data/judge_j1.json

[
  {
    "task_id": "J1_equation_reasoning_000729_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "weak_shortcut",
    "problem": "What value fills the blank?  4648 + 2509 + ___ = 2509 + 7879 + 2086\n(A) 5307  (B) 5337  (C) 5327  (D) 5317",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  4648 + 2509 + ___ = 2509 + 7879 + 2086\n(A) 5307  (B) 5337  (C) 5327  (D) 5317"
  },
  {
    "task_id": "J1_relative_distance_000520_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 4430/9230 or 2182/3968?\n(A) 3054/4091  (B) 4430/9230  (C) 1328/3436  (D) 2182/3968",
    "ground_truth": "YES",
    "shortcut_strength": 0.06994253049313254,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4430/9230 or 2182/3968?\n(A) 3054/4091  (B) 4430/9230  (C) 1328/3436  (D) 2182/3968"
  },
  {
    "task_id": "J1_magnitude_estimation_000414_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "weak_shortcut",
    "problem": "Which of the following is the best estimate for 10100 * 10140?\n(A) 102414010  (B) 102413990  (C) 102414020  (D) 102414000",
    "ground_truth": "YES",
    "shortcut_strength": 0.988,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10100 * 10140?\n(A) 102414010  (B) 102413990  (C) 102414020  (D) 102414000"
  },
  {
    "task_id": "J1_option_elimination_000765_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "control",
    "problem": "What is 9071 × 8363?\n(A) 88380773  (B) 86000773  (C) 80270773  (D) 75860773",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9071 × 8363?\n(A) 88380773  (B) 86000773  (C) 80270773  (D) 75860773"
  },
  {
    "task_id": "J1_landmark_comparison_000677_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 73% of 23770 greater than 9136?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 73% of 23770 greater than 9136?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_option_elimination_000798_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 2760 × 5986?\n(A) 16521360  (B) 16521380  (C) 16521361  (D) 16521359",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 2760 × 5986?\n(A) 16521360  (B) 16521380  (C) 16521361  (D) 16521359"
  },
  {
    "task_id": "J1_structural_shortcuts_000494_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 4697 * 4721?\n(A) 22174547  (B) 22174527  (C) 22174537  (D) 22174557",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 4697 * 4721?\n(A) 22174547  (B) 22174527  (C) 22174537  (D) 22174557"
  },
  {
    "task_id": "J1_magnitude_estimation_000434_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 10200 * 9800?\n(A) 99960000  (B) 99959990  (C) 99960010  (D) 99960020",
    "ground_truth": "YES",
    "shortcut_strength": 0.98,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n(A) 99960000  (B) 99959990  (C) 99960010  (D) 99960020"
  },
  {
    "task_id": "J1_relative_distance_000522_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "control",
    "problem": "Which is larger: 5316/9664 or 4112/7088?\n(A) 5316/9664  (B) 2355/4903  (C) 2683/4441  (D) 4112/7088",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 5316/9664 or 4112/7088?\n(A) 5316/9664  (B) 2355/4903  (C) 2683/4441  (D) 4112/7088"
  },
  {
    "task_id": "J1_structural_shortcuts_000483_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "strong_shortcut",
    "problem": "What is 10001 * 1388?\n(A) 13881388  (B) 13881378  (C) 13881408  (D) 13881398",
    "ground_truth": "YES",
    "shortcut_strength": 0.9999,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 10001 * 1388?\n(A) 13881388  (B) 13881378  (C) 13881408  (D) 13881398"
  },
  {
    "task_id": "J1_compatible_numbers_000647_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 2470 × 5025.\n(A) 12411760  (B) 12411750  (C) 12411770  (D) 12411740",
    "ground_truth": "YES",
    "shortcut_strength": 0.865875,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 2470 × 5025.\n(A) 12411760  (B) 12411750  (C) 12411770  (D) 12411740"
  },
  {
    "task_id": "J1_option_elimination_000752_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "strong_shortcut",
    "problem": "What is 4077 × 6150?\n(A) 25073551  (B) 25073552  (C) 25073550  (D) 25073549",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 4077 × 6150?\n(A) 25073551  (B) 25073552  (C) 25073550  (D) 25073549"
  },
  {
    "task_id": "J1_landmark_comparison_000666_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "strong_shortcut",
    "problem": "Is 52% of 79090 greater than 21700?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.98,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 52% of 79090 greater than 21700?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_relative_distance_000506_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 1561/3253 or 4531/8239?\n(A) 1272/3372  (B) 4531/8239  (C) 4610/8904  (D) 1561/3253",
    "ground_truth": "YES",
    "shortcut_strength": 0.070080641481304,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1561/3253 or 4531/8239?\n(A) 1272/3372  (B) 4531/8239  (C) 4610/8904  (D) 1561/3253"
  },
  {
    "task_id": "J1_equation_reasoning_000731_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "weak_shortcut",
    "problem": "What value fills the blank?  9518 + 9468 + ___ = 9468 + 5370 + 3157\n(A) -991  (B) -1009  (C) -989  (D) -979",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  9518 + 9468 + ___ = 9468 + 5370 + 3157\n(A) -991  (B) -1009  (C) -989  (D) -979"
  },
  {
    "task_id": "J1_equation_reasoning_000717_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "control",
    "problem": "What value fills the blank?  1753 + 7390 + ___ = 8979 + 5093\n(A) 4929  (B) 4939  (C) 4919  (D) 4949",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  1753 + 7390 + ___ = 8979 + 5093\n(A) 4929  (B) 4939  (C) 4919  (D) 4949"
  },
  {
    "task_id": "J1_landmark_comparison_000693_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "strong_shortcut",
    "problem": "Is 26% of 37310 greater than 17689?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.99,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 26% of 37310 greater than 17689?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_magnitude_estimation_000446_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 10100 * 9900?\n(A) 99990000  (B) 99990020  (C) 99989990  (D) 99990010",
    "ground_truth": "YES",
    "shortcut_strength": 0.99,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10100 * 9900?\n(A) 99990000  (B) 99990020  (C) 99989990  (D) 99990010"
  },
  {
    "task_id": "J1_compatible_numbers_000633_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 9047 × 9028.\n(A) 81676306  (B) 81676316  (C) 81676336  (D) 81676326",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 9047 × 9028.\n(A) 81676306  (B) 81676316  (C) 81676336  (D) 81676326"
  },
  {
    "task_id": "J1_option_elimination_000778_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "control",
    "problem": "What is 3947 × 4463?\n(A) 18675461  (B) 17615461  (C) 14985461  (D) 17575461",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 3947 × 4463?\n(A) 18675461  (B) 17615461  (C) 14985461  (D) 17575461"
  },
  {
    "task_id": "J1_relative_distance_000529_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 4754/9905 or 2960/5382?\n(A) 381/1347  (B) 4754/9905  (C) 3484/9906  (D) 2960/5382",
    "ground_truth": "YES",
    "shortcut_strength": 0.07002180319126083,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4754/9905 or 2960/5382?\n(A) 381/1347  (B) 4754/9905  (C) 3484/9906  (D) 2960/5382"
  },
  {
    "task_id": "J1_landmark_comparison_000687_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 73% of 63180 greater than 19879?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 73% of 63180 greater than 19879?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_magnitude_estimation_000445_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "weak_shortcut",
    "problem": "Which of the following is the best estimate for 9900 * 10156?\n(A) 100544390  (B) 100544420  (C) 100544400  (D) 100544410",
    "ground_truth": "YES",
    "shortcut_strength": 0.9872,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 9900 * 10156?\n(A) 100544390  (B) 100544420  (C) 100544400  (D) 100544410"
  },
  {
    "task_id": "J1_compatible_numbers_000641_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 1258 × 5897.\n(A) 7418436  (B) 7418426  (C) 7418446  (D) 7418416",
    "ground_truth": "YES",
    "shortcut_strength": 0.8653625,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1258 × 5897.\n(A) 7418436  (B) 7418426  (C) 7418446  (D) 7418416"
  },
  {
    "task_id": "J1_relative_distance_000504_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 1639/3415 or 3104/5643?\n(A) 1003/1562  (B) 3104/5643  (C) 1639/3415  (D) 2376/3389",
    "ground_truth": "YES",
    "shortcut_strength": 0.0701205888999678,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1639/3415 or 3104/5643?\n(A) 1003/1562  (B) 3104/5643  (C) 1639/3415  (D) 2376/3389"
  },
  {
    "task_id": "J1_magnitude_estimation_000424_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "weak_shortcut",
    "problem": "Which of the following is the best estimate for 10200 * 10200?\n(A) 104040020  (B) 104039990  (C) 104040010  (D) 104040000",
    "ground_truth": "YES",
    "shortcut_strength": 0.98,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10200 * 10200?\n(A) 104040020  (B) 104039990  (C) 104040010  (D) 104040000"
  },
  {
    "task_id": "J1_compatible_numbers_000647_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "strong_shortcut",
    "problem": "Estimate 2530 × 3992.\n(A) 10099760  (B) 10099770  (C) 10099750  (D) 10099780",
    "ground_truth": "YES",
    "shortcut_strength": 0.993,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 2530 × 3992.\n(A) 10099760  (B) 10099770  (C) 10099750  (D) 10099780"
  },
  {
    "task_id": "J1_compatible_numbers_000602_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 2497 × 3111.\n(A) 7768177  (B) 7768167  (C) 7768157  (D) 7768187",
    "ground_truth": "YES",
    "shortcut_strength": 0.888275,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 2497 × 3111.\n(A) 7768177  (B) 7768167  (C) 7768157  (D) 7768187"
  },
  {
