| [ |
| { |
| "task_id": "J3_compatible_numbers_000642", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 5082 × 1800.", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 9147600", |
| "solution_b": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9147600", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5082 × 1800.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9147600\n\nSolution B: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9147600" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000568", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 9227 + 8064 - 8063", |
| "solution_a": "NS approach (2 steps): Near-cancellation: 8064 - 8063 = 1, so answer ≈ 9227 + 1. → 9228", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 9228", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 9227 + 8064 - 8063\n\nSolution A: NS approach (2 steps): Near-cancellation: 8064 - 8063 = 1, so answer ≈ 9227 + 1. → 9228\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 9228" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000709", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 3459 × 5559 × 2959 = ___ × 2959 × 3459", |
| "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 5559", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 5559", |
| "correct_answer": "A", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 3459 × 5559 × 2959 = ___ × 2959 × 3459\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 5559\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 5559" |
| }, |
| { |
| "task_id": "J3_option_elimination_000798", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 1760 × 7480?", |
| "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 13164800", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 13164800", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1760 × 7480?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 13164800\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 13164800" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000415", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 9900 * 9900?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 98010000", |
| "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 98010000", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9900 * 9900?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 98010000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 98010000" |
| }, |
| { |
| "task_id": "J3_relative_distance_000547", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 1518/3038 or 3432/6744?", |
| "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3432/6744", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 3432/6744", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1518/3038 or 3432/6744?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3432/6744\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 3432/6744" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000579", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 1817 + 5124 - 5125", |
| "solution_a": "NS approach (2 steps): Near-cancellation: 5124 - 5125 = -1, so answer ≈ 1817 + -1. → 1816", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 1816", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 1817 + 5124 - 5125\n\nSolution A: NS approach (2 steps): Near-cancellation: 5124 - 5125 = -1, so answer ≈ 1817 + -1. → 1816\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 1816" |
| }, |
| { |
| "task_id": "J3_compatible_numbers_000648", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 2520 × 3623.", |
| "solution_a": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9129960", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 9129960", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2520 × 3623.\n\nSolution A: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9129960\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 9129960" |
| }, |
| { |
| "task_id": "J3_option_elimination_000788", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 2243 × 8255?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 18515965", |
| "solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 18515965", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 2243 × 8255?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 18515965\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 18515965" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000559", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 5670 + 1297 - 1299", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 5668", |
| "solution_b": "NS approach (2 steps): Near-cancellation: 1297 - 1299 = -2, so answer ≈ 5670 + -2. → 5668", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 5670 + 1297 - 1299\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 5668\n\nSolution B: NS approach (2 steps): Near-cancellation: 1297 - 1299 = -2, so answer ≈ 5670 + -2. → 5668" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000664", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 24% of 44600 greater than 13866?", |
| "solution_a": "NS approach (2 steps): Use 25% as landmark: 25% of 44600 = 11150. → No", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → No", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 24% of 44600 greater than 13866?\n\nSolution A: NS approach (2 steps): Use 25% as landmark: 25% of 44600 = 11150. → No\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → No" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000484", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 10001 * 4007?", |
| "solution_a": "NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 40074007", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 40074007", |
| "correct_answer": "A", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 10001 * 4007?\n\nSolution A: NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 40074007\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 40074007" |
| }, |
| { |
| "task_id": "J3_compatible_numbers_000606", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 5081 × 2047.", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 10400807", |
| "solution_b": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 10400807", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5081 × 2047.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 10400807\n\nSolution B: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 10400807" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000454", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 9998 * 5588?", |
| "solution_a": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 55868824", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 55868824", |
| "correct_answer": "A", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 5588?\n\nSolution A: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 55868824\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 55868824" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000729", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 9604 + 3781 = ___ + 3591", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 9794", |
| "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9794", |
| "correct_answer": "B", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 9604 + 3781 = ___ + 3591\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 9794\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9794" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000576", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 5487 + 9932 - 9930", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 5489", |
| "solution_b": "NS approach (2 steps): Near-cancellation: 9932 - 9930 = 2, so answer ≈ 5487 + 2. → 5489", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 5487 + 9932 - 9930\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 5489\n\nSolution B: NS approach (2 steps): Near-cancellation: 9932 - 9930 = 2, so answer ≈ 5487 + 2. → 5489" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000471", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 9998 * 7041?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 70395918", |
