 561 + 50 = 611"], "option_values": [491, 611, 546, 551], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 740, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $0.80 each and 4 erasers at $0.70 each. She split the total cost equally between herself and 3 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $0.80 each and 4 erasers at $0.70 each. She split the total cost equally between herself and 3 friends. Each person paid", "endings": [" $2.30.", " $2.20.", " $2.40.", " $9.20."], "source_id": "deeparithmark_v1_money_depth4_0740", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "230", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "swapped the two unit prices", "charged the marker price for everything", "did not split the total at all"], "solution_steps": ["markers: 8 x 80 = 640", "erasers: 4 x 70 = 280", "total cost: 640 + 280 = 920", "split between 4 people: 920 / 4 = 230"], "option_values": [230, 220, 240, 920], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 741, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 30% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 37 pallets.", " 28 pallets.", " 44 pallets.", " 29 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0741", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "28", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["forgot Tuesday", "correct", "forgot Monday", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 30% of 800 = 240", "left after Monday: 800 - 240 = 560", "Tuesday: 25% of 560 = 140", "left after Tuesday: 560 - 140 = 420", "full pallets: 420 / 15 = 28"], "option_values": [37, 28, 44, 29], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 742, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:40 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:40 a.m. for 95 minutes. The booking ended at", "endings": [" 7:15 a.m.", " 9:45 a.m.", " 10:15 a.m.", " 9:15 a.m."], "source_id": "deeparithmark_v1_time_depth2_0742", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "555", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "ran half an hour long", "added an extra hour", "correct"], "solution_steps": ["convert the start: 460 minutes after midnight", "add the duration: 460 + 95 = 555 minutes"], "option_values": [435, 585, 615, 555], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 743, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $1.20 each and 4 erasers at $0.30 each. She split the total cost equally between herself and 3 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $1.20 each and 4 erasers at $0.30 each. She split the total cost equally between herself and 3 friends. Each person paid", "endings": [" $1.60.", " $2.10.", " $3.20.", " $2.40."], "source_id": "deeparithmark_v1_money_depth4_0743", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "240", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among two more people", "forgot the erasers", "split only between the friends", "correct"], "solution_steps": ["markers: 7 x 120 = 840", "erasers: 4 x 30 = 120", "total cost: 840 + 120 = 960", "split between 4 people: 960 / 4 = 240"], "option_values": [160, 210, 320, 240], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 744, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:22 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:22 a.m. for 65 minutes. The booking ended at", "endings": [" 6:27 a.m.", " 7:57 a.m.", " 7:27 a.m.", " 8:27 a.m."], "source_id": "deeparithmark_v1_time_depth2_0744", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "447", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "ran half an hour long", "correct", "added an extra hour"], "solution_steps": ["convert the start: 382 minutes after midnight", "add the duration: 382 + 65 = 447 minutes"], "option_values": [387, 477, 447, 507], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 745, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $11.00 an hour, and then 3 hours at $14.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $11.00 an hour, and then 3 hours at $14.00 an hour. He earned", "endings": [" $117.00.", " $126.00.", " $225.00.", " $108.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0745", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "10800", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["swapped the two rates", "paid every hour at the second rate", "added the rates together", "correct"], "solution_steps": ["first stretch: 6 x 1100 = 6600", "second stretch: 3 x 1400 = 4200", "total pay: 6600 + 4200 = 10800"], "option_values": [11700, 12600, 22500, 10800], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 746, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 310, then 90 units were shipped out, and 24 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 310, then 90 units were shipped out, and 24 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 105 crates.", " 108 crates.", " 119 crates.", " 35 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0746", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "119", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped twice and damaged twice", "shipped out twice", "correct", "packed the arriving units only"], "solution_steps": ["after delivery: 760 + 310 = 1070", "after shipping: 1070 - 90 = 980", "good units: 980 - 24 = 956", "full crates: 956 / 8 = 119 (remainder 4)"], "option_values": [105, 108, 119, 35], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 747, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $7.80.", " $4.80.", " $4.20.", " $11.40."], "source_id": "deeparithmark_v1_money_percent_depth2_0747", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "420", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the discount", "charged the handling fee twice", "correct", "added the discount instead of removing it"], "solution_steps": ["take 50% of 720 off: 720 - 360 = 360", "add the 60-cent fee: 360 + 60 = 420"], "option_values": [780, 480, 420, 1140], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 748, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:49 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:49 a.m. for 50 minutes. The booking ended at", "endings": [" 10:09 a.m.", " 9:09 a.m.", " 9:39 a.m.", " 8:39 a.m."], "source_id": "deeparithmark_v1_time_depth2_0748", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "519", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran an hour and a half long", "ran half an hour long", "added an extra hour", "correct"], "solution_steps": ["convert the start: 469 minutes after midnight", "add the duration: 469 + 50 = 519 minutes"], "option_values": [609, 549, 579, 519], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 749, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $24.00. A 30% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $24.00. A 30% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $4.88.", " $8.44.", " $5.89.", " $8.84."], "source_id": "deeparithmark_v1_percent_money_depth4_0749", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "884", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "used the coupon twice", "split the total among one more person", "correct"], "solution_steps": ["discount: 2400 - 720 = 1680", "tax on the discounted price: 1680 + 168 = 1848", "coupon: 1848 - 80 = 1768", "split 2 ways: 1768 / 2 = 884"], "option_values": [488, 844, 589, 884], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 750, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.20 was split between two teams in the ratio 5:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.20 was split between two teams in the ratio 5:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.35.", " $0.26.", " $0.31.", " $0.75."], "source_id": "deeparithmark_v1_ratio_depth5_0750", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "35", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "gave twice the share away to charity", "split among one more player", "forgot to deduct the fee"], "solution_steps": ["after the fee: 720 - 300 = 420", "one ratio part: 420 / 6 = 70", "larger share: 5 x 70 = 350", "after charity: 350 - 70 = 280", "per player: 280 / 8 = 35"], "option_values": [35, 26, 31, 75], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 751, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 36 pallets.", " 33 pallets.", " 22 pallets.", " 41 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0751", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "36", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "stacked on larger pallets", "took both percentages twice", "forgot Monday"], "solution_steps": ["Monday: 10% of 600 = 60", "left after Monday: 600 - 60 = 540", "Tuesday: 20% of 540 = 108", "left after Tuesday: 540 - 108 = 432", "full pallets: 432 / 12 = 36"], "option_values": [36, 33, 22, 41], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 752, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:50 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:50 a.m. for 50 minutes. The booking ended at", "endings": [" 8:10 a.m.", " 9:10 a.m.", " 8:40 a.m.", " 7:40 a.m."], "source_id": "deeparithmark_v1_time_depth2_0752", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "460", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran half an hour long", "ran an hour and a half long", "added an extra hour", "correct"], "solution_steps": ["convert the start: 410 minutes after midnight", "add the duration: 410 + 50 = 460 minutes"], "option_values": [490, 550, 520, 460], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 753, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $3.93.", " $4.39.", " $4.14.", " $4.37."], "source_id": "deeparithmark_v1_money_percent_depth2_0753", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "439", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "correct", "forgot the fee", "took the discount off the fee as well"], "solution_steps": ["take 10% of 460 off: 460 - 46 = 414", "add the 25-cent fee: 414 + 25 = 439"], "option_values": [393, 439, 414, 437], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 754, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:31 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:31 a.m. for 65 minutes. The booking ended at", "endings": [" 5:26 a.m.", " 6:36 a.m.", " 7:36 a.m.", " 7:21 a.m."], "source_id": "deeparithmark_v1_time_depth2_0754", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "456", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "dropped the hour carry", "correct", "stopped a quarter of an hour early"], "solution_steps": ["convert the start: 391 minutes after midnight", "add the duration: 391 + 65 = 456 minutes"], "option_values": [326, 396, 456, 441], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 755, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 129 pallets.", " 94 pallets.", " 95 pallets.", " 105 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0755", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "94", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["forgot Monday", "correct", "counted the loose sacks as a pallet", "forgot Tuesday"], "solution_steps": ["Monday: 25% of 1400 = 350", "left after Monday: 1400 - 350 = 1050", "Tuesday: 10% of 1050 = 105", "left after Tuesday: 1050 - 105 = 945", "full pallets: 945 / 10 = 94"], "option_values": [129, 94, 95, 105], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 756, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $1.90.", " $0.60.", " $5.40.", " $2.20."], "source_id": "deeparithmark_v1_money_percent_depth2_0756", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "220", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "took the percentage off twice", "added the discount instead of removing it", "correct"], "solution_steps": ["take 50% of 320 off: 320 - 160 = 160", "add the 60-cent fee: 160 + 60 = 220"], "option_values": [190, 60, 540, 220], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 757, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 25% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 25% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $5.05.", " $12.25.", " $9.85.", " $7.45."], "source_id": "deeparithmark_v1_money_percent_depth2_0757", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "745", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "added the discount instead of removing it", "forgot the discount", "correct"], "solution_steps": ["take 25% of 960 off: 960 - 240 = 720", "add the 25-cent fee: 720 + 25 = 745"], "option_values": [505, 1225, 985, 745], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 758, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $16.00 an hour and 4 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $649.80.", " $693.20.", " $678.60.", " $707.40."], "source_id": "deeparithmark_v1_money_rate_depth5_0758", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "67860", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at the normal rate", "taxed only the regular pay", "correct", "paid overtime at double rate"], "solution_steps": ["regular pay: 38 x 1600 = 60800", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 4 x 2400 = 9600", "gross with bonus: 60800 + 9600 + 5000 = 75400", "take-home: 75400 - 7540 = 67860"], "option_values": [64980, 69320, 67860, 70740], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 759, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 10% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 10% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 52 pallets.", " 54 pallets.", " 49 pallets.", " 28 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0759", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "54", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "correct", "stacked on larger pallets", "took both percentages twice"], "solution_steps": ["Monday: 10% of 800 = 80", "left after Monday: 800 - 80 = 720", "Tuesday: 25% of 720 = 180", "left after Tuesday: 720 - 180 = 540", "full pallets: 540 / 10 = 54"], "option_values": [52, 54, 49, 28], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 760, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:16 a.m.. The first session lasted 45 minutes, the break lasted 10 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:16 a.m.. The first session lasted 45 minutes, the break lasted 10 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 7:11 a.m.", " 7:51 a.m.", " 7:01 a.m.", " 6:51 a.m."], "source_id": "deeparithmark_v1_time_depth3_0760", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "471", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the second session", "correct", "forgot the last session and the break", "dropped the hour carry"], "solution_steps": ["after the first session: 376 + 45 = 421 minutes after midnight", "after the break: 421 + 10 = 431", "after the second session: 431 + 40 = 471"], "option_values": [431, 471, 421, 411], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 761, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 2 metres and 68 centimetres long. A worker cut off 115 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 2 metres and 68 centimetres long. A worker cut off 115 centimetres. The board left was", "endings": [" 53 centimetres.", " 153 centimetres.", " 85 centimetres.", " 483 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0761", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "153", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["cut a whole metre off as well", "correct", "forgot the extra centimetres", "added the cut and a whole metre"], "solution_steps": ["convert metres: 2 x 100 = 200 cm", "add the extra centimetres: 200 + 68 = 268 cm", "subtract the cut: 268 - 115 = 153 cm"], "option_values": [53, 153, 85, 483], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 762, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.20 was split between two teams in the ratio 4:2 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.20 was split between two teams in the ratio 4:2 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.17.", " $0.35.", " $1.05.", " $1.03."], "source_id": "deeparithmark_v1_ratio_depth5_0762", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "35", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "correct", "split the whole prize among one team", "forgot to deduct the fee"], "solution_steps": ["after the fee: 620 - 200 = 420", "one ratio part: 420 / 6 = 70", "larger share: 4 x 70 = 280", "after charity: 280 - 140 = 140", "per player: 140 / 4 = 35"], "option_values": [17, 35, 105, 103], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 763, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 620 units. A delivery added 240, then 90 units were shipped out, and 40 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 620 units. A delivery added 240, then 90 units were shipped out, and 40 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 81 crates.", " 25 crates.", " 91 crates.", " 96 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0763", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "91", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed into larger crates", "packed the arriving units only", "correct", "forgot the damaged units"], "solution_steps": ["after delivery: 620 + 240 = 860", "after shipping: 860 - 90 = 770", "good units: 770 - 40 = 730", "full crates: 730 / 8 = 91 (remainder 2)"], "option_values": [81, 25, 91, 96], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 764, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 67 pallets.", " 65 pallets.", " 63 pallets.", " 76 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0764", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "67", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "took both percentages off the original stock", "stacked on larger pallets", "forgot Monday"], "solution_steps": ["Monday: 10% of 1400 = 140", "left after Monday: 1400 - 140 = 1260", "Tuesday: 20% of 1260 = 252", "left after Tuesday: 1260 - 252 = 1008", "full pallets: 1008 / 15 = 67"], "option_values": [67, 65, 63, 76], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 765, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $1.20 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $1.20 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $4.60.", " $13.80.", " $5.60.", " $6.90."], "source_id": "deeparithmark_v1_money_depth4_0765", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "460", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "did not split the total at all", "charged the marker price for everything", "split only between the friends"], "solution_steps": ["markers: 8 x 120 = 960", "erasers: 6 x 70 = 420", "total cost: 960 + 420 = 1380", "split between 3 people: 1380 / 3 = 460"], "option_values": [460, 1380, 560, 690], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 766, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.50 was split between two teams in the ratio 4:1 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.50 was split between two teams in the ratio 4:1 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.21.", " $0.27.", " $0.07.", " $0.24."], "source_id": "deeparithmark_v1_ratio_depth5_0766", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "27", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "correct", "gave the larger share to the smaller ratio", "gave twice the share away to charity"], "solution_steps": ["after the fee: 650 - 500 = 150", "one ratio part: 150 / 5 = 30", "larger share: 4 x 30 = 120", "after charity: 120 - 12 = 108", "per player: 108 / 4 = 27"], "option_values": [21, 27, 7, 24], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 767, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 280 shirts. It sold 25% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 280 shirts. It sold 25% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 17 boxes.", " 19 boxes.", " 26 boxes.", " 8 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0767", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "26", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["sold twice as many", "took the percentage off the remainder again", "correct", "packed the sold shirts"], "solution_steps": ["sold: 25% of 280 = 70", "left over: 280 - 70 = 210", "full boxes: 210 / 8 = 26 (remainder 2)"], "option_values": [17, 19, 26, 8], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 768, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 260, then 170 units were shipped out, and 40 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 260, then 170 units were shipped out, and 40 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 67 crates.", " 62 crates.", " 74 crates.", " 81 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0768", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "67", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "packed into larger crates", "added the damaged units", "forgot the shipping"], "solution_steps": ["after delivery: 760 + 260 = 1020", "after shipping: 1020 - 170 = 850", "good units: 850 - 40 = 810", "full crates: 810 / 12 = 67 (remainder 6)"], "option_values": [67, 62, 74, 81], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 769, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $2.37.", " $2.28.", " $2.82.", " $2.65."], "source_id": "deeparithmark_v1_money_percent_depth2_0769", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "237", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the discount off the fee as well", "charged the handling fee twice", "read the percentage as a flat number of cents"], "solution_steps": ["take 20% of 240 off: 240 - 48 = 192", "add the 45-cent fee: 192 + 45 = 237"], "option_values": [237, 228, 282, 265], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 770, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:51 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:51 a.m. for 95 minutes. The booking ended at", "endings": [" 7:26 a.m.", " 9:56 a.m.", " 8:56 a.m.", " 8:26 a.m."], "source_id": "deeparithmark_v1_time_depth2_0770", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "506", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added the minutes without the hours", "ran an hour and a half long", "ran half an hour long", "correct"], "solution_steps": ["convert the start: 411 minutes after midnight", "add the duration: 411 + 95 = 506 minutes"], "option_values": [446, 596, 536, 506], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 771, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.50 was split between two teams in the ratio 4:3 after a $3.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.50 was split between two teams in the ratio 4:3 after a $3.