    "task_id": "J1_option_elimination_000797_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 3925 × 5618?\n(A) 22050670  (B) 22050651  (C) 22050649  (D) 22050650",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 3925 × 5618?\n(A) 22050670  (B) 22050651  (C) 22050649  (D) 22050650"
  },
  {
    "task_id": "J1_compatible_numbers_000645_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 3753 × 5259.\n(A) 19737037  (B) 19737027  (C) 19737017  (D) 19737047",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 3753 × 5259.\n(A) 19737037  (B) 19737027  (C) 19737017  (D) 19737047"
  },
  {
    "task_id": "J1_structural_shortcuts_000499_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 10005 * 3275?\n(A) 32766385  (B) 32766365  (C) 32766395  (D) 32766375",
    "ground_truth": "YES",
    "shortcut_strength": 0.9995,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 10005 * 3275?\n(A) 32766385  (B) 32766365  (C) 32766395  (D) 32766375"
  },
  {
    "task_id": "J1_structural_shortcuts_000452_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 4484 * 4590?\n(A) 20581550  (B) 20581580  (C) 20581560  (D) 20581570",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 4484 * 4590?\n(A) 20581550  (B) 20581580  (C) 20581560  (D) 20581570"
  },
  {
    "task_id": "J1_cancellation_identity_000581_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 4268 + 5101 - 2454\n(A) 6935  (B) 6915  (C) 6925  (D) 6905",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 4268 + 5101 - 2454\n(A) 6935  (B) 6915  (C) 6925  (D) 6905"
  },
  {
    "task_id": "J1_structural_shortcuts_000462_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "strong_shortcut",
    "problem": "What is 10002 * 4433?\n(A) 44338886  (B) 44338866  (C) 44338876  (D) 44338856",
    "ground_truth": "YES",
    "shortcut_strength": 0.9998,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 10002 * 4433?\n(A) 44338886  (B) 44338866  (C) 44338876  (D) 44338856"
  },
  {
    "task_id": "J1_magnitude_estimation_000450_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 5162 * 4712?\n(A) 24323364  (B) 24323344  (C) 24323334  (D) 24323354",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 5162 * 4712?\n(A) 24323364  (B) 24323344  (C) 24323334  (D) 24323354"
  },
  {
    "task_id": "J1_cancellation_identity_000571_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "weak_shortcut",
    "problem": "Evaluate: 6789 + 9091 - 9099\n(A) 6781  (B) 6791  (C) 6771  (D) 6801",
    "ground_truth": "YES",
    "shortcut_strength": 0.999120008799912,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 6789 + 9091 - 9099\n(A) 6781  (B) 6791  (C) 6771  (D) 6801"
  },
  {
    "task_id": "J1_option_elimination_000777_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 2895 × 9642?\n(A) 27913591  (B) 27913600  (C) 27913590  (D) 27913589",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 2895 × 9642?\n(A) 27913591  (B) 27913600  (C) 27913590  (D) 27913589"
  },
  {
    "task_id": "J1_cancellation_identity_000556_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 6861 + 5024 - 2865\n(A) 9010  (B) 9030  (C) 9020  (D) 9040",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 6861 + 5024 - 2865\n(A) 9010  (B) 9030  (C) 9020  (D) 9040"
  },
  {
    "task_id": "J1_landmark_comparison_000692_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 3% of 61660 greater than 27126?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.9299999999999999,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 3% of 61660 greater than 27126?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_cancellation_identity_000558_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 3344 + 1236 - 1733\n(A) 2867  (B) 2847  (C) 2837  (D) 2857",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 3344 + 1236 - 1733\n(A) 2867  (B) 2847  (C) 2837  (D) 2857"
  },
  {
    "task_id": "J1_option_elimination_000758_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "control",
    "problem": "What is 1649 × 9833?\n(A) 16214617  (B) 17424617  (C) 14514617  (D) 16024617",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 1649 × 9833?\n(A) 16214617  (B) 17424617  (C) 14514617  (D) 16024617"
  },
  {
    "task_id": "J1_compatible_numbers_000613_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "strong_shortcut",
    "problem": "Estimate 2540 × 3676.\n(A) 9337060  (B) 9337040  (C) 9337050  (D) 9337030",
    "ground_truth": "YES",
    "shortcut_strength": 0.9515,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 2540 × 3676.\n(A) 9337060  (B) 9337040  (C) 9337050  (D) 9337030"
  },
  {
    "task_id": "J1_relative_distance_000523_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 1473/2971 or 843/1672?\n(A) 843/1672  (B) 807/2616  (C) 1473/2971  (D) 2865/4160",
    "ground_truth": "YES",
    "shortcut_strength": 0.008393940467582184,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1473/2971 or 843/1672?\n(A) 843/1672  (B) 807/2616  (C) 1473/2971  (D) 2865/4160"
  },
  {
    "task_id": "J1_option_elimination_000789_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "control",
    "problem": "What is 7373 × 4227?\n(A) 30475671  (B) 31455671  (C) 32725671  (D) 31165671",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 7373 × 4227?\n(A) 30475671  (B) 31455671  (C) 32725671  (D) 31165671"
  },
  {
    "task_id": "J1_landmark_comparison_000668_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 73% of 93060 greater than 31194?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 73% of 93060 greater than 31194?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_compatible_numbers_000649_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 1255 × 10479.\n(A) 13151155  (B) 13151145  (C) 13151165  (D) 13151135",
    "ground_truth": "YES",
    "shortcut_strength": 0.8430625,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1255 × 10479.\n(A) 13151155  (B) 13151145  (C) 13151165  (D) 13151135"
  },
  {
    "task_id": "J1_compatible_numbers_000621_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 2846 × 5764.\n(A) 16404344  (B) 16404364  (C) 16404334  (D) 16404354",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 2846 × 5764.\n(A) 16404344  (B) 16404364  (C) 16404334  (D) 16404354"
  },
  {
    "task_id": "J1_equation_reasoning_000740_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "control",
    "problem": "What value fills the blank?  2555 + 2924 + ___ = 4909 + 6909\n(A) 6359  (B) 6339  (C) 6349  (D) 6329",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  2555 + 2924 + ___ = 4909 + 6909\n(A) 6359  (B) 6339  (C) 6349  (D) 6329"
  },
  {
    "task_id": "J1_landmark_comparison_000684_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 37% of 17490 greater than 8451?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 37% of 17490 greater than 8451?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_cancellation_identity_000599_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "strong_shortcut",
    "problem": "Evaluate: 2021 + 4865 - 4863\n(A) 2033  (B) 2013  (C) 2043  (D) 2023",
    "ground_truth": "YES",
    "shortcut_strength": 0.9995889003083248,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 2021 + 4865 - 4863\n(A) 2033  (B) 2013  (C) 2043  (D) 2023"
  },
  {
    "task_id": "J1_magnitude_estimation_000405_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 5392 * 5454?\n(A) 29407958  (B) 29407978  (C) 29407988  (D) 29407968",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 5392 * 5454?\n(A) 29407958  (B) 29407978  (C) 29407988  (D) 29407968"
  },
  {
    "task_id": "J1_structural_shortcuts_000477_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "strong_shortcut",
    "problem": "What is 9999 * 3736?\n(A) 37356284  (B) 37356254  (C) 37356274  (D) 37356264",
    "ground_truth": "YES",
    "shortcut_strength": 0.9999,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9999 * 3736?\n(A) 37356284  (B) 37356254  (C) 37356274  (D) 37356264"
  },
  {
    "task_id": "J1_structural_shortcuts_000483_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 6722 * 5016?\n(A) 33717552  (B) 33717542  (C) 33717572  (D) 33717562",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 6722 * 5016?\n(A) 33717552  (B) 33717542  (C) 33717572  (D) 33717562"
  },
  {
    "task_id": "J1_compatible_numbers_000634_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 1250 × 10446.\n(A) 13057500  (B) 13057490  (C) 13057520  (D) 13057510",
    "ground_truth": "YES",
    "shortcut_strength": 0.847125,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1250 × 10446.\n(A) 13057500  (B) 13057490  (C) 13057520  (D) 13057510"
  },
  {
    "task_id": "J1_compatible_numbers_000644_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 4235 × 1437.\n(A) 6085685  (B) 6085715  (C) 6085695  (D) 6085705",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 4235 × 1437.\n(A) 6085685  (B) 6085715  (C) 6085695  (D) 6085705"
  },
  {
    "task_id": "J1_cancellation_identity_000588_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 9092 + 3990 - 6160\n(A) 6922  (B) 6912  (C) 6942  (D) 6932",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 9092 + 3990 - 6160\n(A) 6922  (B) 6912  (C) 6942  (D) 6932"
  },
  {
    "task_id": "J1_option_elimination_000761_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "strong_shortcut",
    "problem": "What is 4770 × 3207?\n(A) 15297389  (B) 15297391  (C) 15297390  (D) 15297392",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 4770 × 3207?\n(A) 15297389  (B) 15297391  (C) 15297390  (D) 15297392"
  },
  {
    "task_id": "J1_cancellation_identity_000589_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "strong_shortcut",
    "problem": "Evaluate: 3427 + 1463 - 1462\n(A) 3448  (B) 3438  (C) 3428  (D) 3418",
    "ground_truth": "YES",
    "shortcut_strength": 0.9993164730006835,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 3427 + 1463 - 1462\n(A) 3448  (B) 3438  (C) 3428  (D) 3418"
  },
  {
    "task_id": "J1_relative_distance_000507_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 2407/5014 or 856/1556?\n(A) 2407/5014  (B) 856/1556  (C) 3875/7498  (D) 1229/2946",
    "ground_truth": "YES",
    "shortcut_strength": 0.07007269106655606,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 2407/5014 or 856/1556?\n(A) 2407/5014  (B) 856/1556  (C) 3875/7498  (D) 1229/2946"
  },
  {