| "solution_b": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 70395918", |
| "correct_answer": "B", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 7041?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 70395918\n\nSolution B: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 70395918" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000713", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 5328 × (9719 + 5079) = 5328 × ___ + 5328 × 5079", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 9719", |
| "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9719", |
| "correct_answer": "B", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 5328 × (9719 + 5079) = 5328 × ___ + 5328 × 5079\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 9719\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 9719" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000654", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 10% of 95860 greater than 25675?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → No", |
| "solution_b": "NS approach (2 steps): Use 10% as landmark: 10% of 95860 = 9586. → No", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 10% of 95860 greater than 25675?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 10% as landmark: 10% of 95860 = 9586. → No" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000491", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 9999 * 8827?", |
| "solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 88261173", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 88261173", |
| "correct_answer": "A", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 8827?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 88261173\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 88261173" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000440", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 9900 * 9900?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 98010000", |
| "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 98010000", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9900 * 9900?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 98010000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 98010000" |
| }, |
| { |
| "task_id": "J3_compatible_numbers_000628", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 1248 × 7302.", |
| "solution_a": "NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9112896", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 9112896", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 1248 × 7302.\n\nSolution A: NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9112896\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 9112896" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000485", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 9999 * 9992?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99910008", |
| "solution_b": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 99910008", |
| "correct_answer": "B", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 9992?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99910008\n\nSolution B: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 99910008" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000477", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 9999 * 3736?", |
| "solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 37356264", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 37356264", |
| "correct_answer": "A", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 3736?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 37356264\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 37356264" |
| }, |
| { |
| "task_id": "J3_option_elimination_000778", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 1220 × 5134?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 6263480", |
| "solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6263480", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1220 × 5134?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 6263480\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6263480" |
| }, |
| { |
| "task_id": "J3_compatible_numbers_000638", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 2548 × 3929.", |
| "solution_a": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10011092", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 10011092", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2548 × 3929.\n\nSolution A: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10011092\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 10011092" |
| }, |
| { |
| "task_id": "J3_relative_distance_000515", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 4405/8858 or 4666/9156?", |
| "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4666/9156", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 4666/9156", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 4405/8858 or 4666/9156?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4666/9156\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 4666/9156" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000680", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 23% of 72010 greater than 15760?", |
| "solution_a": "NS approach (2 steps): Use 25% as landmark: 25% of 72010 = 18002. → Yes", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → Yes", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 23% of 72010 greater than 15760?\n\nSolution A: NS approach (2 steps): Use 25% as landmark: 25% of 72010 = 18002. → Yes\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → Yes" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000688", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 27% of 63860 greater than 30514?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → No", |
| "solution_b": "NS approach (2 steps): Use 25% as landmark: 25% of 63860 = 15965. → No", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 27% of 63860 greater than 30514?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 25% as landmark: 25% of 63860 = 15965. → No" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000748", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 3807 + 1362 + ___ = 1362 + 8347 + 3807", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 8347", |
| "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8347", |
| "correct_answer": "B", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 3807 + 1362 + ___ = 1362 + 8347 + 3807\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 8347\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8347" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000556", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 6861 + 5024 - 5026", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 6859", |
| "solution_b": "NS approach (2 steps): Near-cancellation: 5024 - 5026 = -2, so answer ≈ 6861 + -2. → 6859", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 6861 + 5024 - 5026\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 6859\n\nSolution B: NS approach (2 steps): Near-cancellation: 5024 - 5026 = -2, so answer ≈ 6861 + -2. → 6859" |
| }, |
| { |
| "task_id": "J3_relative_distance_000504", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 570/1150 or 4951/9819?", |
| "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4951/9819", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 4951/9819", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 570/1150 or 4951/9819?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4951/9819\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 4951/9819" |
| }, |
| { |
| "task_id": "J3_compatible_numbers_000609", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 5009 × 1968.", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 9857712", |