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.43.", " $0.45.", " $0.36.", " $0.33."], "source_id": "deeparithmark_v1_ratio_depth5_0771", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "45", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the fee and the charity cut", "correct", "split among one more player", "swapped the ratio parts"], "solution_steps": ["after the fee: 650 - 300 = 350", "one ratio part: 350 / 7 = 50", "larger share: 4 x 50 = 200", "after charity: 200 - 20 = 180", "per player: 180 / 4 = 45"], "option_values": [43, 45, 36, 33], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 772, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:07 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:07 a.m. for 80 minutes. The booking ended at", "endings": [" 8:27 a.m.", " 8:57 a.m.", " 9:27 a.m.", " 9:57 a.m."], "source_id": "deeparithmark_v1_time_depth2_0772", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "507", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "ran half an hour long", "added an extra hour", "ran an hour and a half long"], "solution_steps": ["convert the start: 427 minutes after midnight", "add the duration: 427 + 80 = 507 minutes"], "option_values": [507, 537, 567, 597], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 773, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 800 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 800 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 65 pallets.", " 58 pallets.", " 57 pallets.", " 72 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0773", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "57", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["forgot Monday", "counted the loose sacks as a pallet", "correct", "forgot Tuesday"], "solution_steps": ["Monday: 10% of 800 = 80", "left after Monday: 800 - 80 = 720", "Tuesday: 20% of 720 = 144", "left after Tuesday: 720 - 144 = 576", "full pallets: 576 / 10 = 57"], "option_values": [65, 58, 57, 72], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 774, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 9 litres per minute for 10 minutes, then 7 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 9 litres per minute for 10 minutes, then 7 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "endings": [" 338 litres.", " 275 litres.", " 283 litres.", " 248 litres."], "source_id": "deeparithmark_v1_rate_depth4_0774", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "338", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "forgot the second fill", "drained twice", "forgot the first fill"], "solution_steps": ["first fill: 9 x 10 = 90 litres", "second fill: 7 x 9 = 63 litres", "before draining: 240 + 90 + 63 = 393", "after draining: 393 - 55 = 338"], "option_values": [338, 275, 283, 248], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 775, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $16.00. A 25% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $16.00. A 25% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $4.10.", " $12.60.", " $6.60.", " $6.30."], "source_id": "deeparithmark_v1_percent_money_depth4_0775", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "630", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "split the total among one fewer person", "forgot the coupon", "correct"], "solution_steps": ["discount: 1600 - 400 = 1200", "tax on the discounted price: 1200 + 120 = 1320", "coupon: 1320 - 60 = 1260", "split 2 ways: 1260 / 2 = 630"], "option_values": [410, 1260, 660, 630], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 776, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 360 shirts. It sold 30% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 360 shirts. It sold 30% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "endings": [" 42 boxes.", " 18 boxes.", " 29 boxes.", " 24 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0776", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "42", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "packed the sold shirts", "took the percentage off the remainder again", "sold twice as many"], "solution_steps": ["sold: 30% of 360 = 108", "left over: 360 - 108 = 252", "full boxes: 252 / 6 = 42 (remainder 0)"], "option_values": [42, 18, 29, 24], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 777, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:38 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:38 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 9:18 a.m.", " 9:33 a.m.", " 8:48 a.m.", " 8:33 a.m."], "source_id": "deeparithmark_v1_time_depth3_0777", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "513", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["finished half an hour late on top of the break", "counted the first session twice", "counted the break twice", "correct"], "solution_steps": ["after the first session: 398 + 60 = 458 minutes after midnight", "after the break: 458 + 15 = 473", "after the second session: 473 + 40 = 513"], "option_values": [558, 573, 528, 513], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 778, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 440 shirts. It sold 25% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 440 shirts. It sold 25% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 41 boxes.", " 27 boxes.", " 13 boxes.", " 49 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0778", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "41", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "sold twice as many", "packed the sold shirts", "sold only a tenth of the stock"], "solution_steps": ["sold: 25% of 440 = 110", "left over: 440 - 110 = 330", "full boxes: 330 / 8 = 41 (remainder 2)"], "option_values": [41, 27, 13, 49], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 779, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:38 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:38 a.m. for 110 minutes. The booking ended at", "endings": [" 8:28 a.m.", " 9:28 a.m.", " 10:13 a.m.", " 10:28 a.m."], "source_id": "deeparithmark_v1_time_depth2_0779", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "628", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "added the minutes without the hours", "stopped a quarter of an hour early", "correct"], "solution_steps": ["convert the start: 518 minutes after midnight", "add the duration: 518 + 110 = 628 minutes"], "option_values": [508, 568, 613, 628], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 780, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:04 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:04 a.m. for 110 minutes. The booking ended at", "endings": [" 6:14 a.m.", " 9:39 a.m.", " 9:54 a.m.", " 8:54 a.m."], "source_id": "deeparithmark_v1_time_depth2_0780", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "594", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "stopped a quarter of an hour early", "correct", "dropped the hour carry"], "solution_steps": ["convert the start: 484 minutes after midnight", "add the duration: 484 + 110 = 594 minutes"], "option_values": [374, 579, 594, 534], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 781, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $14.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $14.00 an hour and 6 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $422.80.", " $406.30.", " $487.90.", " $513.40."], "source_id": "deeparithmark_v1_money_rate_depth5_0781", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "51340", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "forgot the overtime", "forgot the bonus", "correct"], "solution_steps": ["regular pay: 32 x 1400 = 44800", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 6 x 2100 = 12600", "gross with bonus: 44800 + 12600 + 3000 = 60400", "take-home: 60400 - 9060 = 51340"], "option_values": [42280, 40630, 48790, 51340], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 782, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $8.20 was split between two teams in the ratio 4:3 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $8.20 was split between two teams in the ratio 4:3 after a $4.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.18.", " $0.24.", " $0.22.", " $0.52."], "source_id": "deeparithmark_v1_ratio_depth5_0782", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "24", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "correct", "gave the larger share to the smaller ratio", "split the whole prize among one team"], "solution_steps": ["after the fee: 820 - 400 = 420", "one ratio part: 420 / 7 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 48 = 192", "per player: 192 / 8 = 24"], "option_values": [18, 24, 22, 52], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 783, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 25% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 25% of them on Monday and 40% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 27 pallets.", " 24 pallets.", " 28 pallets.", " 45 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0783", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "27", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "stacked on larger pallets", "counted the loose sacks as a pallet", "forgot Tuesday"], "solution_steps": ["Monday: 25% of 600 = 150", "left after Monday: 600 - 150 = 450", "Tuesday: 40% of 450 = 180", "left after Tuesday: 450 - 180 = 270", "full pallets: 270 / 10 = 27"], "option_values": [27, 24, 28, 45], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 784, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 320 shirts. It sold 40% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 320 shirts. It sold 40% of them, then packed the rest into boxes of 9. The number of full boxes filled was", "endings": [" 21 boxes.", " 22 boxes.", " 64 boxes.", " 32 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0784", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "21", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "rounded the box count up", "divided by the number of boxes left over", "sold only a tenth of the stock"], "solution_steps": ["sold: 40% of 320 = 128", "left over: 320 - 128 = 192", "full boxes: 192 / 9 = 21 (remainder 3)"], "option_values": [21, 22, 64, 32], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 785, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 4 markers at $0.80 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 3 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 4 markers at $0.80 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 3 friends. Each person paid", "endings": [" $1.87.", " $2.46.", " $1.85.", " $2.22."], "source_id": "deeparithmark_v1_money_depth4_0785", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "185", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["added the unit prices instead of multiplying", "split only between the friends", "correct", "bought one extra of each item"], "solution_steps": ["markers: 4 x 80 = 320", "erasers: 6 x 70 = 420", "total cost: 320 + 420 = 740", "split between 4 people: 740 / 4 = 185"], "option_values": [187, 246, 185, 222], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 786, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:17 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:17 a.m. for 95 minutes. The booking ended at", "endings": [" 7:52 a.m.", " 8:37 a.m.", " 10:22 a.m.", " 8:52 a.m."], "source_id": "deeparithmark_v1_time_depth2_0786", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "532", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "stopped a quarter of an hour early", "ran an hour and a half long", "correct"], "solution_steps": ["convert the start: 437 minutes after midnight", "add the duration: 437 + 95 = 532 minutes"], "option_values": [472, 517, 622, 532], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 787, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $24.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $24.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $19.76.", " $6.58.", " $4.94.", " $5.14."], "source_id": "deeparithmark_v1_percent_money_depth4_0787", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "494", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["did not split the cost at all", "split the total among one fewer person", "correct", "added the coupon instead of subtracting it"], "solution_steps": ["discount: 2400 - 480 = 1920", "tax on the discounted price: 1920 + 96 = 2016", "coupon: 2016 - 40 = 1976", "split 4 ways: 1976 / 4 = 494"], "option_values": [1976, 658, 494, 514], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 788, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.90 was split between two teams in the ratio 4:3 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.90 was split between two teams in the ratio 4:3 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.98.", " $0.61.", " $0.56.", " $1.12."], "source_id": "deeparithmark_v1_ratio_depth5_0788", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "56", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot to deduct the fee", "forgot the fee and the charity cut", "correct", "divided between the teams instead of the players"], "solution_steps": ["after the fee: 690 - 200 = 490", "one ratio part: 490 / 7 = 70", "larger share: 4 x 70 = 280", "after charity: 280 - 56 = 224", "per player: 224 / 4 = 56"], "option_values": [98, 61, 56, 112], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 789, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 440 shirts. It sold 15% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 440 shirts. It sold 15% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "endings": [" 45 boxes.", " 31 boxes.", " 53 boxes.", " 44 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0789", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "53", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["took the percentage off the remainder again", "sold half the stock regardless of the percentage", "correct", "sold twice as many"], "solution_steps": ["sold: 15% of 440 = 66", "left over: 440 - 66 = 374", "full boxes: 374 / 7 = 53 (remainder 3)"], "option_values": [45, 31, 53, 44], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 790, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.90 was split between two teams in the ratio 4:3 after a $3.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.90 was split between two teams in the ratio 4:3 after a $3.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.23.", " $0.21.", " $0.28.", " $0.49."], "source_id": "deeparithmark_v1_ratio_depth5_0790", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "28", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "swapped the ratio parts", "correct", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 790 - 300 = 490", "one ratio part: 490 / 7 = 70", "larger share: 4 x 70 = 280", "after charity: 280 - 140 = 140", "per player: 140 / 5 = 28"], "option_values": [23, 21, 28, 49], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 791, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $8.28.", " $9.24.", " $9.18.", " $9.84."], "source_id": "deeparithmark_v1_money_percent_depth2_0791", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "924", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "correct", "took the discount off the fee as well", "charged the handling fee twice"], "solution_steps": ["take 10% of 960 off: 960 - 96 = 864", "add the 60-cent fee: 864 + 60 = 924"], "option_values": [828, 924, 918, 984], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 792, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $20.00. A 25% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 5 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $20.00. A 25% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 5 people split the final cost equally. Each paid", "endings": [" $2.04.", " $3.92.", " $3.46.", " $3.14."], "source_id": "deeparithmark_v1_percent_money_depth4_0792", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "314", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "split the total among one fewer person", "added the coupon instead of subtracting it", "correct"], "solution_steps": ["discount: 2000 - 500 = 1500", "tax on the discounted price: 1500 + 150 = 1650", "coupon: 1650 - 80 = 1570", "split 5 ways: 1570 / 5 = 314"], "option_values": [204, 392, 346, 314], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 793, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 560 units. A delivery added 180, then 140 units were shipped out, and 18 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 560 units. A delivery added 180, then 140 units were shipped out, and 18 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 44 crates.", " 18 crates.", " 64 crates.", " 65 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0793", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "64", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the delivery", "packed the arriving units only", "correct", "counted the loose units as a crate"], "solution_steps": ["after delivery: 560 + 180 = 740", "after shipping: 740 - 140 = 600", "good units: 600 - 18 = 582", "full crates: 582 / 9 = 64 (remainder 6)"], "option_values": [44, 18, 64, 65], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 794, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $3.29.", " $2.88.", " $3.33.", " $3.01."], "source_id": "deeparithmark_v1_money_percent_depth2_0794", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "333", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "forgot the fee", "correct", "took the percentage off twice"], "solution_steps": ["take 10% of 320 off: 320 - 32 = 288", "add the 45-cent fee: 288 + 45 = 333"], "option_values": [329, 288, 333, 301], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 795, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $9.90 was split between two teams in the ratio 5:2 after a $5.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $9.90 was split between two teams in the ratio 5:2 after a $5.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.87.", " $0.49.", " $0.98.", " $0.35."], "source_id": "deeparithmark_v1_ratio_depth5_0795", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "35", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["divided between the teams instead of the players", "took the charity cut off the whole prize", "split the whole prize among one team", "correct"], "solution_steps": ["after the fee: 990 - 500 = 490", "one ratio part: 490 / 7 = 70", "larger share: 5 x 70 = 350", "after charity: 350 - 175 = 175", "per player: 175 / 5 = 35"], "option_values": [87, 49, 98, 35], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 796, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:18 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:18 a.m. for 80 minutes. The booking ended at", "endings": [" 9:38 a.m.", " 8:38 a.m.", " 10:38 a.m.", " 10:08 a.m."], "source_id": "deeparithmark_v1_time_depth2_0796", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "578", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "dropped the hour carry", "added an extra hour", "ran half an hour long"], "solution_steps": ["convert the start: 498 minutes after midnight", "add the duration: 498 + 80 = 578 minutes"], "option_values": [578, 518, 638, 608], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 797, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 20% discount came off it, then 15% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 20% discount came off it, then 15% tax was added to the discounted price, and a $1.20 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $10.64.", " $15.96.", " $11.82.", " $15.36."], "source_id": "deeparithmark_v1_percent_money_depth4_0797", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "1596", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["split the total among one more person", "correct", "applied the discount twice", "used the coupon twice"], "solution_steps": ["discount: 3600 - 720 = 2880", "tax on the discounted price: 2880 + 432 = 3312", "coupon: 3312 - 120 = 3192", "split 2 ways: 3192 / 2 = 1596"], "option_values": [1064, 1596, 1182, 1536], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 798, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 12 litres per minute for 10 minutes, then 3 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 12 litres per minute for 10 minutes, then 3 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 185 litres.", " 325 litres.", " 275 litres.", " 255 litres."], "source_id": "deeparithmark_v1_rate_depth4_0798", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "185", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "added the drain instead of removing it", "added the rates and multiplied once", "forgot the drain"], "solution_steps": ["first fill: 12 x 10 = 120 litres", "second fill: 3 x 5 = 15 litres", "before draining: 120 + 120 + 15 = 255", "after draining: 255 - 70 = 185"], "option_values": [185, 325, 275, 255], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 799, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:27 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:27 a.m. for 125 minutes. The booking ended at", "endings": [" 8:32 a.m.", " 9:02 a.m.", " 9:32 a.m.", " 10:02 a.m."], "source_id": "deeparithmark_v1_time_depth2_0799", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "512", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "ran half an hour long", "added an extra hour", "ran an hour and a half long"], "solution_steps": ["convert the start: 387 minutes after midnight", "add the duration: 387 + 125 = 512 minutes"], "option_values": [512, 542, 572, 602], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 800, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 15 litres per minute for 4 minutes, then 5 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 15 litres per minute for 4 minutes, then 5 litres per minute for 5 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 165 litres.", " 205 litres.", " 245 litres.", " 215 litres."], "source_id": "deeparithmark_v1_rate_depth4_0800", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "165", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "forgot the drain", "added the drain instead of removing it", "used the first rate for both stages"], "solution_steps": ["first fill: 15 x 4 = 60 litres", "second fill: 5 x 5 = 25 litres", "before draining: 120 + 60 + 25 = 205", "after draining: 205 - 40 = 165"], "option_values": [165, 205, 245, 215], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 801, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 5 markers at $0.95 each and 4 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 5 markers at $0.95 each and 4 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.07.", " $1.84.", " $1.88.", " $1.51."], "source_id": "deeparithmark_v1_money_depth4_0801", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "151", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split among two more people", "bought one extra of each item", "split only between the friends", "correct"], "solution_steps": ["markers: 5 x 95 = 475", "erasers: 4 x 70 = 280", "total cost: 475 + 280 = 755", "split between 5 people: 755 / 5 = 151"], "option_values": [107, 184, 188, 151], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 802, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 420 units. A delivery added 260, then 170 units were shipped out, and 18 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 420 units. A delivery added 260, then 170 units were shipped out, and 18 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "endings": [" 35 crates.", " 17 crates.", " 37 crates.", " 47 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0802", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "35", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "packed the arriving units only", "added the damaged units", "forgot the shipping"], "solution_steps": ["after delivery: 420 + 260 = 680", "after shipping: 680 - 170 = 510", "good units: 510 - 18 = 492", "full crates: 492 / 14 = 35 (remainder 2)"], "option_values": [35, 17, 37, 47], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 803, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:36 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:36 a.m. for 50 minutes. The booking ended at", "endings": [" 7:26 a.m.", " 7:11 a.m.", " 8:26 a.m.", " 8:56 a.m."], "source_id": "deeparithmark_v1_time_depth2_0803", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "446", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "stopped a quarter of an hour early", "added an extra hour", "ran an hour and a half long"], "solution_steps": ["convert the start: 396 minutes after midnight", "add the duration: 396 + 50 = 446 minutes"], "option_values": [446, 431, 506, 536], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 804, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 36 km at 18 km/h, rested 25 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 36 km at 18 km/h, rested 25 minutes, then walked 15 km at 5 km/h. Her total time, in minutes, was", "endings": [" 145 minutes.", " 85 minutes.", " 325 minutes.", " 195 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0804", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "325", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "divided by the speed twice", "correct", "used the cycling speed for both legs"], "solution_steps": ["cycling time: 60 x 36 / 18 = 120 minutes", "walking time: 60 x 15 / 5 = 180 minutes", "add the rest: 120 + 25 + 180 = 325 minutes"], "option_values": [145, 85, 325, 195], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 805, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $11.00 an hour, and then 4 hours at $13.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $11.00 an hour, and then 4 hours at $13.00 an hour. He earned", "endings": [" $72.00.", " $96.00.", " $85.00.", " $44.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0805", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "9600", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["worked one hour less in each stretch", "correct", "worked one hour less in the first stretch", "forgot the second stretch"], "solution_steps": ["first stretch: 4 x 1100 = 4400", "second stretch: 4 x 1300 = 5200", "total pay: 4400 + 5200 = 9600"], "option_values": [7200, 9600, 8500, 4400], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 806, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $14.00 an hour and 8 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $14.00 an hour and 8 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 25% of the total was withheld for tax. Jo took home", "endings": [" $504.00.", " $576.00.", " $534.00.", " $712.