    "task_id": "J1_compatible_numbers_000643_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "strong_shortcut",
    "problem": "Estimate 5060 × 1868.\n(A) 9452090  (B) 9452070  (C) 9452080  (D) 9452100",
    "ground_truth": "YES",
    "shortcut_strength": 0.961,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 5060 × 1868.\n(A) 9452090  (B) 9452070  (C) 9452080  (D) 9452100"
  },
  {
    "task_id": "J1_equation_reasoning_000710_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "weak_shortcut",
    "problem": "What value fills the blank?  5015 + 4741 + ___ = 4741 + 8472 + 3907\n(A) 7354  (B) 7374  (C) 7384  (D) 7364",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  5015 + 4741 + ___ = 4741 + 8472 + 3907\n(A) 7354  (B) 7374  (C) 7384  (D) 7364"
  },
  {
    "task_id": "J1_landmark_comparison_000672_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 4% of 52240 greater than 13685?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.94,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 4% of 52240 greater than 13685?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_structural_shortcuts_000471_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "strong_shortcut",
    "problem": "What is 9998 * 7041?\n(A) 70395938  (B) 70395928  (C) 70395908  (D) 70395918",
    "ground_truth": "YES",
    "shortcut_strength": 0.9998,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9998 * 7041?\n(A) 70395938  (B) 70395928  (C) 70395908  (D) 70395918"
  },
  {
    "task_id": "J1_magnitude_estimation_000422_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 5135 * 6644?\n(A) 34116950  (B) 34116960  (C) 34116930  (D) 34116940",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 5135 * 6644?\n(A) 34116950  (B) 34116960  (C) 34116930  (D) 34116940"
  },
  {
    "task_id": "J1_compatible_numbers_000620_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 2518 × 5231.\n(A) 13171668  (B) 13171648  (C) 13171678  (D) 13171658",
    "ground_truth": "YES",
    "shortcut_strength": 0.842525,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 2518 × 5231.\n(A) 13171668  (B) 13171648  (C) 13171678  (D) 13171658"
  },
  {
    "task_id": "J1_magnitude_estimation_000426_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 4403 * 5309?\n(A) 23375527  (B) 23375547  (C) 23375517  (D) 23375537",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 4403 * 5309?\n(A) 23375527  (B) 23375547  (C) 23375517  (D) 23375537"
  },
  {
    "task_id": "J1_landmark_comparison_000696_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 55% of 76930 greater than 26921?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.95,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 55% of 76930 greater than 26921?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_option_elimination_000796_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 3560 × 8686?\n(A) 30922160  (B) 30922159  (C) 30922170  (D) 30922161",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 3560 × 8686?\n(A) 30922160  (B) 30922159  (C) 30922170  (D) 30922161"
  },
  {
    "task_id": "J1_relative_distance_000503_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 1482/3087 or 3374/6134?\n(A) 1482/3087  (B) 574/1027  (C) 4170/7229  (D) 3374/6134",
    "ground_truth": "YES",
    "shortcut_strength": 0.06997116234355305,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1482/3087 or 3374/6134?\n(A) 1482/3087  (B) 574/1027  (C) 4170/7229  (D) 3374/6134"
  },
  {
    "task_id": "J1_magnitude_estimation_000414_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 10200 * 9800?\n(A) 99959990  (B) 99960020  (C) 99960010  (D) 99960000",
    "ground_truth": "YES",
    "shortcut_strength": 0.98,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n(A) 99959990  (B) 99960020  (C) 99960010  (D) 99960000"
  },
  {
    "task_id": "J1_landmark_comparison_000657_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 53% of 43310 greater than 15814?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.97,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 53% of 43310 greater than 15814?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_relative_distance_000549_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 1237/2527 or 1278/2528?\n(A) 995/1455  (B) 1237/2527  (C) 453/1189  (D) 1278/2528",
    "ground_truth": "YES",
    "shortcut_strength": 0.01602471785726811,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1237/2527 or 1278/2528?\n(A) 995/1455  (B) 1237/2527  (C) 453/1189  (D) 1278/2528"
  },
  {
    "task_id": "J1_structural_shortcuts_000472_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 9996 * 7499?\n(A) 74960024  (B) 74960014  (C) 74959994  (D) 74960004",
    "ground_truth": "YES",
    "shortcut_strength": 0.9996,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9996 * 7499?\n(A) 74960024  (B) 74960014  (C) 74959994  (D) 74960004"
  },
  {
    "task_id": "J1_magnitude_estimation_000411_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "weak_shortcut",
    "problem": "Which of the following is the best estimate for 10100 * 10241?\n(A) 103434090  (B) 103434110  (C) 103434100  (D) 103434120",
    "ground_truth": "YES",
    "shortcut_strength": 0.98295,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10100 * 10241?\n(A) 103434090  (B) 103434110  (C) 103434100  (D) 103434120"
  },
  {
    "task_id": "J1_structural_shortcuts_000484_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 6597 * 4578?\n(A) 30201056  (B) 30201086  (C) 30201066  (D) 30201076",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 6597 * 4578?\n(A) 30201056  (B) 30201086  (C) 30201066  (D) 30201076"
  },
  {
    "task_id": "J1_cancellation_identity_000592_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 6703 + 7620 - 4009\n(A) 10304  (B) 10334  (C) 10314  (D) 10324",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 6703 + 7620 - 4009\n(A) 10304  (B) 10334  (C) 10314  (D) 10324"
  },
  {
    "task_id": "J1_option_elimination_000789_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "strong_shortcut",
    "problem": "What is 3121 × 1321?\n(A) 4122842  (B) 4122840  (C) 4122841  (D) 4122844",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 3121 × 1321?\n(A) 4122842  (B) 4122840  (C) 4122841  (D) 4122844"
  },
  {
    "task_id": "J1_magnitude_estimation_000447_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 9900 * 9900?\n(A) 98010020  (B) 98009990  (C) 98010000  (D) 98010010",
    "ground_truth": "YES",
    "shortcut_strength": 0.99,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 9900 * 9900?\n(A) 98010020  (B) 98009990  (C) 98010000  (D) 98010010"
  },
  {
    "task_id": "J1_magnitude_estimation_000436_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 9800 * 9900?\n(A) 97020020  (B) 97020010  (C) 97020000  (D) 97019990",
    "ground_truth": "YES",
    "shortcut_strength": 0.985,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 9800 * 9900?\n(A) 97020020  (B) 97020010  (C) 97020000  (D) 97019990"
  },
  {
    "task_id": "J1_compatible_numbers_000634_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 1554 × 1462.\n(A) 2271938  (B) 2271948  (C) 2271958  (D) 2271968",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1554 × 1462.\n(A) 2271938  (B) 2271948  (C) 2271958  (D) 2271968"
  },
  {
    "task_id": "J1_magnitude_estimation_000431_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 9800 * 9900?\n(A) 97020020  (B) 97019990  (C) 97020010  (D) 97020000",
    "ground_truth": "YES",
    "shortcut_strength": 0.985,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 9800 * 9900?\n(A) 97020020  (B) 97019990  (C) 97020010  (D) 97020000"
  },
  {
    "task_id": "J1_magnitude_estimation_000440_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 6426 * 6564?\n(A) 42180254  (B) 42180264  (C) 42180274  (D) 42180284",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 6426 * 6564?\n(A) 42180254  (B) 42180264  (C) 42180274  (D) 42180284"
  },
  {
    "task_id": "J1_magnitude_estimation_000436_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 4266 * 6408?\n(A) 27336518  (B) 27336528  (C) 27336548  (D) 27336538",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 4266 * 6408?\n(A) 27336518  (B) 27336528  (C) 27336548  (D) 27336538"
  },
  {
    "task_id": "J1_structural_shortcuts_000477_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 9997 * 6286?\n(A) 62841132  (B) 62841142  (C) 62841162  (D) 62841152",
    "ground_truth": "YES",
    "shortcut_strength": 0.9997,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9997 * 6286?\n(A) 62841132  (B) 62841142  (C) 62841162  (D) 62841152"
  },
  {
    "task_id": "J1_cancellation_identity_000579_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "weak_shortcut",
    "problem": "Evaluate: 1817 + 5124 - 5133\n(A) 1798  (B) 1808  (C) 1828  (D) 1818",
    "ground_truth": "YES",
    "shortcut_strength": 0.9982435597189696,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 1817 + 5124 - 5133\n(A) 1798  (B) 1808  (C) 1828  (D) 1818"
  },
  {
    "task_id": "J1_equation_reasoning_000718_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  2661 + 1919 + ___ = 1919 + 6614 + 2661\n(A) 6614  (B) 6624  (C) 6604  (D) 6634",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  2661 + 1919 + ___ = 1919 + 6614 + 2661\n(A) 6614  (B) 6624  (C) 6604  (D) 6634"
  },
  {
    "task_id": "J1_cancellation_identity_000559_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "weak_shortcut",
    "problem": "Evaluate: 5670 + 1297 - 1292\n(A) 5695  (B) 5665  (C) 5685  (D) 5675",
    "ground_truth": "YES",
    "shortcut_strength": 0.9961449498843485,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 5670 + 1297 - 1292\n(A) 5695  (B) 5665  (C) 5685  (D) 5675"
  },
  {
    "task_id": "J1_cancellation_identity_000586_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "weak_shortcut",
    "problem": "Evaluate: 3507 + 2988 - 2983\n(A) 3532  (B) 3512  (C) 3522  (D) 3502",
    "ground_truth": "YES",
    "shortcut_strength": 0.9983266398929049,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 3507 + 2988 - 2983\n(A) 3532  (B) 3512  (C) 3522  (D) 3502"
  },
  {
    "task_id": "J1_cancellation_identity_000588_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "weak_shortcut",
    "problem": "Evaluate: 9092 + 3990 - 3996\n(A) 9086  (B) 9076  (C) 9106  (D) 9096",