| "solution_b": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5009 × 1968.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9857712\n\nSolution B: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712" |
| }, |
| { |
| "task_id": "J3_compatible_numbers_000646", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 2473 × 4227.", |
| "solution_a": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10453371", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 10453371", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2473 × 4227.\n\nSolution A: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 10453371\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 10453371" |
| }, |
| { |
| "task_id": "J3_relative_distance_000524", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 1837/3735 or 2765/5491?", |
| "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 2765/5491", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 2765/5491", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1837/3735 or 2765/5491?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 2765/5491\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 2765/5491" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000595", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 2576 + 4339 - 4341", |
| "solution_a": "NS approach (2 steps): Near-cancellation: 4339 - 4341 = -2, so answer ≈ 2576 + -2. → 2574", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 2574", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 2576 + 4339 - 4341\n\nSolution A: NS approach (2 steps): Near-cancellation: 4339 - 4341 = -2, so answer ≈ 2576 + -2. → 2574\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 2574" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000492", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 9998 * 2912?", |
| "solution_a": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 29114176", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 29114176", |
| "correct_answer": "A", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 2912?\n\nSolution A: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 29114176\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 29114176" |
| }, |
| { |
| "task_id": "J3_option_elimination_000753", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 6918 × 8652?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 59854536", |
| "solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 59854536", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 6918 × 8652?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 59854536\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 59854536" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000441", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 9800 * 10200?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99960000", |
| "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9800 * 10200?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99960000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99960000" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000422", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 9800 * 10200?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99960000", |
| "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9800 * 10200?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99960000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99960000" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000573", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 9000 + 5060 - 5058", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 9002", |
| "solution_b": "NS approach (2 steps): Near-cancellation: 5060 - 5058 = 2, so answer ≈ 9000 + 2. → 9002", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 9000 + 5060 - 5058\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 9002\n\nSolution B: NS approach (2 steps): Near-cancellation: 5060 - 5058 = 2, so answer ≈ 9000 + 2. → 9002" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000457", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 9999 * 2376?", |
| "solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 23757624", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 23757624", |
| "correct_answer": "A", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 2376?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 23757624\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 23757624" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000423", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 10100 * 9800?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 98980000", |
| "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 98980000", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10100 * 9800?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 98980000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 98980000" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000451", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 10001 * 5029?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 50295029", |
| "solution_b": "NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 50295029", |
| "correct_answer": "B", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 10001 * 5029?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 50295029\n\nSolution B: NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 50295029" |
| }, |
| { |
| "task_id": "J3_option_elimination_000780", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 8020 × 2628?", |
| "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 21076560", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 21076560", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 8020 × 2628?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 21076560\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 21076560" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000430", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 10100 * 9900?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99990000", |
| "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99990000", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10100 * 9900?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99990000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99990000" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000721", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 6468 × (2099 + 2237) = 6468 × ___ + 6468 × 2237", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 2099", |
| "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2099", |
| "correct_answer": "B", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 6468 × (2099 + 2237) = 6468 × ___ + 6468 × 2237\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 2099\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2099" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000578", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 5722 + 2063 - 2062", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 5723", |
| "solution_b": "NS approach (2 steps): Near-cancellation: 2063 - 2062 = 1, so answer ≈ 5722 + 1. → 5723", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 5722 + 2063 - 2062\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 5723\n\nSolution B: NS approach (2 steps): Near-cancellation: 2063 - 2062 = 1, so answer ≈ 5722 + 1. → 5723" |
| }, |
| { |
| "task_id": "J3_compatible_numbers_000616", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 1233 × 7868.", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 9701244", |
| "solution_b": "NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9701244", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 1233 × 7868.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9701244\n\nSolution B: NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 9701244" |
| }, |
| { |
| "task_id": "J3_relative_distance_000512", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 1039/2080 or 3210/6396?", |