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0806", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "53400", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "paid overtime at double rate", "correct", "forgot the tax"], "solution_steps": ["regular pay: 36 x 1400 = 50400", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 8 x 2100 = 16800", "gross with bonus: 50400 + 16800 + 4000 = 71200", "take-home: 71200 - 17800 = 53400"], "option_values": [50400, 57600, 53400, 71200], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 807, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:12 a.m.. The first session lasted 60 minutes, the break lasted 10 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:12 a.m.. The first session lasted 60 minutes, the break lasted 10 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 7:12 a.m.", " 8:02 a.m.", " 9:12 a.m.", " 8:12 a.m."], "source_id": "deeparithmark_v1_time_depth3_0807", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "492", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the last session and the break", "forgot the break", "counted the first session twice", "correct"], "solution_steps": ["after the first session: 372 + 60 = 432 minutes after midnight", "after the break: 432 + 10 = 442", "after the second session: 442 + 50 = 492"], "option_values": [432, 482, 552, 492], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 808, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:22 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:22 a.m. for 125 minutes. The booking ended at", "endings": [" 10:57 a.m.", " 9:57 a.m.", " 9:27 a.m.", " 10:27 a.m."], "source_id": "deeparithmark_v1_time_depth2_0808", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "567", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran an hour and a half long", "ran half an hour long", "correct", "added an extra hour"], "solution_steps": ["convert the start: 442 minutes after midnight", "add the duration: 442 + 125 = 567 minutes"], "option_values": [657, 597, 567, 627], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 809, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 6 litres per minute for 6 minutes, then 5 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 6 litres per minute for 6 minutes, then 5 litres per minute for 9 minutes. A drain then removed 55 litres. The tank then held", "endings": [" 376 litres.", " 321 litres.", " 266 litres.", " 275 litres."], "source_id": "deeparithmark_v1_rate_depth4_0809", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "266", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["added the drain instead of removing it", "forgot the drain", "correct", "used the first rate for both stages"], "solution_steps": ["first fill: 6 x 6 = 36 litres", "second fill: 5 x 9 = 45 litres", "before draining: 240 + 36 + 45 = 321", "after draining: 321 - 55 = 266"], "option_values": [376, 321, 266, 275], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 810, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $4.10 was split between two teams in the ratio 4:3 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $4.10 was split between two teams in the ratio 4:3 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.26.", " $0.15.", " $0.22.", " $0.58."], "source_id": "deeparithmark_v1_ratio_depth5_0810", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "15", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["took the charity cut off the whole prize", "correct", "gave the larger share to the smaller ratio", "forgot to deduct the fee"], "solution_steps": ["after the fee: 410 - 200 = 210", "one ratio part: 210 / 7 = 30", "larger share: 4 x 30 = 120", "after charity: 120 - 60 = 60", "per player: 60 / 4 = 15"], "option_values": [26, 15, 22, 58], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 811, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 30% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 30% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 28 pallets.", " 35 pallets.", " 43 pallets.", " 29 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0811", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "28", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "forgot Tuesday", "forgot Monday", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 30% of 600 = 180", "left after Monday: 600 - 180 = 420", "Tuesday: 20% of 420 = 84", "left after Tuesday: 420 - 84 = 336", "full pallets: 336 / 12 = 28"], "option_values": [28, 35, 43, 29], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 812, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 480 shirts. It sold 30% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 480 shirts. It sold 30% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "endings": [" 48 boxes.", " 33 boxes.", " 61 boxes.", " 68 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0812", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "48", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "took the percentage off the remainder again", "sold only a tenth of the stock", "packed the whole stock, not the rest"], "solution_steps": ["sold: 30% of 480 = 144", "left over: 480 - 144 = 336", "full boxes: 336 / 7 = 48 (remainder 0)"], "option_values": [48, 33, 61, 68], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 813, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 25% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 25% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $1.65.", " $2.14.", " $2.25.", " $2.85."], "source_id": "deeparithmark_v1_money_percent_depth2_0813", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "225", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "took the discount off the fee as well", "correct", "forgot the discount"], "solution_steps": ["take 25% of 240 off: 240 - 60 = 180", "add the 45-cent fee: 180 + 45 = 225"], "option_values": [165, 214, 225, 285], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 814, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 40 km at 20 km/h, rested 12 minutes, then walked 10 km at 5 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 40 km at 20 km/h, rested 12 minutes, then walked 10 km at 5 km/h. Her total time, in minutes, was", "endings": [" 132 minutes.", " 162 minutes.", " 612 minutes.", " 252 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0814", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "252", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "used the cycling speed for both legs", "used the walking speed for both legs", "correct"], "solution_steps": ["cycling time: 60 x 40 / 20 = 120 minutes", "walking time: 60 x 10 / 5 = 120 minutes", "add the rest: 120 + 12 + 120 = 252 minutes"], "option_values": [132, 162, 612, 252], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 815, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 240, then 140 units were shipped out, and 40 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 240, then 140 units were shipped out, and 40 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 72 crates.", " 85 crates.", " 102 crates.", " 91 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0815", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "102", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the delivery", "shipped out twice", "correct", "packed into larger crates"], "solution_steps": ["after delivery: 760 + 240 = 1000", "after shipping: 1000 - 140 = 860", "good units: 860 - 40 = 820", "full crates: 820 / 8 = 102 (remainder 4)"], "option_values": [72, 85, 102, 91], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 816, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:22 a.m.. The first session lasted 45 minutes, the break lasted 10 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:22 a.m.. The first session lasted 45 minutes, the break lasted 10 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "endings": [" 8:02 a.m.", " 7:07 a.m.", " 7:17 a.m.", " 8:42 a.m."], "source_id": "deeparithmark_v1_time_depth3_0816", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "482", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["correct", "forgot the last session and the break", "forgot the second session", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 382 + 45 = 427 minutes after midnight", "after the break: 427 + 10 = 437", "after the second session: 437 + 45 = 482"], "option_values": [482, 427, 437, 522], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 817, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 81 pallets.", " 42 pallets.", " 73 pallets.", " 78 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0817", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "81", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "took both percentages twice", "stacked on larger pallets", "took both percentages off the original stock"], "solution_steps": ["Monday: 25% of 1200 = 300", "left after Monday: 1200 - 300 = 900", "Tuesday: 10% of 900 = 90", "left after Tuesday: 900 - 90 = 810", "full pallets: 810 / 10 = 81"], "option_values": [81, 42, 73, 78], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 818, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:03 a.m.. The first session lasted 45 minutes, the break lasted 20 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:03 a.m.. The first session lasted 45 minutes, the break lasted 20 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "endings": [" 7:53 a.m.", " 7:48 a.m.", " 8:53 a.m.", " 9:13 a.m."], "source_id": "deeparithmark_v1_time_depth3_0818", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "533", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["dropped the hour carry", "forgot the last session and the break", "correct", "counted the break twice"], "solution_steps": ["after the first session: 423 + 45 = 468 minutes after midnight", "after the break: 468 + 20 = 488", "after the second session: 488 + 45 = 533"], "option_values": [473, 468, 533, 553], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 819, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1000 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1000 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 57 pallets.", " 77 pallets.", " 56 pallets.", " 62 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0819", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "56", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["counted the loose sacks as a pallet", "forgot Monday", "correct", "forgot Tuesday"], "solution_steps": ["Monday: 25% of 1000 = 250", "left after Monday: 1000 - 250 = 750", "Tuesday: 10% of 750 = 75", "left after Tuesday: 750 - 75 = 675", "full pallets: 675 / 12 = 56"], "option_values": [57, 77, 56, 62], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 820, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $0.60 each and 5 erasers at $0.30 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $0.60 each and 5 erasers at $0.30 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.02.", " $1.27.", " $1.04.", " $1.32."], "source_id": "deeparithmark_v1_money_depth4_0820", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "102", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "split only between the friends", "added the unit prices instead of multiplying", "charged the marker price for everything"], "solution_steps": ["markers: 6 x 60 = 360", "erasers: 5 x 30 = 150", "total cost: 360 + 150 = 510", "split between 5 people: 510 / 5 = 102"], "option_values": [102, 127, 104, 132], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 821, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 420 units. A delivery added 180, then 140 units were shipped out, and 40 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 420 units. A delivery added 180, then 140 units were shipped out, and 40 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 8 crates.", " 26 crates.", " 17 crates.", " 31 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0821", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "26", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed the arriving units only", "correct", "shipped out twice", "added the damaged units"], "solution_steps": ["after delivery: 420 + 180 = 600", "after shipping: 600 - 140 = 460", "good units: 460 - 40 = 420", "full crates: 420 / 16 = 26 (remainder 4)"], "option_values": [8, 26, 17, 31], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 822, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $28.00. A 30% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $28.00. A 30% discount came off it, then 10% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $10.38.", " $9.98.", " $11.18.", " $20.76."], "source_id": "deeparithmark_v1_percent_money_depth4_0822", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "1038", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "used the coupon twice", "added the coupon instead of subtracting it", "split the total among one fewer person"], "solution_steps": ["discount: 2800 - 840 = 1960", "tax on the discounted price: 1960 + 196 = 2156", "coupon: 2156 - 80 = 2076", "split 2 ways: 2076 / 2 = 1038"], "option_values": [1038, 998, 1118, 2076], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 823, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 620 units. A delivery added 180, then 140 units were shipped out, and 24 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 620 units. A delivery added 180, then 140 units were shipped out, and 24 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "endings": [" 35 crates.", " 47 crates.", " 45 crates.", " 55 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0823", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "45", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped out twice", "forgot the damaged units", "correct", "forgot the shipping"], "solution_steps": ["after delivery: 620 + 180 = 800", "after shipping: 800 - 140 = 660", "good units: 660 - 24 = 636", "full crates: 636 / 14 = 45 (remainder 6)"], "option_values": [35, 47, 45, 55], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 824, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 480 units. A delivery added 260, then 90 units were shipped out, and 24 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 480 units. A delivery added 260, then 90 units were shipped out, and 24 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 22 crates.", " 36 crates.", " 44 crates.", " 39 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0824", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "39", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the delivery", "packed into larger crates", "forgot the shipping", "correct"], "solution_steps": ["after delivery: 480 + 260 = 740", "after shipping: 740 - 90 = 650", "good units: 650 - 24 = 626", "full crates: 626 / 16 = 39 (remainder 2)"], "option_values": [22, 36, 44, 39], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 825, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $2.92.", " $3.65.", " $3.01.", " $4.29."], "source_id": "deeparithmark_v1_money_percent_depth2_0825", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "301", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "forgot the discount", "correct", "added the discount instead of removing it"], "solution_steps": ["take 20% of 320 off: 320 - 64 = 256", "add the 45-cent fee: 256 + 45 = 301"], "option_values": [292, 365, 301, 429], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 826, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 25% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 25% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $7.40.", " $9.10.", " $6.30.", " $5.70."], "source_id": "deeparithmark_v1_money_percent_depth2_0826", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "570", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the discount", "added the discount instead of removing it", "charged the handling fee twice", "correct"], "solution_steps": ["take 25% of 680 off: 680 - 170 = 510", "add the 60-cent fee: 510 + 60 = 570"], "option_values": [740, 910, 630, 570], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 827, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.10 was split between two teams in the ratio 2:1 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.10 was split between two teams in the ratio 2:1 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.07.", " $0.13.", " $0.56.", " $0.14."], "source_id": "deeparithmark_v1_ratio_depth5_0827", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "14", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "forgot the fee and the charity cut", "divided between the teams instead of the players", "correct"], "solution_steps": ["after the fee: 710 - 500 = 210", "one ratio part: 210 / 3 = 70", "larger share: 2 x 70 = 140", "after charity: 140 - 28 = 112", "per player: 112 / 8 = 14"], "option_values": [7, 13, 56, 14], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 828, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $20.00 an hour and 4 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $20.00 an hour and 4 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $1116.00.", " $776.00.", " $778.00.", " $744.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0828", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "74400", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["added the tax instead of withholding it", "paid overtime at double rate", "taxed only the regular pay", "correct"], "solution_steps": ["regular pay: 38 x 2000 = 76000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 4 x 3000 = 12000", "gross with bonus: 76000 + 12000 + 5000 = 93000", "take-home: 93000 - 18600 = 74400"], "option_values": [111600, 77600, 77800, 74400], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 829, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 50% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 50% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $3.75.", " $3.68.", " $10.95.", " $6.85."], "source_id": "deeparithmark_v1_money_percent_depth2_0829", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "375", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "took the discount off the fee as well", "added the discount instead of removing it", "read the percentage as a flat number of cents"], "solution_steps": ["take 50% of 720 off: 720 - 360 = 360", "add the 15-cent fee: 360 + 15 = 375"], "option_values": [375, 368, 1095, 685], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 830, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:12 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:12 a.m. for 50 minutes. The booking ended at", "endings": [" 7:22 a.m.", " 9:02 a.m.", " 8:02 a.m.", " 8:47 a.m."], "source_id": "deeparithmark_v1_time_depth2_0830", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "542", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "correct", "dropped the hour carry", "stopped a quarter of an hour early"], "solution_steps": ["convert the start: 492 minutes after midnight", "add the duration: 492 + 50 = 542 minutes"], "option_values": [442, 542, 482, 527], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 831, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $18.00 an hour and 4 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $745.20.", " $694.40.", " $781.20.", " $954.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0831", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "78120", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "taxed twice", "correct", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 40 x 1800 = 72000", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 4 x 2700 = 10800", "gross with bonus: 72000 + 10800 + 4000 = 86800", "take-home: 86800 - 8680 = 78120"], "option_values": [74520, 69440, 78120, 95480], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 832, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $10.60 was split between two teams in the ratio 5:3 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $10.60 was split between two teams in the ratio 5:3 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.46.", " $0.56.", " $0.42.", " $0.33."], "source_id": "deeparithmark_v1_ratio_depth5_0832", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "56", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "correct", "gave the larger share to the smaller ratio", "swapped the ratio parts"], "solution_steps": ["after the fee: 1060 - 500 = 560", "one ratio part: 560 / 8 = 70", "larger share: 5 x 70 = 350", "after charity: 350 - 70 = 280", "per player: 280 / 5 = 56"], "option_values": [46, 56, 42, 33], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 833, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 4 markers at $0.80 each and 3 erasers at $0.50 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 4 markers at $0.80 each and 3 erasers at $0.50 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $0.88.", " $0.64.", " $0.94.", " $0.95."], "source_id": "deeparithmark_v1_money_depth4_0833", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "94", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["swapped the two unit prices", "forgot the erasers", "correct", "added the unit prices instead of multiplying"], "solution_steps": ["markers: 4 x 80 = 320", "erasers: 3 x 50 = 150", "total cost: 320 + 150 = 470", "split between 5 people: 470 / 5 = 94"], "option_values": [88, 64, 94, 95], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 834, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:01 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:01 a.m. for 110 minutes. The booking ended at", "endings": [" 8:51 a.m.", " 8:36 a.m.", " 7:51 a.m.", " 5:11 a.m."], "source_id": "deeparithmark_v1_time_depth2_0834", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "531", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "stopped a quarter of an hour early", "dropped the hour carry", "subtracted the duration instead of adding it"], "solution_steps": ["convert the start: 421 minutes after midnight", "add the duration: 421 + 110 = 531 minutes"], "option_values": [531, 516, 471, 311], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 835, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $541.80.", " $550.80.", " $433.80.", " $595.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0835", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "59580", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at the normal rate", "forgot the bonus", "forgot the overtime", "correct"], "solution_steps": ["regular pay: 36 x 1200 = 43200", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 10 x 1800 = 18000", "gross with bonus: 43200 + 18000 + 5000 = 66200", "take-home: 66200 - 6620 = 59580"], "option_values": [54180, 55080, 43380, 59580], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 836, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 30% discount came off it, then 5% tax was added to the discounted price, and a $1.20 coupon was applied last. 3 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 30% discount came off it, then 5% tax was added to the discounted price, and a $1.20 coupon was applied last. 3 people split the final cost equally. Each paid", "endings": [" $8.42.", " $9.22.", " $8.82.", " $12.63."], "source_id": "deeparithmark_v1_percent_money_depth4_0836", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "842", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "added the coupon instead of subtracting it", "forgot the coupon", "split the total among one fewer person"], "solution_steps": ["discount: 3600 - 1080 = 2520", "tax on the discounted price: 2520 + 126 = 2646", "coupon: 2646 - 120 = 2526", "split 3 ways: 2526 / 3 = 842"], "option_values": [842, 922, 882, 1263], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 837, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 12 litres per minute for 8 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 12 litres per minute for 8 minutes, then 5 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 291 litres.", " 266 litres.", " 391 litres.", " 361 litres."], "source_id": "deeparithmark_v1_rate_depth4_0837", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "291", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "forgot the second fill", "added the rates and multiplied once", "forgot the drain"], "solution_steps": ["first fill: 12 x 8 = 96 litres", "second fill: 5 x 5 = 25 litres", "before draining: 240 + 96 + 25 = 361", "after draining: 361 - 70 = 291"], "option_values": [291, 266, 391, 361], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 838, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Dara baked 120 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Dara baked 120 biscuits. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 10 biscuits.", " 30 biscuits.", " 80 biscuits.", " 20 biscuits."], "source_id": "deeparithmark_v1_fractions_depth3_0838", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "20", "unit": "biscuits", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["split the given-away cookies too", "split all the cookies, not the rest", "stopped after giving the third away", "correct"], "solution_steps": ["one third given away: 120 / 3 = 40", "rest kept: 120 - 40 = 80", "split among 4: 80 / 4 = 20"], "option_values": [10, 30, 80, 20], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 839, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 6 litres per minute for 8 minutes, then 5 litres per minute for 7 minutes. A drain then removed 25 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 6 litres per minute for 8 minutes, then 5 litres per minute for 7 minutes. A drain then removed 25 litres. The tank then held", "endings": [" 238 litres.", " 288 litres.", " 263 litres.", " 245 litres."], "source_id": "deeparithmark_v1_rate_depth4_0839", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "238", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "added the drain instead of removing it", "forgot the drain", "used the first rate for both stages"], "solution_steps": ["first fill: 6 x 8 = 48 litres", "second fill: 5 x 7 = 35 litres", "before draining: 180 + 48 + 35 = 263", "after draining: 263 - 25 = 238"], "option_values": [238, 288, 263, 245], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 840, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 480 shirts. It sold 55% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 480 shirts. It sold 55% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 28 boxes.", " 54 boxes.", " 33 boxes.", " 27 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0840", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "27", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["counted the loose shirts as a box", "sold only a tenth of the stock", "packed the sold shirts", "correct"], "solution_steps": ["sold: 55% of 480 = 264", "left over: 480 - 264 = 216", "full boxes: 216 / 8 = 27 (remainder 0)"], "option_values": [28, 54, 33, 27], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 841, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 2 metres and 38 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 2 metres and 38 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 193 centimetres.", " 155 centimetres.", " 383 centimetres.", " 203 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0841", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "193", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["correct", "forgot the extra centimetres", "added the cut and a whole metre", "stopped ten centimetres short of the cut"], "solution_steps": ["convert metres: 2 x 100 = 200 cm", "add the extra centimetres: 200 + 38 = 238 cm", "subtract the cut: 238 - 45 = 193 cm"], "option_values": [193, 155, 383, 203], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 842, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.50 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.50 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.14.", " $0.43.", " $0.87.", " $0.56."], "source_id": "deeparithmark_v1_ratio_depth5_0842", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "56", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "forgot the fee and the charity cut", "split the whole prize among one team", "correct"], "solution_steps": ["after the fee: 650 - 300 = 350", "one ratio part: 350 / 5 = 70", "larger share: 4 x 70 = 280", "after charity: 280 - 56 = 224", "per player: 224 / 4 = 56"], "option_values": [14, 43, 87, 56], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 843, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $18.00 an hour and 8 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $18.00 an hour and 8 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $707.20.", " $768.40.", " $745.60.", " $956.