    "ground_truth": "YES",
    "shortcut_strength": 0.9984962406015038,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 9092 + 3990 - 3996\n(A) 9086  (B) 9076  (C) 9106  (D) 9096"
  },
  {
    "task_id": "J1_option_elimination_000764_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 1555 × 8380?\n(A) 13030899  (B) 13030901  (C) 13030900  (D) 13030880",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 1555 × 8380?\n(A) 13030899  (B) 13030901  (C) 13030900  (D) 13030880"
  },
  {
    "task_id": "J1_cancellation_identity_000582_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "weak_shortcut",
    "problem": "Evaluate: 3270 + 9632 - 9622\n(A) 3280  (B) 3300  (C) 3290  (D) 3270",
    "ground_truth": "YES",
    "shortcut_strength": 0.9989617940199336,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 3270 + 9632 - 9622\n(A) 3280  (B) 3300  (C) 3290  (D) 3270"
  },
  {
    "task_id": "J1_structural_shortcuts_000451_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 9996 * 5289?\n(A) 52868854  (B) 52868864  (C) 52868834  (D) 52868844",
    "ground_truth": "YES",
    "shortcut_strength": 0.9996,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9996 * 5289?\n(A) 52868854  (B) 52868864  (C) 52868834  (D) 52868844"
  },
  {
    "task_id": "J1_landmark_comparison_000701_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 17% of 21520 greater than 10615?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.9299999999999999,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 17% of 21520 greater than 10615?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_equation_reasoning_000738_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "control",
    "problem": "What value fills the blank?  2848 + 8643 + ___ = 7978 + 3759\n(A) 266  (B) 246  (C) 256  (D) 236",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  2848 + 8643 + ___ = 7978 + 3759\n(A) 266  (B) 246  (C) 256  (D) 236"
  },
  {
    "task_id": "J1_structural_shortcuts_000481_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 9997 * 4873?\n(A) 48715391  (B) 48715401  (C) 48715381  (D) 48715371",
    "ground_truth": "YES",
    "shortcut_strength": 0.9997,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9997 * 4873?\n(A) 48715391  (B) 48715401  (C) 48715381  (D) 48715371"
  },
  {
    "task_id": "J1_option_elimination_000801_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "strong_shortcut",
    "problem": "What is 2531 × 7515?\n(A) 19020468  (B) 19020465  (C) 19020466  (D) 19020464",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 2531 × 7515?\n(A) 19020468  (B) 19020465  (C) 19020466  (D) 19020464"
  },
  {
    "task_id": "J1_landmark_comparison_000695_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 44% of 45760 greater than 12614?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.94,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 44% of 45760 greater than 12614?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_structural_shortcuts_000465_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 9995 * 7322?\n(A) 73183400  (B) 73183380  (C) 73183390  (D) 73183410",
    "ground_truth": "YES",
    "shortcut_strength": 0.9995,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9995 * 7322?\n(A) 73183400  (B) 73183380  (C) 73183390  (D) 73183410"
  },
  {
    "task_id": "J1_relative_distance_000512_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "control",
    "problem": "Which is larger: 4962/9021 or 1488/2565?\n(A) 4962/9021  (B) 1488/2565  (C) 3664/5620  (D) 5274/9666",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4962/9021 or 1488/2565?\n(A) 4962/9021  (B) 1488/2565  (C) 3664/5620  (D) 5274/9666"
  },
  {
    "task_id": "J1_relative_distance_000508_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 1455/2966 or 1459/2910?\n(A) 6428/9015  (B) 1459/2910  (C) 1455/2966  (D) 1265/4685",
    "ground_truth": "YES",
    "shortcut_strength": 0.010814894114975437,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1455/2966 or 1459/2910?\n(A) 6428/9015  (B) 1459/2910  (C) 1455/2966  (D) 1265/4685"
  },
  {
    "task_id": "J1_equation_reasoning_000730_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  5208 + 3100 = ___ + 6290\n(A) 2028  (B) 2018  (C) 2008  (D) 2038",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  5208 + 3100 = ___ + 6290\n(A) 2028  (B) 2018  (C) 2008  (D) 2038"
  },
  {
    "task_id": "J1_landmark_comparison_000696_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "strong_shortcut",
    "problem": "Is 52% of 76930 greater than 26921?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.98,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 52% of 76930 greater than 26921?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_landmark_comparison_000656_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 43% of 38290 greater than 9069?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 43% of 38290 greater than 9069?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_magnitude_estimation_000429_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 10200 * 9800?\n(A) 99960020  (B) 99959990  (C) 99960000  (D) 99960010",
    "ground_truth": "YES",
    "shortcut_strength": 0.98,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n(A) 99960020  (B) 99959990  (C) 99960000  (D) 99960010"
  },
  {
    "task_id": "J1_relative_distance_000525_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "control",
    "problem": "Which is larger: 3053/5550 or 1844/3178?\n(A) 1568/5430  (B) 3053/5550  (C) 2129/5079  (D) 1844/3178",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 3053/5550 or 1844/3178?\n(A) 1568/5430  (B) 3053/5550  (C) 2129/5079  (D) 1844/3178"
  },
  {
    "task_id": "J1_magnitude_estimation_000410_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "weak_shortcut",
    "problem": "Which of the following is the best estimate for 10100 * 10176?\n(A) 102777620  (B) 102777600  (C) 102777590  (D) 102777610",
    "ground_truth": "YES",
    "shortcut_strength": 0.9862,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10100 * 10176?\n(A) 102777620  (B) 102777600  (C) 102777590  (D) 102777610"
  },
  {
    "task_id": "J1_magnitude_estimation_000410_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 9900 * 9800?\n(A) 97020020  (B) 97020010  (C) 97019990  (D) 97020000",
    "ground_truth": "YES",
    "shortcut_strength": 0.985,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 9900 * 9800?\n(A) 97020020  (B) 97020010  (C) 97019990  (D) 97020000"
  },
  {
    "task_id": "J1_compatible_numbers_000619_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 1239 × 9766.\n(A) 12100084  (B) 12100094  (C) 12100074  (D) 12100064",
    "ground_truth": "YES",
    "shortcut_strength": 0.885225,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1239 × 9766.\n(A) 12100084  (B) 12100094  (C) 12100074  (D) 12100064"
  },
  {
    "task_id": "J1_structural_shortcuts_000462_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 9997 * 3276?\n(A) 32750192  (B) 32750172  (C) 32750162  (D) 32750182",
    "ground_truth": "YES",
    "shortcut_strength": 0.9997,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9997 * 3276?\n(A) 32750192  (B) 32750172  (C) 32750162  (D) 32750182"
  },
  {
    "task_id": "J1_structural_shortcuts_000484_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "strong_shortcut",
    "problem": "What is 10001 * 4007?\n(A) 40074017  (B) 40074007  (C) 40074027  (D) 40073997",
    "ground_truth": "YES",
    "shortcut_strength": 0.9999,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 10001 * 4007?\n(A) 40074017  (B) 40074007  (C) 40074027  (D) 40073997"
  },
  {
    "task_id": "J1_cancellation_identity_000584_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "weak_shortcut",
    "problem": "Evaluate: 1890 + 2392 - 2378\n(A) 1894  (B) 1924  (C) 1914  (D) 1904",
    "ground_truth": "YES",
    "shortcut_strength": 0.9941471571906354,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 1890 + 2392 - 2378\n(A) 1894  (B) 1924  (C) 1914  (D) 1904"
  },
  {
    "task_id": "J1_option_elimination_000773_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 9530 × 7204?\n(A) 68654100  (B) 68654120  (C) 68654121  (D) 68654119",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9530 × 7204?\n(A) 68654100  (B) 68654120  (C) 68654121  (D) 68654119"
  },
  {
    "task_id": "J1_cancellation_identity_000560_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "weak_shortcut",
    "problem": "Evaluate: 5500 + 6201 - 6187\n(A) 5504  (B) 5534  (C) 5524  (D) 5514",
    "ground_truth": "YES",
    "shortcut_strength": 0.9977422996290921,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 5500 + 6201 - 6187\n(A) 5504  (B) 5534  (C) 5524  (D) 5514"
  },
  {
    "task_id": "J1_option_elimination_000779_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "control",
    "problem": "What is 6361 × 8057?\n(A) 45500577  (B) 47680577  (C) 55870577  (D) 51250577",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 6361 × 8057?\n(A) 45500577  (B) 47680577  (C) 55870577  (D) 51250577"
  },
  {
    "task_id": "J1_relative_distance_000513_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "control",
    "problem": "Which is larger: 1027/1866 or 4098/7064?\n(A) 3763/5081  (B) 1027/1866  (C) 4098/7064  (D) 4857/7852",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1027/1866 or 4098/7064?\n(A) 3763/5081  (B) 1027/1866  (C) 4098/7064  (D) 4857/7852"
  },
  {
    "task_id": "J1_magnitude_estimation_000436_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "weak_shortcut",
    "problem": "Which of the following is the best estimate for 10200 * 10146?\n(A) 103489190  (B) 103489200  (C) 103489220  (D) 103489210",
    "ground_truth": "YES",
    "shortcut_strength": 0.9827,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10200 * 10146?\n(A) 103489190  (B) 103489200  (C) 103489220  (D) 103489210"
  },
  {
    "task_id": "J1_compatible_numbers_000615_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 5669 × 4738.\n(A) 26859742  (B) 26859722  (C) 26859712  (D) 26859732",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 5669 × 4738.\n(A) 26859742  (B) 26859722  (C) 26859712  (D) 26859732"
  },
  {