| "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3210/6396", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 3210/6396", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1039/2080 or 3210/6396?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3210/6396\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 3210/6396" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000652", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 9% of 48380 greater than 22179?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → No", |
| "solution_b": "NS approach (2 steps): Use 10% as landmark: 10% of 48380 = 4838. → No", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 9% of 48380 greater than 22179?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 10% as landmark: 10% of 48380 = 4838. → No" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000588", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 9092 + 3990 - 3991", |
| "solution_a": "NS approach (2 steps): Near-cancellation: 3990 - 3991 = -1, so answer ≈ 9092 + -1. → 9091", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 9091", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 9092 + 3990 - 3991\n\nSolution A: NS approach (2 steps): Near-cancellation: 3990 - 3991 = -1, so answer ≈ 9092 + -1. → 9091\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 9091" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000727", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 3305 + 5079 + ___ = 5079 + 3905 + 3305", |
| "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 3905", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 3905", |
| "correct_answer": "A", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 3305 + 5079 + ___ = 5079 + 3905 + 3305\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 3905\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 3905" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000704", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 9515 + 8703 = ___ + 7313", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 10905", |
| "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 10905", |
| "correct_answer": "B", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 9515 + 8703 = ___ + 7313\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 10905\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 10905" |
| }, |
| { |
| "task_id": "J3_option_elimination_000800", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 6809 × 9143?", |
| "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 62254687", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 62254687", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 6809 × 9143?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 62254687\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 62254687" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000420", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 10200 * 9800?", |
| "solution_a": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 99960000", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n\nSolution A: NS approach (2 steps): Round both to 10000 and multiply. → 99960000\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 99960000" |
| }, |
| { |
| "task_id": "J3_relative_distance_000509", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 2166/4399 or 1489/2922?", |
| "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1489/2922", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 1489/2922", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 2166/4399 or 1489/2922?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1489/2922\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 1489/2922" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000407", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 9900 * 10100?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99990000", |
| "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99990000", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9900 * 10100?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99990000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99990000" |
| }, |
| { |
| "task_id": "J3_compatible_numbers_000605", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 1274 × 8785.", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 11192090", |
| "solution_b": "NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 11192090", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 1274 × 8785.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 11192090\n\nSolution B: NS approach (2 steps): Round to 1250×8000 for easy mental computation. → 11192090" |
| }, |
| { |
| "task_id": "J3_relative_distance_000543", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 1162/2369 or 1679/3322?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 1679/3322", |
| "solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1679/3322", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1162/2369 or 1679/3322?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 1679/3322\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1679/3322" |
| }, |
| { |
| "task_id": "J3_relative_distance_000527", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 1753/3550 or 4210/8308?", |
| "solution_a": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4210/8308", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 4210/8308", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1753/3550 or 4210/8308?\n\nSolution A: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4210/8308\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 4210/8308" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000726", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 1264 + 1118 = ___ + 7226", |
| "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → -4844", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → -4844", |
| "correct_answer": "A", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 1264 + 1118 = ___ + 7226\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → -4844\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → -4844" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000443", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 9800 * 9800?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 96040000", |
| "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 96040000", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 9800 * 9800?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 96040000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 96040000" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000653", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 48% of 75650 greater than 34563?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → Yes", |
| "solution_b": "NS approach (2 steps): Use 50% as landmark: 50% of 75650 = 37825. → Yes", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 48% of 75650 greater than 34563?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → Yes\n\nSolution B: NS approach (2 steps): Use 50% as landmark: 50% of 75650 = 37825. → Yes" |
| }, |
| { |
| "task_id": "J3_relative_distance_000534", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 4320/8812 or 1806/3591?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 1806/3591", |
| "solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1806/3591", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 4320/8812 or 1806/3591?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 1806/3591\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1806/3591" |
| }, |
| { |
| "task_id": "J3_option_elimination_000782", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 1133 × 1067?", |
| "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 1208911", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 1208911", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1133 × 1067?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 1208911\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 1208911" |