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0843", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "70720", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "paid overtime at double rate", "taxed only the regular pay", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 32 x 1800 = 57600", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 8 x 2700 = 21600", "gross with bonus: 57600 + 21600 + 4000 = 83200", "take-home: 83200 - 12480 = 70720"], "option_values": [70720, 76840, 74560, 95680], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 844, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $24.00. A 25% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $24.00. A 25% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $6.30.", " $9.30.", " $9.60.", " $6.40."], "source_id": "deeparithmark_v1_percent_money_depth4_0844", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "960", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "used the coupon twice", "correct", "split the total among one more person"], "solution_steps": ["discount: 2400 - 600 = 1800", "tax on the discounted price: 1800 + 180 = 1980", "coupon: 1980 - 60 = 1920", "split 2 ways: 1920 / 2 = 960"], "option_values": [630, 930, 960, 640], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 845, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:31 a.m.. The first session lasted 70 minutes, the break lasted 25 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:31 a.m.. The first session lasted 70 minutes, the break lasted 25 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "endings": [" 9:51 a.m.", " 9:06 a.m.", " 8:41 a.m.", " 9:36 a.m."], "source_id": "deeparithmark_v1_time_depth3_0845", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "521", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["counted the first session twice", "counted the break twice", "correct", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 391 + 70 = 461 minutes after midnight", "after the break: 461 + 25 = 486", "after the second session: 486 + 35 = 521"], "option_values": [591, 546, 521, 576], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 846, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 12 litres per minute for 10 minutes, then 7 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 12 litres per minute for 10 minutes, then 7 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 189 litres.", " 389 litres.", " 349 litres.", " 309 litres."], "source_id": "deeparithmark_v1_rate_depth4_0846", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "309", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the first fill", "added the drain instead of removing it", "forgot the drain", "correct"], "solution_steps": ["first fill: 12 x 10 = 120 litres", "second fill: 7 x 7 = 49 litres", "before draining: 180 + 120 + 49 = 349", "after draining: 349 - 40 = 309"], "option_values": [189, 389, 349, 309], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 847, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 25% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 5 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 25% discount came off it, then 15% tax was added to the discounted price, and a $0.80 coupon was applied last. 5 people split the final cost equally. Each paid", "endings": [" $3.98.", " $5.89.", " $6.05.", " $8.28."], "source_id": "deeparithmark_v1_percent_money_depth4_0847", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "605", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["applied the discount twice", "used the coupon twice", "correct", "forgot the discount and the coupon"], "solution_steps": ["discount: 3600 - 900 = 2700", "tax on the discounted price: 2700 + 405 = 3105", "coupon: 3105 - 80 = 3025", "split 5 ways: 3025 / 5 = 605"], "option_values": [398, 589, 605, 828], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 848, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $4.50 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $4.50 was split between two teams in the ratio 4:1 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.09.", " $0.03.", " $0.12.", " $0.45."], "source_id": "deeparithmark_v1_ratio_depth5_0848", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "12", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["gave twice the share away to charity", "gave the larger share to the smaller ratio", "correct", "forgot to deduct the fee"], "solution_steps": ["after the fee: 450 - 300 = 150", "one ratio part: 150 / 5 = 30", "larger share: 4 x 30 = 120", "after charity: 120 - 24 = 96", "per player: 96 / 8 = 12"], "option_values": [9, 3, 12, 45], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 849, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 9 litres per minute for 4 minutes, then 7 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 9 litres per minute for 4 minutes, then 7 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 231 litres.", " 301 litres.", " 266 litres.", " 265 litres."], "source_id": "deeparithmark_v1_rate_depth4_0849", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "301", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "correct", "forgot the second fill", "forgot the first fill"], "solution_steps": ["first fill: 9 x 4 = 36 litres", "second fill: 7 x 5 = 35 litres", "before draining: 300 + 36 + 35 = 371", "after draining: 371 - 70 = 301"], "option_values": [231, 301, 266, 265], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 850, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $2.04.", " $1.92.", " $3.12.", " $2.52."], "source_id": "deeparithmark_v1_money_percent_depth2_0850", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "252", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "forgot the fee", "charged the handling fee twice", "correct"], "solution_steps": ["take 20% of 240 off: 240 - 48 = 192", "add the 60-cent fee: 192 + 60 = 252"], "option_values": [204, 192, 312, 252], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 851, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 3 metres and 74 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 3 metres and 74 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 329 centimetres.", " 419 centimetres.", " 519 centimetres.", " 403 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0851", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "329", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["correct", "added the cut instead of removing it", "added the cut and a whole metre", "counted the extra centimetres twice"], "solution_steps": ["convert metres: 3 x 100 = 300 cm", "add the extra centimetres: 300 + 74 = 374 cm", "subtract the cut: 374 - 45 = 329 cm"], "option_values": [329, 419, 519, 403], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 852, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:16 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:16 a.m. for 125 minutes. The booking ended at", "endings": [" 4:11 a.m.", " 7:21 a.m.", " 9:21 a.m.", " 8:21 a.m."], "source_id": "deeparithmark_v1_time_depth2_0852", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "501", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "forgot the last full hour", "added an extra hour", "correct"], "solution_steps": ["convert the start: 376 minutes after midnight", "add the duration: 376 + 125 = 501 minutes"], "option_values": [251, 441, 561, 501], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 853, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $7.00 was split between two teams in the ratio 3:1 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $7.00 was split between two teams in the ratio 3:1 after a $5.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.24.", " $0.08.", " $0.18.", " $0.32."], "source_id": "deeparithmark_v1_ratio_depth5_0853", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "24", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "swapped the ratio parts", "gave twice the share away to charity", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 700 - 500 = 200", "one ratio part: 200 / 4 = 50", "larger share: 3 x 50 = 150", "after charity: 150 - 30 = 120", "per player: 120 / 5 = 24"], "option_values": [24, 8, 18, 32], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 854, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $20.00 an hour and 10 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $20.00 an hour and 10 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $846.00.", " $783.00.", " $873.00.", " $906.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0854", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "87300", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "paid overtime at the normal rate", "correct", "taxed only the regular pay"], "solution_steps": ["regular pay: 32 x 2000 = 64000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 10 x 3000 = 30000", "gross with bonus: 64000 + 30000 + 3000 = 97000", "take-home: 97000 - 9700 = 87300"], "option_values": [84600, 78300, 87300, 90600], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 855, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:57 a.m.. The first session lasted 45 minutes, the break lasted 20 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:57 a.m.. The first session lasted 45 minutes, the break lasted 20 minutes, and the second session lasted 40 minutes. Rehearsal ended at", "endings": [" 8:22 a.m.", " 7:42 a.m.", " 8:42 a.m.", " 8:02 a.m."], "source_id": "deeparithmark_v1_time_depth3_0855", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "522", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the break", "added the minutes but not the hours", "correct", "forgot the second session"], "solution_steps": ["after the first session: 417 + 45 = 462 minutes after midnight", "after the break: 462 + 20 = 482", "after the second session: 482 + 40 = 522"], "option_values": [502, 462, 522, 482], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 856, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 20 km at 20 km/h, rested 25 minutes, then walked 8 km at 4 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 20 km at 20 km/h, rested 25 minutes, then walked 8 km at 4 km/h. Her total time, in minutes, was", "endings": [" 85 minutes.", " 205 minutes.", " 109 minutes.", " 445 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0856", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "205", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["forgot the walking leg", "correct", "used the cycling speed for both legs", "used the walking speed for both legs"], "solution_steps": ["cycling time: 60 x 20 / 20 = 60 minutes", "walking time: 60 x 8 / 4 = 120 minutes", "add the rest: 60 + 25 + 120 = 205 minutes"], "option_values": [85, 205, 109, 445], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 857, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 7:49 a.m.. The first session lasted 60 minutes, the break lasted 10 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 7:49 a.m.. The first session lasted 60 minutes, the break lasted 10 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 9:49 a.m.", " 10:49 a.m.", " 10:29 a.m.", " 9:59 a.m."], "source_id": "deeparithmark_v1_time_depth3_0857", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "589", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["correct", "counted the first session twice", "finished half an hour late on top of the break", "counted the break twice"], "solution_steps": ["after the first session: 469 + 60 = 529 minutes after midnight", "after the break: 529 + 10 = 539", "after the second session: 539 + 50 = 589"], "option_values": [589, 649, 629, 599], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 858, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 480 shirts. It sold 55% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 480 shirts. It sold 55% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "endings": [" 44 boxes.", " 72 boxes.", " 37 boxes.", " 36 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0858", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "36", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the sold shirts", "sold only a tenth of the stock", "counted the loose shirts as a box", "correct"], "solution_steps": ["sold: 55% of 480 = 264", "left over: 480 - 264 = 216", "full boxes: 216 / 6 = 36 (remainder 0)"], "option_values": [44, 72, 37, 36], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 859, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 620 units. A delivery added 130, then 170 units were shipped out, and 24 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 620 units. A delivery added 130, then 170 units were shipped out, and 24 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 61 crates.", " 69 crates.", " 45 crates.", " 72 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0859", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "69", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed into larger crates", "correct", "shipped twice and damaged twice", "forgot the damaged units"], "solution_steps": ["after delivery: 620 + 130 = 750", "after shipping: 750 - 170 = 580", "good units: 580 - 24 = 556", "full crates: 556 / 8 = 69 (remainder 4)"], "option_values": [61, 69, 45, 72], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 860, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 25% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 25% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $6.30.", " $7.50.", " $6.90.", " $11.10."], "source_id": "deeparithmark_v1_money_percent_depth2_0860", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "690", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "charged the handling fee twice", "correct", "added the discount instead of removing it"], "solution_steps": ["take 25% of 840 off: 840 - 210 = 630", "add the 60-cent fee: 630 + 60 = 690"], "option_values": [630, 750, 690, 1110], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 861, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 25% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 25% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $1.99.", " $2.05.", " $3.25.", " $2.65."], "source_id": "deeparithmark_v1_money_percent_depth2_0861", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "205", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "correct", "added the discount instead of removing it", "forgot the discount"], "solution_steps": ["take 25% of 240 off: 240 - 60 = 180", "add the 25-cent fee: 180 + 25 = 205"], "option_values": [199, 205, 325, 265], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 862, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $4.60. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $4.60. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $4.46.", " $4.49.", " $4.14.", " $4.03."], "source_id": "deeparithmark_v1_money_percent_depth2_0862", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "449", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "correct", "forgot the fee", "took the percentage off twice"], "solution_steps": ["take 10% of 460 off: 460 - 46 = 414", "add the 35-cent fee: 414 + 35 = 449"], "option_values": [446, 449, 414, 403], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 863, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $36.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $36.00. A 20% discount came off it, then 5% tax was added to the discounted price, and a $0.80 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $14.72.", " $14.32.", " $10.94.", " $9.81."], "source_id": "deeparithmark_v1_percent_money_depth4_0863", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "1472", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["correct", "used the coupon twice", "applied the discount twice", "split the total among one more person"], "solution_steps": ["discount: 3600 - 720 = 2880", "tax on the discounted price: 2880 + 144 = 3024", "coupon: 3024 - 80 = 2944", "split 2 ways: 2944 / 2 = 1472"], "option_values": [1472, 1432, 1094, 981], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 864, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 560 units. A delivery added 240, then 210 units were shipped out, and 24 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 560 units. A delivery added 240, then 210 units were shipped out, and 24 were found damaged. The rest were packed into crates of 16. The number of full crates packed was", "endings": [" 48 crates.", " 38 crates.", " 35 crates.", " 36 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0864", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "35", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the shipping", "added the damaged units", "correct", "forgot the damaged units"], "solution_steps": ["after delivery: 560 + 240 = 800", "after shipping: 800 - 210 = 590", "good units: 590 - 24 = 566", "full crates: 566 / 16 = 35 (remainder 6)"], "option_values": [48, 38, 35, 36], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 865, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 9 litres per minute for 4 minutes, then 3 litres per minute for 5 minutes. A drain then removed 55 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 9 litres per minute for 4 minutes, then 3 litres per minute for 5 minutes. A drain then removed 55 litres. The tank then held", "endings": [" 326 litres.", " 296 litres.", " 406 litres.", " 353 litres."], "source_id": "deeparithmark_v1_rate_depth4_0865", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "296", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["used the first rate for both stages", "correct", "added the drain instead of removing it", "added the rates and multiplied once"], "solution_steps": ["first fill: 9 x 4 = 36 litres", "second fill: 3 x 5 = 15 litres", "before draining: 300 + 36 + 15 = 351", "after draining: 351 - 55 = 296"], "option_values": [326, 296, 406, 353], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 866, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $382.80.", " $510.40.", " $481.60.", " $470.40."], "source_id": "deeparithmark_v1_money_rate_depth5_0866", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "51040", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "correct", "paid overtime at the normal rate", "forgot the bonus"], "solution_steps": ["regular pay: 40 x 1200 = 48000", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 6 x 1800 = 10800", "gross with bonus: 48000 + 10800 + 5000 = 63800", "take-home: 63800 - 12760 = 51040"], "option_values": [38280, 51040, 48160, 47040], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 867, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $14.00 an hour and 10 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $14.00 an hour and 10 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $687.60.", " $611.20.", " $624.60.", " $840.40."], "source_id": "deeparithmark_v1_money_rate_depth5_0867", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "68760", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "taxed twice", "paid overtime at the normal rate", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 36 x 1400 = 50400", "overtime rate: 1400 x 1.5 = 2100", "overtime pay: 10 x 2100 = 21000", "gross with bonus: 50400 + 21000 + 5000 = 76400", "take-home: 76400 - 7640 = 68760"], "option_values": [68760, 61120, 62460, 84040], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 868, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 4 metres and 12 centimetres long. A worker cut off 45 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 4 metres and 12 centimetres long. A worker cut off 45 centimetres. The board left was", "endings": [" 355 centimetres.", " 267 centimetres.", " 367 centimetres.", " 379 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0868", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "367", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["forgot the extra centimetres", "cut a whole metre off as well", "correct", "counted the extra centimetres twice"], "solution_steps": ["convert metres: 4 x 100 = 400 cm", "add the extra centimetres: 400 + 12 = 412 cm", "subtract the cut: 412 - 45 = 367 cm"], "option_values": [355, 267, 367, 379], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 869, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 700 units. A delivery added 310, then 250 units were shipped out, and 12 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 700 units. A delivery added 310, then 250 units were shipped out, and 12 were found damaged. The rest were packed into crates of 8. The number of full crates packed was", "endings": [" 93 crates.", " 37 crates.", " 96 crates.", " 94 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0869", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "93", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "packed the arriving units only", "added the damaged units", "counted the loose units as a crate"], "solution_steps": ["after delivery: 700 + 310 = 1010", "after shipping: 1010 - 250 = 760", "good units: 760 - 12 = 748", "full crates: 748 / 8 = 93 (remainder 4)"], "option_values": [93, 37, 96, 94], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 870, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:07 a.m. for 110 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:07 a.m. for 110 minutes. The booking ended at", "endings": [" 7:57 a.m.", " 8:57 a.m.", " 5:17 a.m.", " 10:27 a.m."], "source_id": "deeparithmark_v1_time_depth2_0870", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "537", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "correct", "subtracted the duration instead of adding it", "ran an hour and a half long"], "solution_steps": ["convert the start: 427 minutes after midnight", "add the duration: 427 + 110 = 537 minutes"], "option_values": [477, 537, 317, 627], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 871, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:23 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:23 a.m. for 65 minutes. The booking ended at", "endings": [" 7:28 a.m.", " 8:28 a.m.", " 8:58 a.m.", " 7:58 a.m."], "source_id": "deeparithmark_v1_time_depth2_0871", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "448", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "added an extra hour", "ran an hour and a half long", "ran half an hour long"], "solution_steps": ["convert the start: 383 minutes after midnight", "add the duration: 383 + 65 = 448 minutes"], "option_values": [448, 508, 538, 478], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 872, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $537.20.", " $588.20.", " $567.20.", " $726.80."], "source_id": "deeparithmark_v1_money_rate_depth5_0872", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "53720", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "paid overtime at double rate", "taxed only the regular pay", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 36 x 1200 = 43200", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 10 x 1800 = 18000", "gross with bonus: 43200 + 18000 + 2000 = 63200", "take-home: 63200 - 9480 = 53720"], "option_values": [53720, 58820, 56720, 72680], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 873, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:19 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:19 a.m. for 95 minutes. The booking ended at", "endings": [" 7:54 a.m.", " 8:54 a.m.", " 5:44 a.m.", " 9:54 a.m."], "source_id": "deeparithmark_v1_time_depth2_0873", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "534", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "correct", "subtracted the duration instead of adding it", "added an extra hour"], "solution_steps": ["convert the start: 439 minutes after midnight", "add the duration: 439 + 95 = 534 minutes"], "option_values": [474, 534, 344, 594], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 874, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $7.88.", " $7.91.", " $7.07.", " $7.56."], "source_id": "deeparithmark_v1_money_percent_depth2_0874", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "791", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "correct", "took the percentage off twice", "forgot the fee"], "solution_steps": ["take 10% of 840 off: 840 - 84 = 756", "add the 35-cent fee: 756 + 35 = 791"], "option_values": [788, 791, 707, 756], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 875, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 25% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 65 pallets.", " 67 pallets.", " 62 pallets.", " 35 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0875", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "67", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "correct", "stacked on larger pallets", "took both percentages twice"], "solution_steps": ["Monday: 25% of 1200 = 300", "left after Monday: 1200 - 300 = 900", "Tuesday: 10% of 900 = 90", "left after Tuesday: 900 - 90 = 810", "full pallets: 810 / 12 = 67"], "option_values": [65, 67, 62, 35], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 876, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 320 shirts. It sold 40% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 320 shirts. It sold 40% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "endings": [" 17 boxes.", " 16 boxes.", " 24 boxes.", " 26 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0876", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "16", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["counted the loose shirts as a box", "correct", "sold only a tenth of the stock", "packed the whole stock, not the rest"], "solution_steps": ["sold: 40% of 320 = 128", "left over: 320 - 128 = 192", "full boxes: 192 / 12 = 16 (remainder 0)"], "option_values": [17, 16, 24, 26], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 877, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $2.88.", " $5.16.", " $4.24.", " $3.64."], "source_id": "deeparithmark_v1_money_percent_depth2_0877", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "364", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "added the discount instead of removing it", "charged the handling fee twice", "correct"], "solution_steps": ["take 20% of 380 off: 380 - 76 = 304", "add the 60-cent fee: 304 + 60 = 364"], "option_values": [288, 516, 424, 364], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 878, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.20 was split between two teams in the ratio 4:3 after a $2.