    "task_id": "J1_relative_distance_000513_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 884/1785 or 1924/3797?\n(A) 1696/3960  (B) 1924/3797  (C) 884/1785  (D) 6946/9711",
    "ground_truth": "YES",
    "shortcut_strength": 0.011477733047393301,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 884/1785 or 1924/3797?\n(A) 1696/3960  (B) 1924/3797  (C) 884/1785  (D) 6946/9711"
  },
  {
    "task_id": "J1_compatible_numbers_000649_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 5352 × 4434.\n(A) 23730758  (B) 23730788  (C) 23730778  (D) 23730768",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 5352 × 4434.\n(A) 23730758  (B) 23730788  (C) 23730778  (D) 23730768"
  },
  {
    "task_id": "J1_compatible_numbers_000650_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "strong_shortcut",
    "problem": "Estimate 4925 × 2150.\n(A) 10588770  (B) 10588760  (C) 10588740  (D) 10588750",
    "ground_truth": "YES",
    "shortcut_strength": 0.955,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 4925 × 2150.\n(A) 10588770  (B) 10588760  (C) 10588740  (D) 10588750"
  },
  {
    "task_id": "J1_cancellation_identity_000558_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "strong_shortcut",
    "problem": "Evaluate: 3344 + 1236 - 1234\n(A) 3356  (B) 3336  (C) 3366  (D) 3346",
    "ground_truth": "YES",
    "shortcut_strength": 0.9983818770226537,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 3344 + 1236 - 1234\n(A) 3356  (B) 3336  (C) 3366  (D) 3346"
  },
  {
    "task_id": "J1_cancellation_identity_000585_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 4359 + 9463 - 4639\n(A) 9193  (B) 9203  (C) 9173  (D) 9183",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 4359 + 9463 - 4639\n(A) 9193  (B) 9203  (C) 9173  (D) 9183"
  },
  {
    "task_id": "J1_compatible_numbers_000626_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 1229 × 10560.\n(A) 12978250  (B) 12978240  (C) 12978230  (D) 12978260",
    "ground_truth": "YES",
    "shortcut_strength": 0.8316,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1229 × 10560.\n(A) 12978250  (B) 12978240  (C) 12978230  (D) 12978260"
  },
  {
    "task_id": "J1_equation_reasoning_000721_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "control",
    "problem": "What value fills the blank?  2197 + 8060 + ___ = 5536 + 8630\n(A) 3919  (B) 3909  (C) 3929  (D) 3899",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  2197 + 8060 + ___ = 5536 + 8630\n(A) 3919  (B) 3909  (C) 3929  (D) 3899"
  },
  {
    "task_id": "J1_compatible_numbers_000619_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 7143 × 4661.\n(A) 33293513  (B) 33293543  (C) 33293523  (D) 33293533",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 7143 × 4661.\n(A) 33293513  (B) 33293543  (C) 33293523  (D) 33293533"
  },
  {
    "task_id": "J1_compatible_numbers_000647_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 4536 × 7228.\n(A) 32786218  (B) 32786228  (C) 32786198  (D) 32786208",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 4536 × 7228.\n(A) 32786218  (B) 32786228  (C) 32786198  (D) 32786208"
  },
  {
    "task_id": "J1_relative_distance_000534_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 4320/8812 or 1806/3591?\n(A) 2324/6984  (B) 4320/8812  (C) 1074/2294  (D) 1806/3591",
    "ground_truth": "YES",
    "shortcut_strength": 0.012683395582313295,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4320/8812 or 1806/3591?\n(A) 2324/6984  (B) 4320/8812  (C) 1074/2294  (D) 1806/3591"
  },
  {
    "task_id": "J1_compatible_numbers_000638_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 8668 × 1774.\n(A) 15377052  (B) 15377032  (C) 15377042  (D) 15377022",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 8668 × 1774.\n(A) 15377052  (B) 15377032  (C) 15377042  (D) 15377022"
  },
  {
    "task_id": "J1_option_elimination_000794_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "control",
    "problem": "What is 2459 × 1543?\n(A) 3907237  (B) 3794237  (C) 3474237  (D) 3604237",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 2459 × 1543?\n(A) 3907237  (B) 3794237  (C) 3474237  (D) 3604237"
  },
  {
    "task_id": "J1_option_elimination_000758_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "strong_shortcut",
    "problem": "What is 7525 × 5474?\n(A) 41191853  (B) 41191849  (C) 41191851  (D) 41191850",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 7525 × 5474?\n(A) 41191853  (B) 41191849  (C) 41191851  (D) 41191850"
  },
  {
    "task_id": "J1_landmark_comparison_000683_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "strong_shortcut",
    "problem": "Is 27% of 87480 greater than 24547?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.98,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 27% of 87480 greater than 24547?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_option_elimination_000759_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "strong_shortcut",
    "problem": "What is 7167 × 1638?\n(A) 11739545  (B) 11739546  (C) 11739548  (D) 11739547",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 7167 × 1638?\n(A) 11739545  (B) 11739546  (C) 11739548  (D) 11739547"
  },
  {
    "task_id": "J1_relative_distance_000515_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 4405/8858 or 4666/9156?\n(A) 1966/7643  (B) 4666/9156  (C) 3451/9722  (D) 4405/8858",
    "ground_truth": "YES",
    "shortcut_strength": 0.012320599140992705,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4405/8858 or 4666/9156?\n(A) 1966/7643  (B) 4666/9156  (C) 3451/9722  (D) 4405/8858"
  },
  {
    "task_id": "J1_relative_distance_000536_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 2011/4190 or 2982/5422?\n(A) 2011/4190  (B) 1310/2274  (C) 2982/5422  (D) 907/2776",
    "ground_truth": "YES",
    "shortcut_strength": 0.07002928931807034,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 2011/4190 or 2982/5422?\n(A) 2011/4190  (B) 1310/2274  (C) 2982/5422  (D) 907/2776"
  },
  {
    "task_id": "J1_equation_reasoning_000704_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  9515 + 8703 = ___ + 7313\n(A) 10895  (B) 10925  (C) 10915  (D) 10905",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  9515 + 8703 = ___ + 7313\n(A) 10895  (B) 10925  (C) 10915  (D) 10905"
  },
  {
    "task_id": "J1_equation_reasoning_000711_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "weak_shortcut",
    "problem": "What value fills the blank?  9797 + 1836 + ___ = 1836 + 6224 + 2196\n(A) -1363  (B) -1377  (C) -1393  (D) -1373",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  9797 + 1836 + ___ = 1836 + 6224 + 2196\n(A) -1363  (B) -1377  (C) -1393  (D) -1373"
  },
  {
    "task_id": "J1_structural_shortcuts_000459_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 9995 * 6902?\n(A) 68985500  (B) 68985480  (C) 68985510  (D) 68985490",
    "ground_truth": "YES",
    "shortcut_strength": 0.9995,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9995 * 6902?\n(A) 68985500  (B) 68985480  (C) 68985510  (D) 68985490"
  },
  {
    "task_id": "J1_option_elimination_000776_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "control",
    "problem": "What is 4761 × 9455?\n(A) 39715255  (B) 37465255  (C) 42125255  (D) 45015255",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 4761 × 9455?\n(A) 39715255  (B) 37465255  (C) 42125255  (D) 45015255"
  },
  {
    "task_id": "J1_equation_reasoning_000743_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  6010 × (2659 + 2481) = 6010 × ___ + 6010 × 2481\n(A) 2659  (B) 2679  (C) 2669  (D) 2649",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  6010 × (2659 + 2481) = 6010 × ___ + 6010 × 2481\n(A) 2659  (B) 2679  (C) 2669  (D) 2649"
  },
  {
    "task_id": "J1_cancellation_identity_000552_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "weak_shortcut",
    "problem": "Evaluate: 9781 + 1382 - 1387\n(A) 9786  (B) 9766  (C) 9776  (D) 9796",
    "ground_truth": "YES",
    "shortcut_strength": 0.9963820549927641,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 9781 + 1382 - 1387\n(A) 9786  (B) 9766  (C) 9776  (D) 9796"
  },
  {
    "task_id": "J1_landmark_comparison_000701_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 83% of 21520 greater than 10615?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 83% of 21520 greater than 10615?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_landmark_comparison_000659_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "strong_shortcut",
    "problem": "Is 10% of 71650 greater than 29517?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 10% of 71650 greater than 29517?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_equation_reasoning_000730_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "control",
    "problem": "What value fills the blank?  3336 + 4695 + ___ = 2346 + 2553\n(A) -3118  (B) -3132  (C) -3128  (D) -3148",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  3336 + 4695 + ___ = 2346 + 2553\n(A) -3118  (B) -3132  (C) -3128  (D) -3148"
  },
  {
    "task_id": "J1_structural_shortcuts_000499_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "strong_shortcut",
    "problem": "What is 9998 * 1050?\n(A) 10497900  (B) 10497910  (C) 10497920  (D) 10497890",
    "ground_truth": "YES",
    "shortcut_strength": 0.9998,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9998 * 1050?\n(A) 10497900  (B) 10497910  (C) 10497920  (D) 10497890"
  },
  {
    "task_id": "J1_landmark_comparison_000666_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 44% of 79090 greater than 21700?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.94,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 44% of 79090 greater than 21700?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_compatible_numbers_000631_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 4544 × 1768.\n(A) 8033802  (B) 8033812  (C) 8033782  (D) 8033792",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 4544 × 1768.\n(A) 8033802  (B) 8033812  (C) 8033782  (D) 8033792"
  },
  {
    "task_id": "J1_equation_reasoning_000750_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "control",
    "problem": "What value fills the blank?  7677 + 7247 + ___ = 8772 + 3269\n(A) -2877  (B) -2897  (C) -2883  (D) -2867",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  7677 + 7247 + ___ = 8772 + 3269\n(A) -2877  (B) -2897  (C) -2883  (D) -2867"