| }, |
| { |
| "task_id": "J3_compatible_numbers_000608", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 5009 × 1968.", |
| "solution_a": "NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 9857712", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 5009 × 1968.\n\nSolution A: NS approach (2 steps): Round to 5000×2000 for easy mental computation. → 9857712\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 9857712" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000699", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 11% of 57250 greater than 11559?", |
| "solution_a": "NS approach (2 steps): Use 10% as landmark: 10% of 57250 = 5725. → No", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → No", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 11% of 57250 greater than 11559?\n\nSolution A: NS approach (2 steps): Use 10% as landmark: 10% of 57250 = 5725. → No\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → No" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000599", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 2021 + 4865 - 4863", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 2023", |
| "solution_b": "NS approach (2 steps): Near-cancellation: 4865 - 4863 = 2, so answer ≈ 2021 + 2. → 2023", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 2021 + 4865 - 4863\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 2023\n\nSolution B: NS approach (2 steps): Near-cancellation: 4865 - 4863 = 2, so answer ≈ 2021 + 2. → 2023" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000460", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 10001 * 4123?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 41234123", |
| "solution_b": "NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 41234123", |
| "correct_answer": "B", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 10001 * 4123?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 41234123\n\nSolution B: NS approach (3 steps): Use (10000+1)*m = 10000*m + 1*m. → 41234123" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000478", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 9999 * 2734?", |
| "solution_a": "NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 27337266", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 27337266", |
| "correct_answer": "A", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9999 * 2734?\n\nSolution A: NS approach (3 steps): Use (10000-1)*m = 10000*m - 1*m. → 27337266\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 27337266" |
| }, |
| { |
| "task_id": "J3_option_elimination_000758", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 7525 × 5474?", |
| "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 41191850", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 41191850", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 7525 × 5474?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 41191850\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 41191850" |
| }, |
| { |
| "task_id": "J3_relative_distance_000541", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 1748/3532 or 1376/2725?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 1376/2725", |
| "solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1376/2725", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 1748/3532 or 1376/2725?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 1376/2725\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 1376/2725" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000695", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 50% of 45760 greater than 12614?", |
| "solution_a": "NS approach (2 steps): Use 50% as landmark: 50% of 45760 = 22880. → Yes", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → Yes", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 50% of 45760 greater than 12614?\n\nSolution A: NS approach (2 steps): Use 50% as landmark: 50% of 45760 = 22880. → Yes\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → Yes" |
| }, |
| { |
| "task_id": "J3_option_elimination_000776", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 6135 × 7717?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 47343795", |
| "solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 47343795", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 6135 × 7717?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 47343795\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 47343795" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000402", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 10100 * 9900?", |
| "solution_a": "NS approach (2 steps): Round both to 10000 and multiply. → 99990000", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 99990000", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10100 * 9900?\n\nSolution A: NS approach (2 steps): Round both to 10000 and multiply. → 99990000\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 99990000" |
| }, |
| { |
| "task_id": "J3_structural_shortcuts_000496", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "structural_shortcuts", |
| "problem": "What is 9998 * 3721?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 37202558", |
| "solution_b": "NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 37202558", |
| "correct_answer": "B", |
| "ns_steps": 3, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 9998 * 3721?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 37202558\n\nSolution B: NS approach (3 steps): Use (10000-2)*m = 10000*m - 2*m. → 37202558" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000734", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 5844 + 3069 + ___ = 3069 + 6695 + 5844", |
| "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6695", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 6695", |
| "correct_answer": "A", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 5844 + 3069 + ___ = 3069 + 6695 + 5844\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6695\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 6695" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000414", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 10200 * 9800?", |
| "solution_a": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 99960000", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n\nSolution A: NS approach (2 steps): Round both to 10000 and multiply. → 99960000\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 99960000" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000555", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 7126 + 2057 - 2055", |
| "solution_a": "NS approach (2 steps): Near-cancellation: 2057 - 2055 = 2, so answer ≈ 7126 + 2. → 7128", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 7128", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 7126 + 2057 - 2055\n\nSolution A: NS approach (2 steps): Near-cancellation: 2057 - 2055 = 2, so answer ≈ 7126 + 2. → 7128\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 7128" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000703", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 4391 + 8555 + ___ = 8555 + 8523 + 4391", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 8523", |
| "solution_b": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8523", |
| "correct_answer": "B", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 4391 + 8555 + ___ = 8555 + 8523 + 4391\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 8523\n\nSolution B: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 8523" |
| }, |
| { |
| "task_id": "J3_compatible_numbers_000603", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 2520 × 3783.", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 9533160", |
| "solution_b": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9533160", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2520 × 3783.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9533160\n\nSolution B: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9533160" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000681", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 9% of 52080 greater than 22238?", |