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.20 was split between two teams in the ratio 4:3 after a $2.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.36.", " $0.88.", " $1.05.", " $0.45."], "source_id": "deeparithmark_v1_ratio_depth5_0878", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "45", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "forgot to deduct the fee", "split the whole prize among one team", "correct"], "solution_steps": ["after the fee: 620 - 200 = 420", "one ratio part: 420 / 7 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 60 = 180", "per player: 180 / 4 = 45"], "option_values": [36, 88, 105, 45], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 879, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:12 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:12 a.m. for 80 minutes. The booking ended at", "endings": [" 8:32 a.m.", " 7:32 a.m.", " 8:02 a.m.", " 9:02 a.m."], "source_id": "deeparithmark_v1_time_depth2_0879", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "452", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added an extra hour", "correct", "ran half an hour long", "ran an hour and a half long"], "solution_steps": ["convert the start: 372 minutes after midnight", "add the duration: 372 + 80 = 452 minutes"], "option_values": [512, 452, 482, 542], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 880, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 5 metres and 55 centimetres long. A worker cut off 90 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 5 metres and 55 centimetres long. A worker cut off 90 centimetres. The board left was", "endings": [" 745 centimetres.", " 645 centimetres.", " 465 centimetres.", " 475 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0880", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "465", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["added the cut and a whole metre", "added the cut instead of removing it", "correct", "stopped ten centimetres short of the cut"], "solution_steps": ["convert metres: 5 x 100 = 500 cm", "add the extra centimetres: 500 + 55 = 555 cm", "subtract the cut: 555 - 90 = 465 cm"], "option_values": [745, 645, 465, 475], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 881, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $12.50 an hour, and then 2 hours at $17.50 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $12.50 an hour, and then 2 hours at $17.50 an hour. He earned", "endings": [" $75.00.", " $35.00.", " $95.00.", " $85.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0881", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "8500", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid every hour at the first rate", "forgot the first stretch", "swapped the two rates", "correct"], "solution_steps": ["first stretch: 4 x 1250 = 5000", "second stretch: 2 x 1750 = 3500", "total pay: 5000 + 3500 = 8500"], "option_values": [7500, 3500, 9500, 8500], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 882, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 50% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 50% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $2.08.", " $3.65.", " $6.05.", " $2.25."], "source_id": "deeparithmark_v1_money_percent_depth2_0882", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "225", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "read the percentage as a flat number of cents", "added the discount instead of removing it", "correct"], "solution_steps": ["take 50% of 380 off: 380 - 190 = 190", "add the 35-cent fee: 190 + 35 = 225"], "option_values": [208, 365, 605, 225], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 883, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 45 km at 15 km/h, rested 25 minutes, then walked 12 km at 4 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 45 km at 15 km/h, rested 25 minutes, then walked 12 km at 4 km/h. Her total time, in minutes, was", "endings": [" 385 minutes.", " 253 minutes.", " 205 minutes.", " 115 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0883", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "385", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["correct", "used the cycling speed for both legs", "forgot the walking leg", "divided by the speed twice"], "solution_steps": ["cycling time: 60 x 45 / 15 = 180 minutes", "walking time: 60 x 12 / 4 = 180 minutes", "add the rest: 180 + 25 + 180 = 385 minutes"], "option_values": [385, 253, 205, 115], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 884, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:20 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:20 a.m. for 95 minutes. The booking ended at", "endings": [" 9:25 a.m.", " 9:55 a.m.", " 8:55 a.m.", " 10:25 a.m."], "source_id": "deeparithmark_v1_time_depth2_0884", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "535", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["ran half an hour long", "added an extra hour", "correct", "ran an hour and a half long"], "solution_steps": ["convert the start: 440 minutes after midnight", "add the duration: 440 + 95 = 535 minutes"], "option_values": [565, 595, 535, 625], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 885, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 20% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $8.85.", " $7.62.", " $8.65.", " $7.17."], "source_id": "deeparithmark_v1_money_percent_depth2_0885", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "717", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the discount", "charged the handling fee twice", "read the percentage as a flat number of cents", "correct"], "solution_steps": ["take 20% of 840 off: 840 - 168 = 672", "add the 45-cent fee: 672 + 45 = 717"], "option_values": [885, 762, 865, 717], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 886, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $0.75 each and 6 erasers at $0.65 each. She split the total cost equally between herself and 5 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $0.75 each and 6 erasers at $0.65 each. She split the total cost equally between herself and 5 friends. Each person paid", "endings": [" $1.61.", " $1.67.", " $1.98.", " $1.65."], "source_id": "deeparithmark_v1_money_depth4_0886", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "165", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["swapped the two unit prices", "added the unit prices instead of multiplying", "split only between the friends", "correct"], "solution_steps": ["markers: 8 x 75 = 600", "erasers: 6 x 65 = 390", "total cost: 600 + 390 = 990", "split between 6 people: 990 / 6 = 165"], "option_values": [161, 167, 198, 165], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 887, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:37 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:37 a.m. for 80 minutes. The booking ended at", "endings": [" 9:57 a.m.", " 9:42 a.m.", " 7:17 a.m.", " 10:27 a.m."], "source_id": "deeparithmark_v1_time_depth2_0887", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "597", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "stopped a quarter of an hour early", "subtracted the duration instead of adding it", "ran half an hour long"], "solution_steps": ["convert the start: 517 minutes after midnight", "add the duration: 517 + 80 = 597 minutes"], "option_values": [597, 582, 437, 627], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 888, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Nia baked 135 cookies. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Nia baked 135 cookies. One third went to a neighbour, and the rest were split equally among 5 grandchildren. Each grandchild got", "endings": [" 7 cookies.", " 18 cookies.", " 9 cookies.", " 22 cookies."], "source_id": "deeparithmark_v1_fractions_depth3_0888", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "18", "unit": "cookies", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away two thirds and split among one more child", "correct", "split the given-away cookies too", "split all the cookies among one more child"], "solution_steps": ["one third given away: 135 / 3 = 45", "rest kept: 135 - 45 = 90", "split among 5: 90 / 5 = 18"], "option_values": [7, 18, 9, 22], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 889, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:04 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:04 a.m. for 65 minutes. The booking ended at", "endings": [" 6:59 a.m.", " 8:09 a.m.", " 9:09 a.m.", " 10:09 a.m."], "source_id": "deeparithmark_v1_time_depth2_0889", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "549", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "dropped the hour carry", "correct", "added an extra hour"], "solution_steps": ["convert the start: 484 minutes after midnight", "add the duration: 484 + 65 = 549 minutes"], "option_values": [419, 489, 549, 609], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 890, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 760 units. A delivery added 130, then 90 units were shipped out, and 40 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 760 units. A delivery added 130, then 90 units were shipped out, and 40 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 63 crates.", " 55 crates.", " 58 crates.", " 52 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0890", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "63", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "shipped out twice", "packed into larger crates", "shipped twice and damaged twice"], "solution_steps": ["after delivery: 760 + 130 = 890", "after shipping: 890 - 90 = 800", "good units: 800 - 40 = 760", "full crates: 760 / 12 = 63 (remainder 4)"], "option_values": [63, 55, 58, 52], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 891, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 420 units. A delivery added 310, then 140 units were shipped out, and 40 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 420 units. A delivery added 310, then 140 units were shipped out, and 40 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 42 crates.", " 34 crates.", " 45 crates.", " 57 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0891", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "45", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed into larger crates", "shipped out twice", "correct", "forgot the shipping"], "solution_steps": ["after delivery: 420 + 310 = 730", "after shipping: 730 - 140 = 590", "good units: 590 - 40 = 550", "full crates: 550 / 12 = 45 (remainder 10)"], "option_values": [42, 34, 45, 57], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 892, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 25% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 25% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $3.85.", " $9.25.", " $7.45.", " $5.65."], "source_id": "deeparithmark_v1_money_percent_depth2_0892", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "565", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "added the discount instead of removing it", "forgot the discount", "correct"], "solution_steps": ["take 25% of 720 off: 720 - 180 = 540", "add the 25-cent fee: 540 + 25 = 565"], "option_values": [385, 925, 745, 565], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 893, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:17 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:17 a.m.. The first session lasted 60 minutes, the break lasted 15 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "endings": [" 10:07 a.m.", " 10:22 a.m.", " 11:07 a.m.", " 10:52 a.m."], "source_id": "deeparithmark_v1_time_depth3_0893", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "607", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["correct", "counted the break twice", "counted the first session twice", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 497 + 60 = 557 minutes after midnight", "after the break: 557 + 15 = 572", "after the second session: 572 + 35 = 607"], "option_values": [607, 622, 667, 652], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 894, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 12 litres per minute for 6 minutes, then 3 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 12 litres per minute for 6 minutes, then 3 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 133 litres.", " 236 litres.", " 173 litres.", " 253 litres."], "source_id": "deeparithmark_v1_rate_depth4_0894", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "173", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "used the first rate for both stages", "correct", "added the drain instead of removing it"], "solution_steps": ["first fill: 12 x 6 = 72 litres", "second fill: 3 x 7 = 21 litres", "before draining: 120 + 72 + 21 = 213", "after draining: 213 - 40 = 173"], "option_values": [133, 236, 173, 253], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 895, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:37 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:37 a.m. for 95 minutes. The booking ended at", "endings": [" 9:12 a.m.", " 8:12 a.m.", " 8:42 a.m.", " 9:42 a.m."], "source_id": "deeparithmark_v1_time_depth2_0895", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "492", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added an extra hour", "correct", "ran half an hour long", "ran an hour and a half long"], "solution_steps": ["convert the start: 397 minutes after midnight", "add the duration: 397 + 95 = 492 minutes"], "option_values": [552, 492, 522, 582], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 896, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:50 a.m. for 50 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:50 a.m. for 50 minutes. The booking ended at", "endings": [" 9:40 a.m.", " 10:10 a.m.", " 9:10 a.m.", " 8:40 a.m."], "source_id": "deeparithmark_v1_time_depth2_0896", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "520", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added an extra hour", "ran an hour and a half long", "ran half an hour long", "correct"], "solution_steps": ["convert the start: 470 minutes after midnight", "add the duration: 470 + 50 = 520 minutes"], "option_values": [580, 610, 550, 520], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 897, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 180 litres. A pipe added 15 litres per minute for 10 minutes, then 7 litres per minute for 7 minutes. A drain then removed 55 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 180 litres. A pipe added 15 litres per minute for 10 minutes, then 7 litres per minute for 7 minutes. A drain then removed 55 litres. The tank then held", "endings": [" 275 litres.", " 174 litres.", " 324 litres.", " 499 litres."], "source_id": "deeparithmark_v1_rate_depth4_0897", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "324", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the second fill", "forgot the first fill", "correct", "added the rates and multiplied once"], "solution_steps": ["first fill: 15 x 10 = 150 litres", "second fill: 7 x 7 = 49 litres", "before draining: 180 + 150 + 49 = 379", "after draining: 379 - 55 = 324"], "option_values": [275, 174, 324, 499], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 898, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:13 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:13 a.m. for 125 minutes. The booking ended at", "endings": [" 10:18 a.m.", " 9:18 a.m.", " 6:08 a.m.", " 8:18 a.m."], "source_id": "deeparithmark_v1_time_depth2_0898", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "618", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "forgot the last full hour", "subtracted the duration instead of adding it", "dropped the hour carry"], "solution_steps": ["convert the start: 493 minutes after midnight", "add the duration: 493 + 125 = 618 minutes"], "option_values": [618, 558, 368, 498], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 899, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 5 metres and 25 centimetres long. A worker cut off 90 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 5 metres and 25 centimetres long. A worker cut off 90 centimetres. The board left was", "endings": [" 715 centimetres.", " 615 centimetres.", " 435 centimetres.", " 445 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0899", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "435", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["added the cut and a whole metre", "added the cut instead of removing it", "correct", "stopped ten centimetres short of the cut"], "solution_steps": ["convert metres: 5 x 100 = 500 cm", "add the extra centimetres: 500 + 25 = 525 cm", "subtract the cut: 525 - 90 = 435 cm"], "option_values": [715, 615, 435, 445], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 900, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $18.00 an hour and 6 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $18.00 an hour and 6 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $649.60.", " $519.60.", " $692.80.", " $563.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0900", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "69280", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at the normal rate", "taxed twice", "correct", "forgot the overtime"], "solution_steps": ["regular pay: 38 x 1800 = 68400", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 6 x 2700 = 16200", "gross with bonus: 68400 + 16200 + 2000 = 86600", "take-home: 86600 - 17320 = 69280"], "option_values": [64960, 51960, 69280, 56320], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 901, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:26 a.m. for 65 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:26 a.m. for 65 minutes. The booking ended at", "endings": [" 7:21 a.m.", " 11:01 a.m.", " 10:01 a.m.", " 9:31 a.m."], "source_id": "deeparithmark_v1_time_depth2_0901", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "571", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "ran an hour and a half long", "ran half an hour long", "correct"], "solution_steps": ["convert the start: 506 minutes after midnight", "add the duration: 506 + 65 = 571 minutes"], "option_values": [441, 661, 601, 571], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 902, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:07 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:07 a.m. for 125 minutes. The booking ended at", "endings": [" 8:12 a.m.", " 9:57 a.m.", " 9:12 a.m.", " 10:12 a.m."], "source_id": "deeparithmark_v1_time_depth2_0902", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "612", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "stopped a quarter of an hour early", "forgot the last full hour", "correct"], "solution_steps": ["convert the start: 487 minutes after midnight", "add the duration: 487 + 125 = 612 minutes"], "option_values": [492, 597, 552, 612], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 903, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.20. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.20. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $3.48.", " $2.88.", " $3.42.", " $3.16."], "source_id": "deeparithmark_v1_money_percent_depth2_0903", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "348", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "forgot the fee", "took the discount off the fee as well", "took the percentage off twice"], "solution_steps": ["take 10% of 320 off: 320 - 32 = 288", "add the 60-cent fee: 288 + 60 = 348"], "option_values": [348, 288, 342, 316], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 904, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 33 pallets.", " 72 pallets.", " 69 pallets.", " 76 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0904", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "76", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages twice", "took both percentages off the original stock", "stacked on larger pallets", "correct"], "solution_steps": ["Monday: 20% of 1200 = 240", "left after Monday: 1200 - 240 = 960", "Tuesday: 20% of 960 = 192", "left after Tuesday: 960 - 192 = 768", "full pallets: 768 / 10 = 76"], "option_values": [33, 72, 69, 76], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 905, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $12.00 an hour and 6 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $486.20.", " $516.80.", " $547.40.", " $699.