  },
  {
    "task_id": "J1_magnitude_estimation_000434_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "weak_shortcut",
    "problem": "Which of the following is the best estimate for 10200 * 10147?\n(A) 103499420  (B) 103499410  (C) 103499390  (D) 103499400",
    "ground_truth": "YES",
    "shortcut_strength": 0.98265,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10200 * 10147?\n(A) 103499420  (B) 103499410  (C) 103499390  (D) 103499400"
  },
  {
    "task_id": "J1_equation_reasoning_000710_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  8317 + 9567 + ___ = 9567 + 5062 + 8317\n(A) 5082  (B) 5062  (C) 5052  (D) 5072",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  8317 + 9567 + ___ = 9567 + 5062 + 8317\n(A) 5082  (B) 5062  (C) 5052  (D) 5072"
  },
  {
    "task_id": "J1_landmark_comparison_000688_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 67% of 63860 greater than 30514?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 67% of 63860 greater than 30514?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_relative_distance_000529_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "control",
    "problem": "Which is larger: 1475/2680 or 5441/9381?\n(A) 721/1019  (B) 2531/7804  (C) 5441/9381  (D) 1475/2680",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1475/2680 or 5441/9381?\n(A) 721/1019  (B) 2531/7804  (C) 5441/9381  (D) 1475/2680"
  },
  {
    "task_id": "J1_equation_reasoning_000711_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "control",
    "problem": "What value fills the blank?  8240 + 2366 + ___ = 8799 + 4234\n(A) 2437  (B) 2417  (C) 2447  (D) 2427",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  8240 + 2366 + ___ = 8799 + 4234\n(A) 2437  (B) 2417  (C) 2447  (D) 2427"
  },
  {
    "task_id": "J1_cancellation_identity_000590_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "strong_shortcut",
    "problem": "Evaluate: 5536 + 1154 - 1155\n(A) 5545  (B) 5535  (C) 5525  (D) 5555",
    "ground_truth": "YES",
    "shortcut_strength": 0.9991334488734835,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 5536 + 1154 - 1155\n(A) 5545  (B) 5535  (C) 5525  (D) 5555"
  },
  {
    "task_id": "J1_relative_distance_000518_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 4809/9788 or 2737/5415?\n(A) 3374/8198  (B) 4809/9788  (C) 2737/5415  (D) 1546/3291",
    "ground_truth": "YES",
    "shortcut_strength": 0.014131933084814474,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4809/9788 or 2737/5415?\n(A) 3374/8198  (B) 4809/9788  (C) 2737/5415  (D) 1546/3291"
  },
  {
    "task_id": "J1_relative_distance_000524_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 1837/3735 or 2765/5491?\n(A) 2765/5491  (B) 1312/1996  (C) 1015/1744  (D) 1837/3735",
    "ground_truth": "YES",
    "shortcut_strength": 0.011717263030145253,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1837/3735 or 2765/5491?\n(A) 2765/5491  (B) 1312/1996  (C) 1015/1744  (D) 1837/3735"
  },
  {
    "task_id": "J1_structural_shortcuts_000451_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 5551 * 6681?\n(A) 37086251  (B) 37086221  (C) 37086241  (D) 37086231",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 5551 * 6681?\n(A) 37086251  (B) 37086221  (C) 37086241  (D) 37086231"
  },
  {
    "task_id": "J1_option_elimination_000797_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "strong_shortcut",
    "problem": "What is 6777 × 6015?\n(A) 4076361  (B) 4076365567  (C) 40763655  (D) 8152727",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 6777 × 6015?\n(A) 4076361  (B) 4076365567  (C) 40763655  (D) 8152727"
  },
  {
    "task_id": "J1_landmark_comparison_000690_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 18% of 37850 greater than 18596?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.9299999999999999,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 18% of 37850 greater than 18596?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_equation_reasoning_000728_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  6981 × 2792 × 3660 = ___ × 3660 × 6981\n(A) 2812  (B) 2782  (C) 2802  (D) 2792",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  6981 × 2792 × 3660 = ___ × 3660 × 6981\n(A) 2812  (B) 2782  (C) 2802  (D) 2792"
  },
  {
    "task_id": "J1_relative_distance_000516_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "control",
    "problem": "Which is larger: 4723/8586 or 5220/8999?\n(A) 5220/8999  (B) 745/1096  (C) 4723/8586  (D) 849/1942",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4723/8586 or 5220/8999?\n(A) 5220/8999  (B) 745/1096  (C) 4723/8586  (D) 849/1942"
  },
  {
    "task_id": "J1_landmark_comparison_000692_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "strong_shortcut",
    "problem": "Is 10% of 61660 greater than 27126?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 10% of 61660 greater than 27126?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_relative_distance_000516_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 4279/8915 or 3195/5809?\n(A) 2206/5337  (B) 3195/5809  (C) 662/1036  (D) 4279/8915",
    "ground_truth": "YES",
    "shortcut_strength": 0.07003104143327987,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4279/8915 or 3195/5809?\n(A) 2206/5337  (B) 3195/5809  (C) 662/1036  (D) 4279/8915"
  },
  {
    "task_id": "J1_magnitude_estimation_000432_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 4064 * 6832?\n(A) 27765238  (B) 27765248  (C) 27765268  (D) 27765258",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 4064 * 6832?\n(A) 27765238  (B) 27765248  (C) 27765268  (D) 27765258"
  },
  {
    "task_id": "J1_option_elimination_000787_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 4010 × 6726?\n(A) 26971261  (B) 26971259  (C) 26971260  (D) 26971240",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 4010 × 6726?\n(A) 26971261  (B) 26971259  (C) 26971260  (D) 26971240"
  },
  {
    "task_id": "J1_structural_shortcuts_000480_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "strong_shortcut",
    "problem": "What is 9999 * 6440?\n(A) 64393560  (B) 64393550  (C) 64393580  (D) 64393570",
    "ground_truth": "YES",
    "shortcut_strength": 0.9999,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9999 * 6440?\n(A) 64393560  (B) 64393550  (C) 64393580  (D) 64393570"
  },
  {
    "task_id": "J1_structural_shortcuts_000500_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 9995 * 6278?\n(A) 62748600  (B) 62748620  (C) 62748630  (D) 62748610",
    "ground_truth": "YES",
    "shortcut_strength": 0.9995,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9995 * 6278?\n(A) 62748600  (B) 62748620  (C) 62748630  (D) 62748610"
  },
  {
    "task_id": "J1_equation_reasoning_000708_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "weak_shortcut",
    "problem": "What value fills the blank?  7192 + 8950 + ___ = 8950 + 3770 + 9605\n(A) 6203  (B) 6193  (C) 6183  (D) 6173",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  7192 + 8950 + ___ = 8950 + 3770 + 9605\n(A) 6203  (B) 6193  (C) 6183  (D) 6173"
  },
  {
    "task_id": "J1_compatible_numbers_000621_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 2463 × 5175.\n(A) 12746045  (B) 12746035  (C) 12746015  (D) 12746025",
    "ground_truth": "YES",
    "shortcut_strength": 0.8457250000000001,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 2463 × 5175.\n(A) 12746045  (B) 12746035  (C) 12746015  (D) 12746025"
  },
  {
    "task_id": "J1_structural_shortcuts_000460_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 9995 * 5906?\n(A) 59030470  (B) 59030460  (C) 59030480  (D) 59030490",
    "ground_truth": "YES",
    "shortcut_strength": 0.9995,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9995 * 5906?\n(A) 59030470  (B) 59030460  (C) 59030480  (D) 59030490"
  },
  {
    "task_id": "J1_magnitude_estimation_000421_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 10200 * 10100?\n(A) 103020000  (B) 103020020  (C) 103020010  (D) 103019990",
    "ground_truth": "YES",
    "shortcut_strength": 0.985,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10200 * 10100?\n(A) 103020000  (B) 103020020  (C) 103020010  (D) 103019990"
  },
  {
    "task_id": "J1_magnitude_estimation_000412_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 4150 * 6200?\n(A) 25729990  (B) 25730000  (C) 25730010  (D) 25730020",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 4150 * 6200?\n(A) 25729990  (B) 25730000  (C) 25730010  (D) 25730020"
  },
  {
    "task_id": "J1_option_elimination_000795_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 4260 × 6314?\n(A) 26897620  (B) 26897641  (C) 26897640  (D) 26897639",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 4260 × 6314?\n(A) 26897620  (B) 26897641  (C) 26897640  (D) 26897639"
  },
  {
    "task_id": "J1_option_elimination_000779_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 5240 × 2594?\n(A) 13592550  (B) 13592561  (C) 13592560  (D) 13592559",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 5240 × 2594?\n(A) 13592550  (B) 13592561  (C) 13592560  (D) 13592559"
  },
  {
    "task_id": "J1_landmark_comparison_000701_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "strong_shortcut",
    "problem": "Is 8% of 21520 greater than 10615?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.98,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 8% of 21520 greater than 10615?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_structural_shortcuts_000461_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 5394 * 4350?\n(A) 23463890  (B) 23463910  (C) 23463900  (D) 23463920",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 5394 * 4350?\n(A) 23463890  (B) 23463910  (C) 23463900  (D) 23463920"
  },
  {
    "task_id": "J1_relative_distance_000512_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 1250/2604 or 3948/7179?\n(A) 3948/7179  (B) 932/2720  (C) 2710/4640  (D) 1250/2604",
    "ground_truth": "YES",
    "shortcut_strength": 0.06990659520888814,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1250/2604 or 3948/7179?\n(A) 3948/7179  (B) 932/2720  (C) 2710/4640  (D) 1250/2604"
  },
  {
    "task_id": "J1_compatible_numbers_000629_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 1262 × 10295.\n(A) 12992300  (B) 12992280  (C) 12992290  (D) 12992310",