| "solution_a": "NS approach (2 steps): Use 10% as landmark: 10% of 52080 = 5208. → No", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → No", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 9% of 52080 greater than 22238?\n\nSolution A: NS approach (2 steps): Use 10% as landmark: 10% of 52080 = 5208. → No\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → No" |
| }, |
| { |
| "task_id": "J3_magnitude_estimation_000434", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "magnitude_estimation", |
| "problem": "Which of the following is the best estimate for 10200 * 9800?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 99960000", |
| "solution_b": "NS approach (2 steps): Round both to 10000 and multiply. → 99960000", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 99960000\n\nSolution B: NS approach (2 steps): Round both to 10000 and multiply. → 99960000" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000718", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 2661 + 1919 + ___ = 1919 + 6614 + 2661", |
| "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6614", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 6614", |
| "correct_answer": "A", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 2661 + 1919 + ___ = 1919 + 6614 + 2661\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 6614\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 6614" |
| }, |
| { |
| "task_id": "J3_relative_distance_000530", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 3937/7998 or 3703/7314?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 3703/7314", |
| "solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3703/7314", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 3937/7998 or 3703/7314?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 3703/7314\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 3703/7314" |
| }, |
| { |
| "task_id": "J3_relative_distance_000528", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "relative_distance", |
| "problem": "Which is larger: 2499/5018 or 4280/8455?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 4280/8455", |
| "solution_b": "NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4280/8455", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Which is larger: 2499/5018 or 4280/8455?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 4280/8455\n\nSolution B: NS approach (2 steps): One is below 1/2, the other above; no computation needed. → 4280/8455" |
| }, |
| { |
| "task_id": "J3_option_elimination_000771", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 5562 × 7803?", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 43400286", |
| "solution_b": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 43400286", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 5562 × 7803?\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 43400286\n\nSolution B: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 43400286" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000668", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 10% of 93060 greater than 31194?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → No", |
| "solution_b": "NS approach (2 steps): Use 10% as landmark: 10% of 93060 = 9306. → No", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 10% of 93060 greater than 31194?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 10% as landmark: 10% of 93060 = 9306. → No" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000677", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 48% of 23770 greater than 9136?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → Yes", |
| "solution_b": "NS approach (2 steps): Use 50% as landmark: 50% of 23770 = 11885. → Yes", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 48% of 23770 greater than 9136?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → Yes\n\nSolution B: NS approach (2 steps): Use 50% as landmark: 50% of 23770 = 11885. → Yes" |
| }, |
| { |
| "task_id": "J3_landmark_comparison_000694", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "landmark_comparison", |
| "problem": "Is 24% of 90400 greater than 25771?", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → No", |
| "solution_b": "NS approach (2 steps): Use 25% as landmark: 25% of 90400 = 22600. → No", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Is 24% of 90400 greater than 25771?\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → No\n\nSolution B: NS approach (2 steps): Use 25% as landmark: 25% of 90400 = 22600. → No" |
| }, |
| { |
| "task_id": "J3_option_elimination_000792", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 4893 × 1523?", |
| "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 7452039", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 7452039", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 4893 × 1523?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 7452039\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 7452039" |
| }, |
| { |
| "task_id": "J3_compatible_numbers_000613", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "compatible_numbers", |
| "problem": "Estimate 2540 × 3676.", |
| "solution_a": "Algorithmic approach (4 steps): Compute step by step → 9337040", |
| "solution_b": "NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9337040", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Estimate 2540 × 3676.\n\nSolution A: Algorithmic approach (4 steps): Compute step by step → 9337040\n\nSolution B: NS approach (2 steps): Round to 2500×4000 for easy mental computation. → 9337040" |
| }, |
| { |
| "task_id": "J3_cancellation_identity_000585", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "cancellation_identity", |
| "problem": "Evaluate: 4359 + 9463 - 9464", |
| "solution_a": "Algorithmic approach (3 steps): Compute step by step → 4358", |
| "solution_b": "NS approach (2 steps): Near-cancellation: 9463 - 9464 = -1, so answer ≈ 4359 + -1. → 4358", |
| "correct_answer": "B", |
| "ns_steps": 2, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: Evaluate: 4359 + 9463 - 9464\n\nSolution A: Algorithmic approach (3 steps): Compute step by step → 4358\n\nSolution B: NS approach (2 steps): Near-cancellation: 9463 - 9464 = -1, so answer ≈ 4359 + -1. → 4358" |
| }, |
| { |
| "task_id": "J3_equation_reasoning_000743", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "equation_reasoning", |
| "problem": "What value fills the blank? 6010 × (2659 + 2481) = 6010 × ___ + 6010 × 2481", |
| "solution_a": "NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2659", |
| "solution_b": "Algorithmic approach (3 steps): Compute step by step → 2659", |
| "correct_answer": "A", |
| "ns_steps": 1, |
| "algo_steps": 3, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What value fills the blank? 6010 × (2659 + 2481) = 6010 × ___ + 6010 × 2481\n\nSolution A: NS approach (1 steps): Recognize commutativity/distributive law — matching terms cancel. → 2659\n\nSolution B: Algorithmic approach (3 steps): Compute step by step → 2659" |
| }, |
| { |
| "task_id": "J3_option_elimination_000765", |
| "task_type": "J3_pairwise_efficiency", |
| "category": "option_elimination", |
| "problem": "What is 1104 × 5487?", |
| "solution_a": "NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6057648", |
| "solution_b": "Algorithmic approach (4 steps): Compute step by step → 6057648", |
| "correct_answer": "A", |
| "ns_steps": 2, |
| "algo_steps": 4, |
| "prompt": "Both solutions below are correct. Which one uses fewer reasoning steps? Answer A or B.\n\nProblem: What is 1104 × 5487?\n\nSolution A: NS approach (2 steps): Check trailing digit / parity / magnitude — only one option matches. → 6057648\n\nSolution B: Algorithmic approach (4 steps): Compute step by step → 6057648" |
| } |
| ] |