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0905", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "51680", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at the normal rate", "correct", "paid overtime at double rate", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 40 x 1200 = 48000", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 6 x 1800 = 10800", "gross with bonus: 48000 + 10800 + 2000 = 60800", "take-home: 60800 - 9120 = 51680"], "option_values": [48620, 51680, 54740, 69920], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 906, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $0.45 each and 4 erasers at $0.30 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $0.45 each and 4 erasers at $0.30 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $4.80.", " $1.60.", " $1.80.", " $2.40."], "source_id": "deeparithmark_v1_money_depth4_0906", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "160", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["did not split the total at all", "correct", "charged the marker price for everything", "split only between the friends"], "solution_steps": ["markers: 8 x 45 = 360", "erasers: 4 x 30 = 120", "total cost: 360 + 120 = 480", "split between 3 people: 480 / 3 = 160"], "option_values": [480, 160, 180, 240], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 907, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $0.95 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $0.95 each and 6 erasers at $0.70 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $2.17.", " $1.55.", " $2.12.", " $1.33."], "source_id": "deeparithmark_v1_money_depth4_0907", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "217", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "split among two more people", "swapped the two unit prices", "forgot the erasers"], "solution_steps": ["markers: 7 x 95 = 665", "erasers: 6 x 70 = 420", "total cost: 665 + 420 = 1085", "split between 5 people: 1085 / 5 = 217"], "option_values": [217, 155, 212, 133], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 908, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 360 shirts. It sold 25% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 360 shirts. It sold 25% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "endings": [" 22 boxes.", " 7 boxes.", " 27 boxes.", " 23 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0908", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "22", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "packed the sold shirts", "sold only a tenth of the stock", "rounded the box count up"], "solution_steps": ["sold: 25% of 360 = 90", "left over: 360 - 90 = 270", "full boxes: 270 / 12 = 22 (remainder 6)"], "option_values": [22, 7, 27, 23], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 909, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:31 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:31 a.m. for 80 minutes. The booking ended at", "endings": [" 8:51 a.m.", " 8:36 a.m.", " 6:11 a.m.", " 9:21 a.m."], "source_id": "deeparithmark_v1_time_depth2_0909", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "531", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "stopped a quarter of an hour early", "subtracted the duration instead of adding it", "ran half an hour long"], "solution_steps": ["convert the start: 451 minutes after midnight", "add the duration: 451 + 80 = 531 minutes"], "option_values": [531, 516, 371, 561], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 910, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 840 units. A delivery added 180, then 250 units were shipped out, and 24 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 840 units. A delivery added 180, then 250 units were shipped out, and 24 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "endings": [" 33 crates.", " 71 crates.", " 56 crates.", " 53 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0910", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "53", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["shipped twice and damaged twice", "forgot the shipping", "added the damaged units", "correct"], "solution_steps": ["after delivery: 840 + 180 = 1020", "after shipping: 1020 - 250 = 770", "good units: 770 - 24 = 746", "full crates: 746 / 14 = 53 (remainder 4)"], "option_values": [33, 71, 56, 53], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 911, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $3.50 was split between two teams in the ratio 4:1 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $3.50 was split between two teams in the ratio 4:1 after a $2.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.19.", " $0.48.", " $0.24.", " $0.37."], "source_id": "deeparithmark_v1_ratio_depth5_0911", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "24", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["split among one more player", "divided between the teams instead of the players", "correct", "split the whole prize among one team"], "solution_steps": ["after the fee: 350 - 200 = 150", "one ratio part: 150 / 5 = 30", "larger share: 4 x 30 = 120", "after charity: 120 - 24 = 96", "per player: 96 / 4 = 24"], "option_values": [19, 48, 24, 37], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 912, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $12.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $12.00. A 10% discount came off it, then 10% tax was added to the discounted price, and a $0.60 coupon was applied last. 2 people split the final cost equally. Each paid", "endings": [" $5.34.", " $3.76.", " $4.98.", " $5.64."], "source_id": "deeparithmark_v1_percent_money_depth4_0912", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "564", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["used the coupon twice", "split the total among one more person", "applied the discount twice", "correct"], "solution_steps": ["discount: 1200 - 120 = 1080", "tax on the discounted price: 1080 + 108 = 1188", "coupon: 1188 - 60 = 1128", "split 2 ways: 1128 / 2 = 564"], "option_values": [534, 376, 498, 564], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 913, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 480 shirts. It sold 30% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 480 shirts. It sold 30% of them, then packed the rest into boxes of 8. The number of full boxes filled was", "endings": [" 42 boxes.", " 29 boxes.", " 18 boxes.", " 24 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0913", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "42", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["correct", "took the percentage off the remainder again", "packed the sold shirts", "sold twice as many"], "solution_steps": ["sold: 30% of 480 = 144", "left over: 480 - 144 = 336", "full boxes: 336 / 8 = 42 (remainder 0)"], "option_values": [42, 29, 18, 24], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 914, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:01 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:01 a.m. for 125 minutes. The booking ended at", "endings": [" 9:06 a.m.", " 4:56 a.m.", " 8:51 a.m.", " 10:36 a.m."], "source_id": "deeparithmark_v1_time_depth2_0914", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "546", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "subtracted the duration instead of adding it", "stopped a quarter of an hour early", "ran an hour and a half long"], "solution_steps": ["convert the start: 421 minutes after midnight", "add the duration: 421 + 125 = 546 minutes"], "option_values": [546, 296, 531, 636], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 915, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 240 shirts. It sold 40% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 240 shirts. It sold 40% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "endings": [" 16 boxes.", " 24 boxes.", " 8 boxes.", " 14 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0915", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "24", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the sold shirts", "correct", "sold twice as many", "took the percentage off the remainder again"], "solution_steps": ["sold: 40% of 240 = 96", "left over: 240 - 96 = 144", "full boxes: 144 / 6 = 24 (remainder 0)"], "option_values": [16, 24, 8, 14], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 916, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $9.20 was split between two teams in the ratio 4:3 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "ctx_b": "", "ctx": "A prize of $9.20 was split between two teams in the ratio 4:3 after a $5.00 fee was deducted. The larger team gave 10% of its share to charity and split the rest equally among its 4 players. Each player got", "endings": [" $0.54.", " $0.45.", " $0.43.", " $0.52."], "source_id": "deeparithmark_v1_ratio_depth5_0916", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "54", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "gave the larger share to the smaller ratio", "split among one more player", "forgot the fee and the charity cut"], "solution_steps": ["after the fee: 920 - 500 = 420", "one ratio part: 420 / 7 = 60", "larger share: 4 x 60 = 240", "after charity: 240 - 24 = 216", "per player: 216 / 4 = 54"], "option_values": [54, 45, 43, 52], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 917, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 3 hours at $15.00 an hour, and then 2 hours at $18.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 3 hours at $15.00 an hour, and then 2 hours at $18.00 an hour. He earned", "endings": [" $66.00.", " $165.00.", " $81.00.", " $84.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0917", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "8100", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["worked one hour less in the first stretch", "added the rates together", "correct", "swapped the two rates"], "solution_steps": ["first stretch: 3 x 1500 = 4500", "second stretch: 2 x 1800 = 3600", "total pay: 4500 + 3600 = 8100"], "option_values": [6600, 16500, 8100, 8400], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 918, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:15 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:15 a.m. for 95 minutes. The booking ended at", "endings": [" 5:40 a.m.", " 9:50 a.m.", " 10:20 a.m.", " 8:50 a.m."], "source_id": "deeparithmark_v1_time_depth2_0918", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "530", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["subtracted the duration instead of adding it", "added an extra hour", "ran an hour and a half long", "correct"], "solution_steps": ["convert the start: 435 minutes after midnight", "add the duration: 435 + 95 = 530 minutes"], "option_values": [340, 590, 620, 530], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 919, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 12 litres per minute for 4 minutes, then 5 litres per minute for 9 minutes. A drain then removed 25 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 12 litres per minute for 4 minutes, then 5 litres per minute for 9 minutes. A drain then removed 25 litres. The tank then held", "endings": [" 368 litres.", " 393 litres.", " 496 litres.", " 418 litres."], "source_id": "deeparithmark_v1_rate_depth4_0919", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "368", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["correct", "forgot the drain", "added the rates and multiplied once", "added the drain instead of removing it"], "solution_steps": ["first fill: 12 x 4 = 48 litres", "second fill: 5 x 9 = 45 litres", "before draining: 300 + 48 + 45 = 393", "after draining: 393 - 25 = 368"], "option_values": [368, 393, 496, 418], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 920, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Priya baked 144 cookies. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Priya baked 144 cookies. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 18 cookies.", " 24 cookies.", " 96 cookies.", " 36 cookies."], "source_id": "deeparithmark_v1_fractions_depth3_0920", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "24", "unit": "cookies", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away a half instead of a third", "correct", "stopped after giving the third away", "split all the cookies, not the rest"], "solution_steps": ["one third given away: 144 / 3 = 48", "rest kept: 144 - 48 = 96", "split among 4: 96 / 4 = 24"], "option_values": [18, 24, 96, 36], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 921, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $18.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $18.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $797.40.", " $716.40.", " $554.40.", " $974.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0921", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "79740", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "paid overtime at the normal rate", "forgot the overtime", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 32 x 1800 = 57600", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 10 x 2700 = 27000", "gross with bonus: 57600 + 27000 + 4000 = 88600", "take-home: 88600 - 8860 = 79740"], "option_values": [79740, 71640, 55440, 97460], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 922, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 280 shirts. It sold 30% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 280 shirts. It sold 30% of them, then packed the rest into boxes of 7. The number of full boxes filled was", "endings": [" 12 boxes.", " 16 boxes.", " 29 boxes.", " 28 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0922", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "28", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the sold shirts", "sold twice as many", "counted the loose shirts as a box", "correct"], "solution_steps": ["sold: 30% of 280 = 84", "left over: 280 - 84 = 196", "full boxes: 196 / 7 = 28 (remainder 0)"], "option_values": [12, 16, 29, 28], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 923, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 6 markers at $0.80 each and 3 erasers at $0.30 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 6 markers at $0.80 each and 3 erasers at $0.30 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.14.", " $0.81.", " $0.95.", " $1.42."], "source_id": "deeparithmark_v1_money_depth4_0923", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "114", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["correct", "split among two more people", "split among one more person", "split only between the friends"], "solution_steps": ["markers: 6 x 80 = 480", "erasers: 3 x 30 = 90", "total cost: 480 + 90 = 570", "split between 5 people: 570 / 5 = 114"], "option_values": [114, 81, 95, 142], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 924, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $18.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $18.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $844.90.", " $615.40.", " $768.40.", " $810.90."], "source_id": "deeparithmark_v1_money_rate_depth5_0924", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "84490", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "forgot the overtime", "paid overtime at the normal rate", "forgot the bonus"], "solution_steps": ["regular pay: 38 x 1800 = 68400", "overtime rate: 1800 x 1.5 = 2700", "overtime pay: 10 x 2700 = 27000", "gross with bonus: 68400 + 27000 + 4000 = 99400", "take-home: 99400 - 14910 = 84490"], "option_values": [84490, 61540, 76840, 81090], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 925, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $16.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $16.00 an hour and 10 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 15% of the total was withheld for tax. Jo took home", "endings": [" $656.20.", " $540.40.", " $452.20.", " $695.20."], "source_id": "deeparithmark_v1_money_rate_depth5_0925", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "65620", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["correct", "taxed twice", "forgot the overtime", "taxed only the regular pay"], "solution_steps": ["regular pay: 32 x 1600 = 51200", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 10 x 2400 = 24000", "gross with bonus: 51200 + 24000 + 2000 = 77200", "take-home: 77200 - 11580 = 65620"], "option_values": [65620, 54040, 45220, 69520], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 926, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 20% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 20% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 15. The number of full pallets was", "endings": [" 58 pallets.", " 21 pallets.", " 85 pallets.", " 64 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0926", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "64", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "took both percentages twice", "forgot Tuesday", "correct"], "solution_steps": ["Monday: 20% of 1600 = 320", "left after Monday: 1600 - 320 = 1280", "Tuesday: 25% of 1280 = 320", "left after Tuesday: 1280 - 320 = 960", "full pallets: 960 / 15 = 64"], "option_values": [58, 21, 85, 64], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 927, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $8.65.", " $9.49.", " $7.81.", " $8.06."], "source_id": "deeparithmark_v1_money_percent_depth2_0927", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "781", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the discount", "added the discount instead of removing it", "correct", "charged the handling fee twice"], "solution_steps": ["take 10% of 840 off: 840 - 84 = 756", "add the 25-cent fee: 756 + 25 = 781"], "option_values": [865, 949, 781, 806], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 928, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 15 km at 15 km/h, rested 15 minutes, then walked 6 km at 6 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 15 km at 15 km/h, rested 15 minutes, then walked 6 km at 6 km/h. Her total time, in minutes, was", "endings": [" 99 minutes.", " 35 minutes.", " 75 minutes.", " 135 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0928", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "135", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["used the cycling speed for both legs", "divided by the speed twice", "forgot the walking leg", "correct"], "solution_steps": ["cycling time: 60 x 15 / 15 = 60 minutes", "walking time: 60 x 6 / 6 = 60 minutes", "add the rest: 60 + 15 + 60 = 135 minutes"], "option_values": [99, 35, 75, 135], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 929, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 38 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 38 regular hours at $12.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $630.40.", " $662.40.", " $743.60.", " $608.40."], "source_id": "deeparithmark_v1_money_rate_depth5_0929", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "60840", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed only the regular pay", "paid overtime at double rate", "added the tax instead of withholding it", "correct"], "solution_steps": ["regular pay: 38 x 1200 = 45600", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 10 x 1800 = 18000", "gross with bonus: 45600 + 18000 + 4000 = 67600", "take-home: 67600 - 6760 = 60840"], "option_values": [63040, 66240, 74360, 60840], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 930, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:08 a.m.. The first session lasted 55 minutes, the break lasted 25 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:08 a.m.. The first session lasted 55 minutes, the break lasted 25 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "endings": [" 6:03 a.m.", " 7:38 a.m.", " 8:03 a.m.", " 8:28 a.m."], "source_id": "deeparithmark_v1_time_depth3_0930", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "483", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["dropped the hour carry", "forgot the break", "correct", "counted the break twice"], "solution_steps": ["after the first session: 368 + 55 = 423 minutes after midnight", "after the break: 423 + 25 = 448", "after the second session: 448 + 35 = 483"], "option_values": [363, 458, 483, 508], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 931, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 10% off the pass and then charged a handling fee of $0.25. In total, the pass cost", "endings": [" $7.45.", " $6.73.", " $6.98.", " $8.17."], "source_id": "deeparithmark_v1_money_percent_depth2_0931", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "673", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the discount", "correct", "charged the handling fee twice", "added the discount instead of removing it"], "solution_steps": ["take 10% of 720 off: 720 - 72 = 648", "add the 25-cent fee: 648 + 25 = 673"], "option_values": [745, 673, 698, 817], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 932, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 620 units. A delivery added 180, then 210 units were shipped out, and 32 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 620 units. A delivery added 180, then 210 units were shipped out, and 32 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 42 crates.", " 51 crates.", " 46 crates.", " 49 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0932", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "46", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed into larger crates", "added the damaged units", "correct", "forgot the damaged units"], "solution_steps": ["after delivery: 620 + 180 = 800", "after shipping: 800 - 210 = 590", "good units: 590 - 32 = 558", "full crates: 558 / 12 = 46 (remainder 6)"], "option_values": [42, 51, 46, 49], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 933, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $20.00 an hour and 4 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $20.00 an hour and 4 overtime hours at one and a half times that rate. A $30.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $664.00.", " $662.00.", " $632.00.", " $948.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0933", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "63200", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["paid overtime at double rate", "taxed only the regular pay", "correct", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 32 x 2000 = 64000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 4 x 3000 = 12000", "gross with bonus: 64000 + 12000 + 3000 = 79000", "take-home: 79000 - 15800 = 63200"], "option_values": [66400, 66200, 63200, 94800], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 934, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 240 litres. A pipe added 6 litres per minute for 4 minutes, then 3 litres per minute for 9 minutes. A drain then removed 25 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 240 litres. A pipe added 6 litres per minute for 4 minutes, then 3 litres per minute for 9 minutes. A drain then removed 25 litres. The tank then held", "endings": [" 241 litres.", " 291 litres.", " 266 litres.", " 316 litres."], "source_id": "deeparithmark_v1_rate_depth4_0934", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "266", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["drained twice", "forgot the drain", "correct", "added the drain instead of removing it"], "solution_steps": ["first fill: 6 x 4 = 24 litres", "second fill: 3 x 9 = 27 litres", "before draining: 240 + 24 + 27 = 291", "after draining: 291 - 25 = 266"], "option_values": [241, 291, 266, 316], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 935, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Ivo baked 144 cookies. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Ivo baked 144 cookies. One third went to a neighbour, and the rest were split equally among 4 grandchildren. Each grandchild got", "endings": [" 18 cookies.", " 36 cookies.", " 96 cookies.", " 24 cookies."], "source_id": "deeparithmark_v1_fractions_depth3_0935", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "24", "unit": "cookies", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away a half instead of a third", "split all the cookies, not the rest", "stopped after giving the third away", "correct"], "solution_steps": ["one third given away: 144 / 3 = 48", "rest kept: 144 - 48 = 96", "split among 4: 96 / 4 = 24"], "option_values": [18, 36, 96, 24], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 936, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.90 was split between two teams in the ratio 4:3 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.90 was split between two teams in the ratio 4:3 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.56.", " $0.28.", " $0.42.", " $0.49."], "source_id": "deeparithmark_v1_ratio_depth5_0936", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "28", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["forgot the charity cut", "correct", "gave the larger share to the smaller ratio", "took the charity cut off the whole prize"], "solution_steps": ["after the fee: 690 - 200 = 490", "one ratio part: 490 / 7 = 70", "larger share: 4 x 70 = 280", "after charity: 280 - 140 = 140", "per player: 140 / 5 = 28"], "option_values": [56, 28, 42, 49], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 937, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 280 shirts. It sold 25% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 280 shirts. It sold 25% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "endings": [" 26 boxes.", " 23 boxes.", " 11 boxes.", " 35 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0937", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "35", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["took the percentage off the remainder again", "sold twice as many", "packed the sold shirts", "correct"], "solution_steps": ["sold: 25% of 280 = 70", "left over: 280 - 70 = 210", "full boxes: 210 / 6 = 35 (remainder 0)"], "option_values": [26, 23, 11, 35], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 938, "activity_label": "deeparithmark::deeparithmark-1::rate_time::depth3::hard", "ctx_a": "Nadia cycled 15 km at 15 km/h, rested 12 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "ctx_b": "", "ctx": "Nadia cycled 15 km at 15 km/h, rested 12 minutes, then walked 12 km at 6 km/h. Her total time, in minutes, was", "endings": [" 192 minutes.", " 72 minutes.", " 282 minutes.", " 204 minutes."], "source_id": "deeparithmark_v1_rate_time_depth3_0938", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "192", "unit": "minutes", "topic": "rate_time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "trip_minutes", "depth": 3, "option_sources": ["correct", "forgot the walking leg", "used the walking speed for both legs", "counted the rest twice"], "solution_steps": ["cycling time: 60 x 15 / 15 = 60 minutes", "walking time: 60 x 12 / 6 = 120 minutes", "add the rest: 60 + 12 + 120 = 192 minutes"], "option_values": [192, 72, 282, 204], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 939, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:12 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:12 a.m. for 80 minutes. The booking ended at", "endings": [" 9:17 a.m.", " 6:52 a.m.", " 9:32 a.m.", " 10:32 a.m."], "source_id": "deeparithmark_v1_time_depth2_0939", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "572", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "subtracted the duration instead of adding it", "correct", "added an extra hour"], "solution_steps": ["convert the start: 492 minutes after midnight", "add the duration: 492 + 80 = 572 minutes"], "option_values": [557, 412, 572, 632], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 940, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 480 shirts. It sold 30% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 480 shirts. It sold 30% of them, then packed the rest into boxes of 6. The number of full boxes filled was", "endings": [" 39 boxes.", " 57 boxes.", " 72 boxes.", " 56 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0940", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "56", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["took the percentage off the remainder again", "counted the loose shirts as a box", "sold only a tenth of the stock", "correct"], "solution_steps": ["sold: 30% of 480 = 144", "left over: 480 - 144 = 336", "full boxes: 336 / 6 = 56 (remainder 0)"], "option_values": [39, 57, 72, 56], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 941, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $0.45 each and 3 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $0.45 each and 3 erasers at $0.65 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $0.99.", " $0.92.", " $1.11.", " $0.79."], "source_id": "deeparithmark_v1_money_depth4_0941", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "111", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["charged the marker price for everything", "split among one more person", "correct", "split among two more people"], "solution_steps": ["markers: 8 x 45 = 360", "erasers: 3 x 65 = 195", "total cost: 360 + 195 = 555", "split between 5 people: 555 / 5 = 111"], "option_values": [99, 92, 111, 79], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 942, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 10% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $6.48.", " $6.83.", " $7.55.", " $8.27."], "source_id": "deeparithmark_v1_money_percent_depth2_0942", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "683", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the fee", "correct", "forgot the discount", "added the discount instead of removing it"], "solution_steps": ["take 10% of 720 off: 720 - 72 = 648", "add the 35-cent fee: 648 + 35 = 683"], "option_values": [648, 683, 755, 827], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 943, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 10% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $6.93.", " $6.48.", " $7.55.", " $8.37."], "source_id": "deeparithmark_v1_money_percent_depth2_0943", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "693", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "forgot the fee", "read the percentage as a flat number of cents", "added the discount instead of removing it"], "solution_steps": ["take 10% of 720 off: 720 - 72 = 648", "add the 45-cent fee: 648 + 45 = 693"], "option_values": [693, 648, 755, 837], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 944, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 7:38 a.m. for 95 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 7:38 a.m. for 95 minutes. The booking ended at", "endings": [" 9:13 a.m.", " 8:13 a.m.", " 6:03 a.m.", " 10:43 a.m."], "source_id": "deeparithmark_v1_time_depth2_0944", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "553", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["correct", "added the minutes without the hours", "subtracted the duration instead of adding it", "ran an hour and a half long"], "solution_steps": ["convert the start: 458 minutes after midnight", "add the duration: 458 + 95 = 553 minutes"], "option_values": [553, 493, 363, 643], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 945, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 7 markers at $0.45 each and 6 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 7 markers at $0.45 each and 6 erasers at $0.35 each. She split the total cost equally between herself and 2 friends. Each person paid", "endings": [" $1.71.", " $2.01.", " $2.62.", " $1.75."], "source_id": "deeparithmark_v1_money_depth4_0945", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "175", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["swapped the two unit prices", "bought one extra of each item", "split only between the friends", "correct"], "solution_steps": ["markers: 7 x 45 = 315", "erasers: 6 x 35 = 210", "total cost: 315 + 210 = 525", "split between 3 people: 525 / 3 = 175"], "option_values": [171, 201, 262, 175], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 946, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 10% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $6.04.", " $6.12.", " $6.72.", " $6.66."], "source_id": "deeparithmark_v1_money_percent_depth2_0946", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "672", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "forgot the fee", "correct", "took the discount off the fee as well"], "solution_steps": ["take 10% of 680 off: 680 - 68 = 612", "add the 60-cent fee: 612 + 60 = 672"], "option_values": [604, 612, 672, 666], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 947, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 560 units. A delivery added 180, then 250 units were shipped out, and 24 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 560 units. A delivery added 180, then 250 units were shipped out, and 24 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 38 crates.", " 35 crates.", " 23 crates.", " 16 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0947", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "38", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "packed into larger crates", "forgot the delivery", "shipped twice and damaged twice"], "solution_steps": ["after delivery: 560 + 180 = 740", "after shipping: 740 - 250 = 490", "good units: 490 - 24 = 466", "full crates: 466 / 12 = 38 (remainder 10)"], "option_values": [38, 35, 23, 16], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 948, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 105 pallets.", " 113 pallets.", " 79 pallets.", " 78 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0948", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "78", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["forgot Tuesday", "forgot Monday", "counted the loose sacks as a pallet", "correct"], "solution_steps": ["Monday: 25% of 1400 = 350", "left after Monday: 1400 - 350 = 1050", "Tuesday: 25% of 1050 = 262", "left after Tuesday: 1050 - 262 = 788", "full pallets: 788 / 10 = 78"], "option_values": [105, 113, 79, 78], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 949, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 20% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $4.23.", " $5.56.", " $5.44.", " $5.59."], "source_id": "deeparithmark_v1_money_percent_depth2_0949", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "559", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "took the discount off the fee as well", "forgot the fee", "correct"], "solution_steps": ["take 20% of 680 off: 680 - 136 = 544", "add the 15-cent fee: 544 + 15 = 559"], "option_values": [423, 556, 544, 559], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 950, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 3 hours at $14.00 an hour, and then 3 hours at $19.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 3 hours at $14.00 an hour, and then 3 hours at $19.00 an hour. He earned", "endings": [" $57.00.", " $42.00.", " $99.00.", " $85.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0950", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "9900", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["forgot the first stretch", "forgot the second stretch", "correct", "worked one hour less in the first stretch"], "solution_steps": ["first stretch: 3 x 1400 = 4200", "second stretch: 3 x 1900 = 5700", "total pay: 4200 + 5700 = 9900"], "option_values": [5700, 4200, 9900, 8500], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 951, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:49 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:49 a.m. for 125 minutes. The booking ended at", "endings": [" 9:54 a.m.", " 8:54 a.m.", " 9:24 a.m.", " 10:24 a.m."], "source_id": "deeparithmark_v1_time_depth2_0951", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "534", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["added an extra hour", "correct", "ran half an hour long", "ran an hour and a half long"], "solution_steps": ["convert the start: 409 minutes after midnight", "add the duration: 409 + 125 = 534 minutes"], "option_values": [594, 534, 564, 624], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 952, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 5 hours at $15.00 an hour, and then 3 hours at $17.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 5 hours at $15.00 an hour, and then 3 hours at $17.00 an hour. He earned", "endings": [" $94.00.", " $111.00.", " $51.00.", " $126.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0952", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "12600", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["worked one hour less in each stretch", "worked one hour less in the first stretch", "forgot the first stretch", "correct"], "solution_steps": ["first stretch: 5 x 1500 = 7500", "second stretch: 3 x 1700 = 5100", "total pay: 7500 + 5100 = 12600"], "option_values": [9400, 11100, 5100, 12600], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 953, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1000 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1000 sacks. It sent out 25% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 51 pallets.", " 75 pallets.", " 57 pallets.", " 56 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0953", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "56", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["stacked on larger pallets", "forgot Tuesday", "counted the loose sacks as a pallet", "correct"], "solution_steps": ["Monday: 25% of 1000 = 250", "left after Monday: 1000 - 250 = 750", "Tuesday: 25% of 750 = 187", "left after Tuesday: 750 - 187 = 563", "full pallets: 563 / 10 = 56"], "option_values": [51, 75, 57, 56], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 954, "activity_label": "deeparithmark::deeparithmark-1::measurement::depth3::medium", "ctx_a": "A board was 6 metres and 74 centimetres long. A worker cut off 115 centimetres. The board left was", "ctx_b": "", "ctx": "A board was 6 metres and 74 centimetres long. A worker cut off 115 centimetres. The board left was", "endings": [" 459 centimetres.", " 485 centimetres.", " 789 centimetres.", " 559 centimetres."], "source_id": "deeparithmark_v1_measurement_depth3_0954", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "559", "unit": "centimetres", "topic": "measurement", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "measure_cm_cut", "depth": 3, "option_sources": ["cut a whole metre off as well", "forgot the extra centimetres", "added the cut instead of removing it", "correct"], "solution_steps": ["convert metres: 6 x 100 = 600 cm", "add the extra centimetres: 600 + 74 = 674 cm", "subtract the cut: 674 - 115 = 559 cm"], "option_values": [459, 485, 789, 559], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 955, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 4 hours at $12.50 an hour, and then 3 hours at $15.50 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 4 hours at $12.50 an hour, and then 3 hours at $15.50 an hour. He earned", "endings": [" $68.50.", " $108.50.", " $99.50.", " $96.50."], "source_id": "deeparithmark_v1_rate_pay_depth3_0955", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "9650", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["worked one hour less in each stretch", "paid every hour at the second rate", "swapped the two rates", "correct"], "solution_steps": ["first stretch: 4 x 1250 = 5000", "second stretch: 3 x 1550 = 4650", "total pay: 5000 + 4650 = 9650"], "option_values": [6850, 10850, 9950, 9650], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 956, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:01 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:01 a.m. for 125 minutes. The booking ended at", "endings": [" 7:06 a.m.", " 6:06 a.m.", " 3:56 a.m.", " 8:06 a.m."], "source_id": "deeparithmark_v1_time_depth2_0956", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "486", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["forgot the last full hour", "dropped the hour carry", "subtracted the duration instead of adding it", "correct"], "solution_steps": ["convert the start: 361 minutes after midnight", "add the duration: 361 + 125 = 486 minutes"], "option_values": [426, 366, 236, 486], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 957, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $3.80. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $3.80. The booth took 10% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $3.56.", " $3.19.", " $3.42.", " $3.57."], "source_id": "deeparithmark_v1_money_percent_depth2_0957", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "357", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "took the percentage off twice", "forgot the fee", "correct"], "solution_steps": ["take 10% of 380 off: 380 - 38 = 342", "add the 15-cent fee: 342 + 15 = 357"], "option_values": [356, 319, 342, 357], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 958, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $12.00 an hour and 8 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $12.00 an hour and 8 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $635.80.", " $520.20.", " $563.40.", " $539.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0958", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "52020", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["added the tax instead of withholding it", "correct", "paid overtime at double rate", "taxed only the regular pay"], "solution_steps": ["regular pay: 32 x 1200 = 38400", "overtime rate: 1200 x 1.5 = 1800", "overtime pay: 8 x 1800 = 14400", "gross with bonus: 38400 + 14400 + 5000 = 57800", "take-home: 57800 - 5780 = 52020"], "option_values": [63580, 52020, 56340, 53960], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 959, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $4.50 was split between two teams in the ratio 3:2 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "ctx_b": "", "ctx": "A prize of $4.50 was split between two teams in the ratio 3:2 after a $3.00 fee was deducted. The larger team gave 20% of its share to charity and split the rest equally among its 8 players. Each player got", "endings": [" $0.09.", " $0.18.", " $0.33.", " $0.11."], "source_id": "deeparithmark_v1_ratio_depth5_0959", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "9", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "split the whole prize among one team", "forgot to deduct the fee", "forgot the charity cut"], "solution_steps": ["after the fee: 450 - 300 = 150", "one ratio part: 150 / 5 = 30", "larger share: 3 x 30 = 90", "after charity: 90 - 18 = 72", "per player: 72 / 8 = 9"], "option_values": [9, 18, 33, 11], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 960, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1000 sacks. It sent out 10% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1000 sacks. It sent out 10% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 8. The number of full pallets was", "endings": [" 81 pallets.", " 75 pallets.", " 84 pallets.", " 43 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0960", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "84", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "stacked on larger pallets", "correct", "took both percentages twice"], "solution_steps": ["Monday: 10% of 1000 = 100", "left after Monday: 1000 - 100 = 900", "Tuesday: 25% of 900 = 225", "left after Tuesday: 900 - 225 = 675", "full pallets: 675 / 8 = 84"], "option_values": [81, 75, 84, 43], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 961, "activity_label": "deeparithmark::deeparithmark-1::percent_money::depth4::hard", "ctx_a": "An order cost $24.00. A 30% discount came off it, then 10% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "ctx_b": "", "ctx": "An order cost $24.00. A 30% discount came off it, then 10% tax was added to the discounted price, and a $0.40 coupon was applied last. 4 people split the final cost equally. Each paid", "endings": [" $4.42.", " $18.08.", " $4.52.", " $4.72."], "source_id": "deeparithmark_v1_percent_money_depth4_0961", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "452", "unit": "dollars", "topic": "percent_money", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "discount_tax_coupon_split", "depth": 4, "option_sources": ["used the coupon twice", "did not split the cost at all", "correct", "added the coupon instead of subtracting it"], "solution_steps": ["discount: 2400 - 720 = 1680", "tax on the discounted price: 1680 + 168 = 1848", "coupon: 1848 - 40 = 1808", "split 4 ways: 1808 / 4 = 452"], "option_values": [442, 1808, 452, 472], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 962, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $6.20 was split between two teams in the ratio 4:2 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $6.20 was split between two teams in the ratio 4:2 after a $2.00 fee was deducted. The larger team gave 50% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.14.", " $0.56.", " $0.84.", " $0.28."], "source_id": "deeparithmark_v1_ratio_depth5_0962", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "28", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["swapped the ratio parts", "forgot the charity cut", "split the whole prize among one team", "correct"], "solution_steps": ["after the fee: 620 - 200 = 420", "one ratio part: 420 / 6 = 70", "larger share: 4 x 70 = 280", "after charity: 280 - 140 = 140", "per player: 140 / 5 = 28"], "option_values": [14, 56, 84, 28], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 963, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 40 regular hours at $20.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 40 regular hours at $20.00 an hour and 10 overtime hours at one and a half times that rate. A $40.00 bonus was added, and then 20% of the total was withheld for tax. Jo took home", "endings": [" $684.00.", " $672.00.", " $912.00.", " $832.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0963", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "91200", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed twice", "forgot the overtime", "correct", "paid overtime at the normal rate"], "solution_steps": ["regular pay: 40 x 2000 = 80000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 10 x 3000 = 30000", "gross with bonus: 80000 + 30000 + 4000 = 114000", "take-home: 114000 - 22800 = 91200"], "option_values": [68400, 67200, 91200, 83200], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 964, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 620 units. A delivery added 180, then 140 units were shipped out, and 18 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 620 units. A delivery added 180, then 140 units were shipped out, and 18 were found damaged. The rest were packed into crates of 14. The number of full crates packed was", "endings": [" 55 crates.", " 47 crates.", " 45 crates.", " 48 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0964", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "45", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["forgot the shipping", "forgot the damaged units", "correct", "added the damaged units"], "solution_steps": ["after delivery: 620 + 180 = 800", "after shipping: 800 - 140 = 660", "good units: 660 - 18 = 642", "full crates: 642 / 14 = 45 (remainder 12)"], "option_values": [55, 47, 45, 48], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 965, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 8:04 a.m.. The first session lasted 45 minutes, the break lasted 10 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 8:04 a.m.. The first session lasted 45 minutes, the break lasted 10 minutes, and the second session lasted 45 minutes. Rehearsal ended at", "endings": [" 8:49 a.m.", " 8:44 a.m.", " 9:44 a.m.", " 10:24 a.m."], "source_id": "deeparithmark_v1_time_depth3_0965", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "584", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["forgot the last session and the break", "dropped the hour carry", "correct", "finished half an hour late on top of the break"], "solution_steps": ["after the first session: 484 + 45 = 529 minutes after midnight", "after the break: 529 + 10 = 539", "after the second session: 539 + 45 = 584"], "option_values": [529, 524, 584, 624], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 966, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1200 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1200 sacks. It sent out 10% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 84 pallets.", " 52 pallets.", " 86 pallets.", " 78 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0966", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "86", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["took both percentages off the original stock", "took both percentages twice", "correct", "stacked on larger pallets"], "solution_steps": ["Monday: 10% of 1200 = 120", "left after Monday: 1200 - 120 = 1080", "Tuesday: 20% of 1080 = 216", "left after Tuesday: 1080 - 216 = 864", "full pallets: 864 / 10 = 86"], "option_values": [84, 52, 86, 78], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 967, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 20% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $6.36.", " $5.76.", " $4.92.", " $9.24."], "source_id": "deeparithmark_v1_money_percent_depth2_0967", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "636", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["correct", "forgot the fee", "took the percentage off twice", "added the discount instead of removing it"], "solution_steps": ["take 20% of 720 off: 720 - 144 = 576", "add the 60-cent fee: 576 + 60 = 636"], "option_values": [636, 576, 492, 924], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 968, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 44 pallets.", " 55 pallets.", " 48 pallets.", " 43 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0968", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "43", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["counted the loose sacks as a pallet", "forgot Monday", "forgot Tuesday", "correct"], "solution_steps": ["Monday: 20% of 600 = 120", "left after Monday: 600 - 120 = 480", "Tuesday: 10% of 480 = 48", "left after Tuesday: 480 - 48 = 432", "full pallets: 432 / 10 = 43"], "option_values": [44, 55, 48, 43], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 969, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 50% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $1.50.", " $1.80.", " $1.20.", " $0.60."], "source_id": "deeparithmark_v1_money_percent_depth2_0969", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "180", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "correct", "forgot the fee", "took the percentage off twice"], "solution_steps": ["take 50% of 240 off: 240 - 120 = 120", "add the 60-cent fee: 120 + 60 = 180"], "option_values": [150, 180, 120, 60], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 970, "activity_label": "deeparithmark::deeparithmark-1::ratio::depth5::hard", "ctx_a": "A prize of $5.50 was split between two teams in the ratio 4:1 after a $4.