    "ground_truth": "YES",
    "shortcut_strength": 0.8517625,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1262 × 10295.\n(A) 12992300  (B) 12992280  (C) 12992290  (D) 12992310"
  },
  {
    "task_id": "J1_landmark_comparison_000654_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 13% of 95860 greater than 25675?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.97,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 13% of 95860 greater than 25675?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_relative_distance_000541_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 1748/3532 or 1376/2725?\n(A) 2065/3592  (B) 1748/3532  (C) 5382/7541  (D) 1376/2725",
    "ground_truth": "YES",
    "shortcut_strength": 0.010050391181023854,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1748/3532 or 1376/2725?\n(A) 2065/3592  (B) 1748/3532  (C) 5382/7541  (D) 1376/2725"
  },
  {
    "task_id": "J1_relative_distance_000538_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 1099/2290 or 1390/2528?\n(A) 1390/2528  (B) 2400/3307  (C) 2081/4794  (D) 1099/2290",
    "ground_truth": "YES",
    "shortcut_strength": 0.06992910839644029,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1099/2290 or 1390/2528?\n(A) 1390/2528  (B) 2400/3307  (C) 2081/4794  (D) 1099/2290"
  },
  {
    "task_id": "J1_cancellation_identity_000596_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "strong_shortcut",
    "problem": "Evaluate: 9205 + 6773 - 6772\n(A) 9226  (B) 9196  (C) 9206  (D) 9216",
    "ground_truth": "YES",
    "shortcut_strength": 0.9998523549387273,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 9205 + 6773 - 6772\n(A) 9226  (B) 9196  (C) 9206  (D) 9216"
  },
  {
    "task_id": "J1_compatible_numbers_000605_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 1273 × 5384.\n(A) 6853832  (B) 6853842  (C) 6853852  (D) 6853822",
    "ground_truth": "YES",
    "shortcut_strength": 0.8272999999999999,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1273 × 5384.\n(A) 6853832  (B) 6853842  (C) 6853852  (D) 6853822"
  },
  {
    "task_id": "J1_option_elimination_000799_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 9135 × 5574?\n(A) 50918470  (B) 50918489  (C) 50918490  (D) 50918491",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9135 × 5574?\n(A) 50918470  (B) 50918489  (C) 50918490  (D) 50918491"
  },
  {
    "task_id": "J1_cancellation_identity_000575_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 3423 + 7727 - 5044\n(A) 6116  (B) 6106  (C) 6126  (D) 6096",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 3423 + 7727 - 5044\n(A) 6116  (B) 6106  (C) 6126  (D) 6096"
  },
  {
    "task_id": "J1_structural_shortcuts_000497_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 10005 * 1685?\n(A) 16858435  (B) 16858445  (C) 16858415  (D) 16858425",
    "ground_truth": "YES",
    "shortcut_strength": 0.9995,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 10005 * 1685?\n(A) 16858435  (B) 16858445  (C) 16858415  (D) 16858425"
  },
  {
    "task_id": "J1_compatible_numbers_000622_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "strong_shortcut",
    "problem": "Estimate 4910 × 1977.\n(A) 9707060  (B) 9707080  (C) 9707090  (D) 9707070",
    "ground_truth": "YES",
    "shortcut_strength": 0.98525,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 4910 × 1977.\n(A) 9707060  (B) 9707080  (C) 9707090  (D) 9707070"
  },
  {
    "task_id": "J1_option_elimination_000787_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "strong_shortcut",
    "problem": "What is 3567 × 7987?\n(A) 28489629  (B) 28489630  (C) 28489628  (D) 28489632",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 3567 × 7987?\n(A) 28489629  (B) 28489630  (C) 28489628  (D) 28489632"
  },
  {
    "task_id": "J1_cancellation_identity_000575_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "strong_shortcut",
    "problem": "Evaluate: 3423 + 7727 - 7728\n(A) 3422  (B) 3442  (C) 3412  (D) 3432",
    "ground_truth": "YES",
    "shortcut_strength": 0.9998705836676589,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 3423 + 7727 - 7728\n(A) 3422  (B) 3442  (C) 3412  (D) 3432"
  },
  {
    "task_id": "J1_structural_shortcuts_000470_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 6858 * 6974?\n(A) 47827692  (B) 47827712  (C) 47827682  (D) 47827702",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 6858 * 6974?\n(A) 47827692  (B) 47827712  (C) 47827682  (D) 47827702"
  },
  {
    "task_id": "J1_relative_distance_000548_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 3650/7604 or 3417/6212?\n(A) 3650/7604  (B) 2987/8166  (C) 3665/9475  (D) 3417/6212",
    "ground_truth": "YES",
    "shortcut_strength": 0.07005387072178432,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 3650/7604 or 3417/6212?\n(A) 3650/7604  (B) 2987/8166  (C) 3665/9475  (D) 3417/6212"
  },
  {
    "task_id": "J1_structural_shortcuts_000489_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 10003 * 7465?\n(A) 74672395  (B) 74672385  (C) 74672405  (D) 74672415",
    "ground_truth": "YES",
    "shortcut_strength": 0.9997,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 10003 * 7465?\n(A) 74672395  (B) 74672385  (C) 74672405  (D) 74672415"
  },
  {
    "task_id": "J1_equation_reasoning_000725_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  3042 + 2521 = ___ + 3868\n(A) 1705  (B) 1715  (C) 1685  (D) 1695",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  3042 + 2521 = ___ + 3868\n(A) 1705  (B) 1715  (C) 1685  (D) 1695"
  },
  {
    "task_id": "J1_relative_distance_000535_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 3812/7941 or 1963/3569?\n(A) 5478/9544  (B) 1963/3569  (C) 1739/5453  (D) 3812/7941",
    "ground_truth": "YES",
    "shortcut_strength": 0.06997371233468863,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 3812/7941 or 1963/3569?\n(A) 5478/9544  (B) 1963/3569  (C) 1739/5453  (D) 3812/7941"
  },
  {
    "task_id": "J1_landmark_comparison_000693_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 20% of 37310 greater than 17689?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.95,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 20% of 37310 greater than 17689?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_relative_distance_000539_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "control",
    "problem": "Which is larger: 1164/2116 or 3242/5589?\n(A) 3242/5589  (B) 760/2461  (C) 3185/6952  (D) 1164/2116",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1164/2116 or 3242/5589?\n(A) 3242/5589  (B) 760/2461  (C) 3185/6952  (D) 1164/2116"
  },
  {
    "task_id": "J1_compatible_numbers_000626_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "strong_shortcut",
    "problem": "Estimate 1227 × 7737.\n(A) 9493309  (B) 9493299  (C) 9493319  (D) 9493289",
    "ground_truth": "YES",
    "shortcut_strength": 0.9743625,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1227 × 7737.\n(A) 9493309  (B) 9493299  (C) 9493319  (D) 9493289"
  },
  {
    "task_id": "J1_relative_distance_000544_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "control",
    "problem": "Which is larger: 4599/8361 or 1506/2596?\n(A) 1506/2596  (B) 1878/4074  (C) 622/1597  (D) 4599/8361",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4599/8361 or 1506/2596?\n(A) 1506/2596  (B) 1878/4074  (C) 622/1597  (D) 4599/8361"
  },
  {
    "task_id": "J1_compatible_numbers_000649_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "strong_shortcut",
    "problem": "Estimate 1266 × 7268.\n(A) 9201308  (B) 9201288  (C) 9201278  (D) 9201298",
    "ground_truth": "YES",
    "shortcut_strength": 0.94785,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1266 × 7268.\n(A) 9201308  (B) 9201288  (C) 9201278  (D) 9201298"
  },
  {
    "task_id": "J1_magnitude_estimation_000443_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 9800 * 9800?\n(A) 96040000  (B) 96039990  (C) 96040010  (D) 96040020",
    "ground_truth": "YES",
    "shortcut_strength": 0.98,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 9800 * 9800?\n(A) 96040000  (B) 96039990  (C) 96040010  (D) 96040020"
  },
  {
    "task_id": "J1_landmark_comparison_000666_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 37% of 79090 greater than 21700?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 37% of 79090 greater than 21700?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_option_elimination_000765_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "strong_shortcut",
    "problem": "What is 1104 × 5487?\n(A) 6057649  (B) 6057647  (C) 6057650  (D) 6057648",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 1104 × 5487?\n(A) 6057649  (B) 6057647  (C) 6057650  (D) 6057648"
  },
  {
    "task_id": "J1_compatible_numbers_000636_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 1262 × 9859.\n(A) 12442068  (B) 12442048  (C) 12442058  (D) 12442078",
    "ground_truth": "YES",
    "shortcut_strength": 0.8790125,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1262 × 9859.\n(A) 12442068  (B) 12442048  (C) 12442058  (D) 12442078"
  },
  {
    "task_id": "J1_magnitude_estimation_000446_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 4233 * 4971?\n(A) 21042233  (B) 21042263  (C) 21042253  (D) 21042243",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 4233 * 4971?\n(A) 21042233  (B) 21042263  (C) 21042253  (D) 21042243"
  },
  {
    "task_id": "J1_magnitude_estimation_000422_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "weak_shortcut",
    "problem": "Which of the following is the best estimate for 10100 * 10194?\n(A) 102959390  (B) 102959410  (C) 102959420  (D) 102959400",
    "ground_truth": "YES",
    "shortcut_strength": 0.9853,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10100 * 10194?\n(A) 102959390  (B) 102959410  (C) 102959420  (D) 102959400"
  },
  {
    "task_id": "J1_structural_shortcuts_000462_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 6046 * 6697?\n(A) 40490052  (B) 40490062  (C) 40490072  (D) 40490082",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 6046 * 6697?\n(A) 40490052  (B) 40490062  (C) 40490072  (D) 40490082"
  },
  {