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "ctx_b": "", "ctx": "A prize of $5.50 was split between two teams in the ratio 4:1 after a $4.00 fee was deducted. The larger team gave 25% of its share to charity and split the rest equally among its 5 players. Each player got", "endings": [" $0.18.", " $0.15.", " $0.22.", " $0.45."], "source_id": "deeparithmark_v1_ratio_depth5_0970", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "18", "unit": "dollars", "topic": "ratio", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "prize_ratio_charity", "depth": 5, "option_sources": ["correct", "split among one more player", "took the charity cut off the whole prize", "divided between the teams instead of the players"], "solution_steps": ["after the fee: 550 - 400 = 150", "one ratio part: 150 / 5 = 30", "larger share: 4 x 30 = 120", "after charity: 120 - 30 = 90", "per player: 90 / 5 = 18"], "option_values": [18, 15, 22, 45], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 971, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 620 units. A delivery added 260, then 170 units were shipped out, and 32 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 620 units. A delivery added 260, then 170 units were shipped out, and 32 were found damaged. The rest were packed into crates of 9. The number of full crates packed was", "endings": [" 75 crates.", " 46 crates.", " 52 crates.", " 94 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0971", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "75", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["correct", "forgot the delivery", "shipped twice and damaged twice", "forgot the shipping"], "solution_steps": ["after delivery: 620 + 260 = 880", "after shipping: 880 - 170 = 710", "good units: 710 - 32 = 678", "full crates: 678 / 9 = 75 (remainder 3)"], "option_values": [75, 46, 52, 94], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 972, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $0.45 each and 6 erasers at $0.30 each. She split the total cost equally between herself and 3 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $0.45 each and 6 erasers at $0.30 each. She split the total cost equally between herself and 3 friends. Each person paid", "endings": [" $1.27.", " $1.08.", " $1.53.", " $1.35."], "source_id": "deeparithmark_v1_money_depth4_0972", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "135", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["swapped the two unit prices", "split among one more person", "bought one extra of each item", "correct"], "solution_steps": ["markers: 8 x 45 = 360", "erasers: 6 x 30 = 180", "total cost: 360 + 180 = 540", "split between 4 people: 540 / 4 = 135"], "option_values": [127, 108, 153, 135], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 973, "activity_label": "deeparithmark::deeparithmark-1::percent::depth3::hard", "ctx_a": "A shop had 480 shirts. It sold 30% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "ctx_b": "", "ctx": "A shop had 480 shirts. It sold 30% of them, then packed the rest into boxes of 12. The number of full boxes filled was", "endings": [" 12 boxes.", " 28 boxes.", " 36 boxes.", " 29 boxes."], "source_id": "deeparithmark_v1_percent_depth3_0973", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "28", "unit": "boxes", "topic": "percent", "difficulty": "hard", "grade_band": "grades_6", "template_id": "stock_percent_pack", "depth": 3, "option_sources": ["packed the sold shirts", "correct", "sold only a tenth of the stock", "counted the loose shirts as a box"], "solution_steps": ["sold: 30% of 480 = 144", "left over: 480 - 144 = 336", "full boxes: 336 / 12 = 28 (remainder 0)"], "option_values": [12, 28, 36, 29], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 974, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1600 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1600 sacks. It sent out 20% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 103 pallets.", " 134 pallets.", " 102 pallets.", " 128 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0974", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "102", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["counted the loose sacks as a pallet", "forgot Monday", "correct", "forgot Tuesday"], "solution_steps": ["Monday: 20% of 1600 = 320", "left after Monday: 1600 - 320 = 1280", "Tuesday: 20% of 1280 = 256", "left after Tuesday: 1280 - 256 = 1024", "full pallets: 1024 / 10 = 102"], "option_values": [103, 134, 102, 128], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 975, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 600 sacks. It sent out 30% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 600 sacks. It sent out 30% of them on Monday and 20% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 33 pallets.", " 42 pallets.", " 34 pallets.", " 51 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0975", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "33", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "forgot Tuesday", "counted the loose sacks as a pallet", "forgot Monday"], "solution_steps": ["Monday: 30% of 600 = 180", "left after Monday: 600 - 180 = 420", "Tuesday: 20% of 420 = 84", "left after Tuesday: 420 - 84 = 336", "full pallets: 336 / 10 = 33"], "option_values": [33, 42, 34, 51], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 976, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 5 hours at $15.00 an hour, and then 4 hours at $19.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 5 hours at $15.00 an hour, and then 4 hours at $19.00 an hour. He earned", "endings": [" $171.00.", " $155.00.", " $151.00.", " $306.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0976", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "15100", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["paid every hour at the second rate", "swapped the two rates", "correct", "added the rates together"], "solution_steps": ["first stretch: 5 x 1500 = 7500", "second stretch: 4 x 1900 = 7600", "total pay: 7500 + 7600 = 15100"], "option_values": [17100, 15500, 15100, 30600], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 977, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $7.20. The booth took 25% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $7.20. The booth took 25% off the pass and then charged a handling fee of $0.35. In total, the pass cost", "endings": [" $3.95.", " $5.67.", " $7.55.", " $5.75."], "source_id": "deeparithmark_v1_money_percent_depth2_0977", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "575", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "took the discount off the fee as well", "forgot the discount", "correct"], "solution_steps": ["take 25% of 720 off: 720 - 180 = 540", "add the 35-cent fee: 540 + 35 = 575"], "option_values": [395, 567, 755, 575], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 978, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 300 litres. A pipe added 12 litres per minute for 6 minutes, then 7 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 300 litres. A pipe added 12 litres per minute for 6 minutes, then 7 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 309 litres.", " 381 litres.", " 421 litres.", " 461 litres."], "source_id": "deeparithmark_v1_rate_depth4_0978", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "381", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the first fill", "correct", "forgot the drain", "added the drain instead of removing it"], "solution_steps": ["first fill: 12 x 6 = 72 litres", "second fill: 7 x 7 = 49 litres", "before draining: 300 + 72 + 49 = 421", "after draining: 421 - 40 = 381"], "option_values": [309, 381, 421, 461], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 979, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $14.00 an hour, and then 3 hours at $16.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $14.00 an hour, and then 3 hours at $16.00 an hour. He earned", "endings": [" $84.00.", " $132.00.", " $102.00.", " $144.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0979", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "13200", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["forgot the second stretch", "correct", "worked one hour less in each stretch", "paid every hour at the second rate"], "solution_steps": ["first stretch: 6 x 1400 = 8400", "second stretch: 3 x 1600 = 4800", "total pay: 8400 + 4800 = 13200"], "option_values": [8400, 13200, 10200, 14400], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 980, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1000 sacks. It sent out 10% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1000 sacks. It sent out 10% of them on Monday and 25% of the remainder on Tuesday. The rest were stacked on pallets of 10. The number of full pallets was", "endings": [" 67 pallets.", " 35 pallets.", " 61 pallets.", " 68 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0980", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "67", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["correct", "took both percentages twice", "stacked on larger pallets", "counted the loose sacks as a pallet"], "solution_steps": ["Monday: 10% of 1000 = 100", "left after Monday: 1000 - 100 = 900", "Tuesday: 25% of 900 = 225", "left after Tuesday: 900 - 225 = 675", "full pallets: 675 / 10 = 67"], "option_values": [67, 35, 61, 68], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 981, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:54 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:54 a.m. for 80 minutes. The booking ended at", "endings": [" 7:59 a.m.", " 9:14 a.m.", " 8:44 a.m.", " 8:14 a.m."], "source_id": "deeparithmark_v1_time_depth2_0981", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "494", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["stopped a quarter of an hour early", "added an extra hour", "ran half an hour long", "correct"], "solution_steps": ["convert the start: 414 minutes after midnight", "add the duration: 414 + 80 = 494 minutes"], "option_values": [479, 554, 524, 494], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 982, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:59 a.m.. The first session lasted 55 minutes, the break lasted 10 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:59 a.m.. The first session lasted 55 minutes, the break lasted 10 minutes, and the second session lasted 50 minutes. Rehearsal ended at", "endings": [" 8:54 a.m.", " 6:54 a.m.", " 7:54 a.m.", " 9:04 a.m."], "source_id": "deeparithmark_v1_time_depth3_0982", "split": "test", "split_type": "synthetic", "label": "0", "metadata": {"answer": "534", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["correct", "dropped the hour carry", "added the minutes but not the hours", "counted the break twice"], "solution_steps": ["after the first session: 419 + 55 = 474 minutes after midnight", "after the break: 474 + 10 = 484", "after the second session: 484 + 50 = 534"], "option_values": [534, 414, 474, 544], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 983, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 36 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 36 regular hours at $20.00 an hour and 8 overtime hours at one and a half times that rate. A $20.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $908.00.", " $882.00.", " $1078.00.", " $954.00."], "source_id": "deeparithmark_v1_money_rate_depth5_0983", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "88200", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["taxed only the regular pay", "correct", "added the tax instead of withholding it", "paid overtime at double rate"], "solution_steps": ["regular pay: 36 x 2000 = 72000", "overtime rate: 2000 x 1.5 = 3000", "overtime pay: 8 x 3000 = 24000", "gross with bonus: 72000 + 24000 + 2000 = 98000", "take-home: 98000 - 9800 = 88200"], "option_values": [90800, 88200, 107800, 95400], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 984, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $2.40. The booth took 50% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $2.40. The booth took 50% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $2.55.", " $1.35.", " $2.05.", " $3.75."], "source_id": "deeparithmark_v1_money_percent_depth2_0984", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "135", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["forgot the discount", "correct", "read the percentage as a flat number of cents", "added the discount instead of removing it"], "solution_steps": ["take 50% of 240 off: 240 - 120 = 120", "add the 15-cent fee: 120 + 15 = 135"], "option_values": [255, 135, 205, 375], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 985, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $1.20 each and 3 erasers at $0.50 each. She split the total cost equally between herself and 5 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $1.20 each and 3 erasers at $0.50 each. She split the total cost equally between herself and 5 friends. Each person paid", "endings": [" $2.22.", " $1.85.", " $1.86.", " $2.13."], "source_id": "deeparithmark_v1_money_depth4_0985", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "185", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["split only between the friends", "correct", "added the unit prices instead of multiplying", "bought one extra of each item"], "solution_steps": ["markers: 8 x 120 = 960", "erasers: 3 x 50 = 150", "total cost: 960 + 150 = 1110", "split between 6 people: 1110 / 6 = 185"], "option_values": [222, 185, 186, 213], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 986, "activity_label": "deeparithmark::deeparithmark-1::fractions::depth3::hard", "ctx_a": "Kofi baked 108 cookies. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "ctx_b": "", "ctx": "Kofi baked 108 cookies. One third went to a neighbour, and the rest were split equally among 6 grandchildren. Each grandchild got", "endings": [" 9 cookies.", " 6 cookies.", " 15 cookies.", " 12 cookies."], "source_id": "deeparithmark_v1_fractions_depth3_0986", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "12", "unit": "cookies", "topic": "fractions", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "share_then_split", "depth": 3, "option_sources": ["gave away a half instead of a third", "split the given-away cookies too", "split all the cookies among one more child", "correct"], "solution_steps": ["one third given away: 108 / 3 = 36", "rest kept: 108 - 36 = 72", "split among 6: 72 / 6 = 12"], "option_values": [9, 6, 15, 12], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 987, "activity_label": "deeparithmark::deeparithmark-1::multi_step_inventory::depth4::hard", "ctx_a": "A warehouse held 620 units. A delivery added 310, then 210 units were shipped out, and 12 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "ctx_b": "", "ctx": "A warehouse held 620 units. A delivery added 310, then 210 units were shipped out, and 12 were found damaged. The rest were packed into crates of 12. The number of full crates packed was", "endings": [" 54 crates.", " 41 crates.", " 59 crates.", " 76 crates."], "source_id": "deeparithmark_v1_multi_step_inventory_depth4_0987", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "59", "unit": "crates", "topic": "multi_step_inventory", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "inventory_boxes", "depth": 4, "option_sources": ["packed into larger crates", "shipped out twice", "correct", "forgot the shipping"], "solution_steps": ["after delivery: 620 + 310 = 930", "after shipping: 930 - 210 = 720", "good units: 720 - 12 = 708", "full crates: 708 / 12 = 59 (remainder 0)"], "option_values": [54, 41, 59, 76], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 988, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $6.80. The booth took 50% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $6.80. The booth took 50% off the pass and then charged a handling fee of $0.45. In total, the pass cost", "endings": [" $3.63.", " $7.25.", " $10.65.", " $3.85."], "source_id": "deeparithmark_v1_money_percent_depth2_0988", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "385", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "forgot the discount", "added the discount instead of removing it", "correct"], "solution_steps": ["take 50% of 680 off: 680 - 340 = 340", "add the 45-cent fee: 340 + 45 = 385"], "option_values": [363, 725, 1065, 385], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 989, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 6:31 a.m. for 80 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 6:31 a.m. for 80 minutes. The booking ended at", "endings": [" 6:51 a.m.", " 7:36 a.m.", " 7:51 a.m.", " 9:21 a.m."], "source_id": "deeparithmark_v1_time_depth2_0989", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "471", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "stopped a quarter of an hour early", "correct", "ran an hour and a half long"], "solution_steps": ["convert the start: 391 minutes after midnight", "add the duration: 391 + 80 = 471 minutes"], "option_values": [411, 456, 471, 561], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 990, "activity_label": "deeparithmark::deeparithmark-1::money::depth4::hard", "ctx_a": "Priya bought 8 markers at $0.80 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "ctx_b": "", "ctx": "Priya bought 8 markers at $0.80 each and 3 erasers at $0.35 each. She split the total cost equally between herself and 4 friends. Each person paid", "endings": [" $1.04.", " $1.49.", " $1.24.", " $1.06."], "source_id": "deeparithmark_v1_money_depth4_0990", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "149", "unit": "dollars", "topic": "money", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "mix_split", "depth": 4, "option_sources": ["swapped the two unit prices", "correct", "split among one more person", "split among two more people"], "solution_steps": ["markers: 8 x 80 = 640", "erasers: 3 x 35 = 105", "total cost: 640 + 105 = 745", "split between 5 people: 745 / 5 = 149"], "option_values": [104, 149, 124, 106], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 991, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 9 litres per minute for 8 minutes, then 3 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 9 litres per minute for 8 minutes, then 3 litres per minute for 5 minutes. A drain then removed 70 litres. The tank then held", "endings": [" 207 litres.", " 206 litres.", " 167 litres.", " 137 litres."], "source_id": "deeparithmark_v1_rate_depth4_0991", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "137", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["forgot the drain", "added the rates and multiplied once", "used the first rate for both stages", "correct"], "solution_steps": ["first fill: 9 x 8 = 72 litres", "second fill: 3 x 5 = 15 litres", "before draining: 120 + 72 + 15 = 207", "after draining: 207 - 70 = 137"], "option_values": [207, 206, 167, 137], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 992, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $9.60. The booth took 25% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $9.60. The booth took 25% off the pass and then charged a handling fee of $0.60. In total, the pass cost", "endings": [" $5.40.", " $7.80.", " $7.20.", " $10.20."], "source_id": "deeparithmark_v1_money_percent_depth2_0992", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "780", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the percentage off twice", "correct", "forgot the fee", "forgot the discount"], "solution_steps": ["take 25% of 960 off: 960 - 240 = 720", "add the 60-cent fee: 720 + 60 = 780"], "option_values": [540, 780, 720, 1020], "answer_rank": 2, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 993, "activity_label": "deeparithmark::deeparithmark-1::percent_multi_step::depth5::hard", "ctx_a": "A depot held 1400 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "ctx_b": "", "ctx": "A depot held 1400 sacks. It sent out 20% of them on Monday and 10% of the remainder on Tuesday. The rest were stacked on pallets of 12. The number of full pallets was", "endings": [" 85 pallets.", " 93 pallets.", " 107 pallets.", " 84 pallets."], "source_id": "deeparithmark_v1_percent_multi_step_depth5_0993", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "84", "unit": "pallets", "topic": "percent_multi_step", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "inventory_percent_chain", "depth": 5, "option_sources": ["counted the loose sacks as a pallet", "forgot Tuesday", "forgot Monday", "correct"], "solution_steps": ["Monday: 20% of 1400 = 280", "left after Monday: 1400 - 280 = 1120", "Tuesday: 10% of 1120 = 112", "left after Tuesday: 1120 - 112 = 1008", "full pallets: 1008 / 12 = 84"], "option_values": [85, 93, 107, 84], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 994, "activity_label": "deeparithmark::deeparithmark-1::money_rate::depth5::hard", "ctx_a": "Jo worked 32 regular hours at $16.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "ctx_b": "", "ctx": "Jo worked 32 regular hours at $16.00 an hour and 6 overtime hours at one and a half times that rate. A $50.00 bonus was added, and then 10% of the total was withheld for tax. Jo took home", "endings": [" $590.40.", " $635.40.", " $678.60.", " $776.60."], "source_id": "deeparithmark_v1_money_rate_depth5_0994", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "63540", "unit": "dollars", "topic": "money_rate", "difficulty": "hard", "grade_band": "grades_7_8", "template_id": "salary_overtime_tax", "depth": 5, "option_sources": ["forgot the bonus", "correct", "paid overtime at double rate", "added the tax instead of withholding it"], "solution_steps": ["regular pay: 32 x 1600 = 51200", "overtime rate: 1600 x 1.5 = 2400", "overtime pay: 6 x 2400 = 14400", "gross with bonus: 51200 + 14400 + 5000 = 70600", "take-home: 70600 - 7060 = 63540"], "option_values": [59040, 63540, 67860, 77660], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 995, "activity_label": "deeparithmark::deeparithmark-1::money_percent::depth2::medium", "ctx_a": "At the fair, a ride pass cost $8.40. The booth took 50% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "ctx_b": "", "ctx": "At the fair, a ride pass cost $8.40. The booth took 50% off the pass and then charged a handling fee of $0.15. In total, the pass cost", "endings": [" $4.28.", " $4.35.", " $8.55.", " $8.05."], "source_id": "deeparithmark_v1_money_percent_depth2_0995", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "435", "unit": "dollars", "topic": "money_percent", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "money_discount_fee", "depth": 2, "option_sources": ["took the discount off the fee as well", "correct", "forgot the discount", "read the percentage as a flat number of cents"], "solution_steps": ["take 50% of 840 off: 840 - 420 = 420", "add the 15-cent fee: 420 + 15 = 435"], "option_values": [428, 435, 855, 805], "answer_rank": 1, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 996, "activity_label": "deeparithmark::deeparithmark-1::rate::depth4::hard", "ctx_a": "A tank held 120 litres. A pipe added 6 litres per minute for 8 minutes, then 5 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "ctx_b": "", "ctx": "A tank held 120 litres. A pipe added 6 litres per minute for 8 minutes, then 5 litres per minute for 7 minutes. A drain then removed 40 litres. The tank then held", "endings": [" 243 litres.", " 203 litres.", " 163 litres.", " 245 litres."], "source_id": "deeparithmark_v1_rate_depth4_0996", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "163", "unit": "litres", "topic": "rate", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "tank_fill", "depth": 4, "option_sources": ["added the drain instead of removing it", "forgot the drain", "correct", "added the rates and multiplied once"], "solution_steps": ["first fill: 6 x 8 = 48 litres", "second fill: 5 x 7 = 35 litres", "before draining: 120 + 48 + 35 = 203", "after draining: 203 - 40 = 163"], "option_values": [243, 203, 163, 245], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 997, "activity_label": "deeparithmark::deeparithmark-1::time::depth2::medium", "ctx_a": "The hall was booked from 8:23 a.m. for 125 minutes. The booking ended at", "ctx_b": "", "ctx": "The hall was booked from 8:23 a.m. for 125 minutes. The booking ended at", "endings": [" 8:28 a.m.", " 6:18 a.m.", " 9:28 a.m.", " 10:28 a.m."], "source_id": "deeparithmark_v1_time_depth2_0997", "split": "test", "split_type": "synthetic", "label": "3", "metadata": {"answer": "628", "unit": "clock time", "topic": "time", "difficulty": "medium", "grade_band": "grades_4_5", "template_id": "time_clock_end", "depth": 2, "option_sources": ["dropped the hour carry", "subtracted the duration instead of adding it", "forgot the last full hour", "correct"], "solution_steps": ["convert the start: 503 minutes after midnight", "add the duration: 503 + 125 = 628 minutes"], "option_values": [508, 378, 568, 628], "answer_rank": 3, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 998, "activity_label": "deeparithmark::deeparithmark-1::time::depth3::hard", "ctx_a": "Rehearsal began at 6:29 a.m.. The first session lasted 45 minutes, the break lasted 20 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "ctx_b": "", "ctx": "Rehearsal began at 6:29 a.m.. The first session lasted 45 minutes, the break lasted 20 minutes, and the second session lasted 35 minutes. Rehearsal ended at", "endings": [" 8:29 a.m.", " 8:59 a.m.", " 8:09 a.m.", " 8:54 a.m."], "source_id": "deeparithmark_v1_time_depth3_0998", "split": "test", "split_type": "synthetic", "label": "2", "metadata": {"answer": "489", "unit": "clock time", "topic": "time", "difficulty": "hard", "grade_band": "grades_6_7", "template_id": "schedule_sessions", "depth": 3, "option_sources": ["counted the break twice", "finished half an hour late on top of the break", "correct", "counted the first session twice"], "solution_steps": ["after the first session: 389 + 45 = 434 minutes after midnight", "after the break: 434 + 20 = 454", "after the second session: 454 + 35 = 489"], "option_values": [509, 539, 489, 534], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}
{"ind": 999, "activity_label": "deeparithmark::deeparithmark-1::rate_pay::depth3::hard", "ctx_a": "Ravi worked 6 hours at $14.00 an hour, and then 3 hours at $19.00 an hour. He earned", "ctx_b": "", "ctx": "Ravi worked 6 hours at $14.00 an hour, and then 3 hours at $19.00 an hour. He earned", "endings": [" $297.00.", " $141.00.", " $171.00.", " $156.00."], "source_id": "deeparithmark_v1_rate_pay_depth3_0999", "split": "test", "split_type": "synthetic", "label": "1", "metadata": {"answer": "14100", "unit": "dollars", "topic": "rate_pay", "difficulty": "hard", "grade_band": "grades_5_6", "template_id": "two_rate_pay", "depth": 3, "option_sources": ["added the rates together", "correct", "paid every hour at the second rate", "swapped the two rates"], "solution_steps": ["first stretch: 6 x 1400 = 8400", "second stretch: 3 x 1900 = 5700", "total pay: 8400 + 5700 = 14100"], "option_values": [29700, 14100, 17100, 15600], "answer_rank": 0, "format_note": "Continuation-style prompt for base-model log-likelihood scoring; endings include leading spaces and share one unit phrase."}}