    "task_id": "J1_cancellation_identity_000565_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 2712 + 6582 - 10045\n(A) -749  (B) -751  (C) -739  (D) -769",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 2712 + 6582 - 10045\n(A) -749  (B) -751  (C) -739  (D) -769"
  },
  {
    "task_id": "J1_structural_shortcuts_000467_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "strong_shortcut",
    "problem": "What is 10002 * 4382?\n(A) 43828784  (B) 43828754  (C) 43828764  (D) 43828774",
    "ground_truth": "YES",
    "shortcut_strength": 0.9998,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 10002 * 4382?\n(A) 43828784  (B) 43828754  (C) 43828764  (D) 43828774"
  },
  {
    "task_id": "J1_magnitude_estimation_000411_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 10100 * 10200?\n(A) 103020000  (B) 103020010  (C) 103020020  (D) 103019990",
    "ground_truth": "YES",
    "shortcut_strength": 0.985,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10100 * 10200?\n(A) 103020000  (B) 103020010  (C) 103020020  (D) 103019990"
  },
  {
    "task_id": "J1_compatible_numbers_000638_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "strong_shortcut",
    "problem": "Estimate 2548 × 3929.\n(A) 10011112  (B) 10011092  (C) 10011082  (D) 10011102",
    "ground_truth": "YES",
    "shortcut_strength": 0.981525,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 2548 × 3929.\n(A) 10011112  (B) 10011092  (C) 10011082  (D) 10011102"
  },
  {
    "task_id": "J1_landmark_comparison_000693_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 83% of 37310 greater than 17689?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 83% of 37310 greater than 17689?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_option_elimination_000766_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 8240 × 8382?\n(A) 69067681  (B) 69067679  (C) 69067680  (D) 69067670",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 8240 × 8382?\n(A) 69067681  (B) 69067679  (C) 69067680  (D) 69067670"
  },
  {
    "task_id": "J1_cancellation_identity_000566_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "strong_shortcut",
    "problem": "Evaluate: 7556 + 4084 - 4086\n(A) 7544  (B) 7554  (C) 7564  (D) 7574",
    "ground_truth": "YES",
    "shortcut_strength": 0.9995102840352595,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 7556 + 4084 - 4086\n(A) 7544  (B) 7554  (C) 7564  (D) 7574"
  },
  {
    "task_id": "J1_magnitude_estimation_000444_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 6427 * 4792?\n(A) 30798184  (B) 30798174  (C) 30798204  (D) 30798194",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 6427 * 4792?\n(A) 30798184  (B) 30798174  (C) 30798204  (D) 30798194"
  },
  {
    "task_id": "J1_structural_shortcuts_000460_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "strong_shortcut",
    "problem": "What is 10001 * 4123?\n(A) 41234123  (B) 41234113  (C) 41234143  (D) 41234133",
    "ground_truth": "YES",
    "shortcut_strength": 0.9999,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 10001 * 4123?\n(A) 41234123  (B) 41234113  (C) 41234143  (D) 41234133"
  },
  {
    "task_id": "J1_compatible_numbers_000650_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 9874 × 9535.\n(A) 94148600  (B) 94148590  (C) 94148580  (D) 94148610",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 9874 × 9535.\n(A) 94148600  (B) 94148590  (C) 94148580  (D) 94148610"
  },
  {
    "task_id": "J1_relative_distance_000505_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 1728/3501 or 2270/4450?\n(A) 2270/4450  (B) 1728/3501  (C) 1351/1861  (D) 2737/3933",
    "ground_truth": "YES",
    "shortcut_strength": 0.016539094769070783,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1728/3501 or 2270/4450?\n(A) 2270/4450  (B) 1728/3501  (C) 1351/1861  (D) 2737/3933"
  },
  {
    "task_id": "J1_option_elimination_000787_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "control",
    "problem": "What is 7953 × 6161?\n(A) 39698433  (B) 47548433  (C) 48998433  (D) 39668433",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 7953 × 6161?\n(A) 39698433  (B) 47548433  (C) 48998433  (D) 39668433"
  },
  {
    "task_id": "J1_magnitude_estimation_000449_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 10200 * 9900?\n(A) 100980000  (B) 100980020  (C) 100979990  (D) 100980010",
    "ground_truth": "YES",
    "shortcut_strength": 0.985,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10200 * 9900?\n(A) 100980000  (B) 100980020  (C) 100979990  (D) 100980010"
  },
  {
    "task_id": "J1_compatible_numbers_000620_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 5669 × 4738.\n(A) 26859742  (B) 26859722  (C) 26859712  (D) 26859732",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 5669 × 4738.\n(A) 26859742  (B) 26859722  (C) 26859712  (D) 26859732"
  },
  {
    "task_id": "J1_landmark_comparison_000690_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 37% of 37850 greater than 18596?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 37% of 37850 greater than 18596?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_equation_reasoning_000714_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "weak_shortcut",
    "problem": "What value fills the blank?  4797 + 4493 + ___ = 4493 + 6033 + 9221\n(A) 10457  (B) 10447  (C) 10467  (D) 10477",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  4797 + 4493 + ___ = 4493 + 6033 + 9221\n(A) 10457  (B) 10447  (C) 10467  (D) 10477"
  },
  {
    "task_id": "J1_option_elimination_000791_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 2605 × 5854?\n(A) 15249650  (B) 15249670  (C) 15249669  (D) 15249671",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 2605 × 5854?\n(A) 15249650  (B) 15249670  (C) 15249669  (D) 15249671"
  },
  {
    "task_id": "J1_compatible_numbers_000636_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 3753 × 5259.\n(A) 19737037  (B) 19737027  (C) 19737017  (D) 19737047",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 3753 × 5259.\n(A) 19737037  (B) 19737027  (C) 19737017  (D) 19737047"
  },
  {
    "task_id": "J1_option_elimination_000759_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 4760 × 9768?\n(A) 46495681  (B) 46495679  (C) 46495690  (D) 46495680",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 4760 × 9768?\n(A) 46495681  (B) 46495679  (C) 46495690  (D) 46495680"
  },
  {
    "task_id": "J1_cancellation_identity_000596_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "weak_shortcut",
    "problem": "Evaluate: 9205 + 6773 - 6758\n(A) 9230  (B) 9240  (C) 9220  (D) 9210",
    "ground_truth": "YES",
    "shortcut_strength": 0.9977853240809095,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 9205 + 6773 - 6758\n(A) 9230  (B) 9240  (C) 9220  (D) 9210"
  },
  {
    "task_id": "J1_cancellation_identity_000572_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 1208 + 8780 - 13847\n(A) -3851  (B) -3859  (C) -3841  (D) -3871",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 1208 + 8780 - 13847\n(A) -3851  (B) -3859  (C) -3841  (D) -3871"
  },
  {
    "task_id": "J1_equation_reasoning_000709_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "weak_shortcut",
    "problem": "What value fills the blank?  8525 + 1199 + ___ = 1199 + 9587 + 4741\n(A) 5823  (B) 5803  (C) 5793  (D) 5813",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  8525 + 1199 + ___ = 1199 + 9587 + 4741\n(A) 5823  (B) 5803  (C) 5793  (D) 5813"
  },
  {
    "task_id": "J1_equation_reasoning_000714_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  8261 + 6610 + ___ = 6610 + 9824 + 8261\n(A) 9814  (B) 9844  (C) 9824  (D) 9834",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  8261 + 6610 + ___ = 6610 + 9824 + 8261\n(A) 9814  (B) 9844  (C) 9824  (D) 9834"
  },
  {
    "task_id": "J1_compatible_numbers_000644_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 2451 × 2846.\n(A) 6975546  (B) 6975556  (C) 6975566  (D) 6975536",
    "ground_truth": "YES",
    "shortcut_strength": 0.84595,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 2451 × 2846.\n(A) 6975546  (B) 6975556  (C) 6975566  (D) 6975536"
  },
  {
    "task_id": "J1_equation_reasoning_000725_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "control",
    "problem": "What value fills the blank?  2487 + 9305 + ___ = 6895 + 8831\n(A) 3944  (B) 3934  (C) 3924  (D) 3954",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  2487 + 9305 + ___ = 6895 + 8831\n(A) 3944  (B) 3934  (C) 3924  (D) 3954"
  },
  {
    "task_id": "J1_magnitude_estimation_000401_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 10200 * 10100?\n(A) 103019990  (B) 103020020  (C) 103020010  (D) 103020000",
    "ground_truth": "YES",
    "shortcut_strength": 0.985,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10200 * 10100?\n(A) 103019990  (B) 103020020  (C) 103020010  (D) 103020000"
  },
  {
    "task_id": "J1_landmark_comparison_000683_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 83% of 87480 greater than 24547?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 83% of 87480 greater than 24547?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_compatible_numbers_000605_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 3736 × 9032.\n(A) 33743572  (B) 33743562  (C) 33743542  (D) 33743552",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 3736 × 9032.\n(A) 33743572  (B) 33743562  (C) 33743542  (D) 33743552"
  },
  {
    "task_id": "J1_relative_distance_000518_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "weak_shortcut",
    "problem": "Which is larger: 2040/4251 or 1547/2813?\n(A) 1547/2813  (B) 2192/4105  (C) 2040/4251  (D) 550/1659",
    "ground_truth": "YES",
    "shortcut_strength": 0.07005959075479029,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 2040/4251 or 1547/2813?\n(A) 1547/2813  (B) 2192/4105  (C) 2040/4251  (D) 550/1659"
  },
  {
    "task_id": "J1_magnitude_estimation_000424_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 9900 * 9900?\n(A) 98010020  (B) 98010010  (C) 98010000  (D) 98009990",
    "ground_truth": "YES",
    "shortcut_strength": 0.99,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 9900 * 9900?\n(A) 98010020  (B) 98010010  (C) 98010000  (D) 98009990"
  },
  {
    "task_id": "J1_cancellation_identity_000584_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 1890 + 2392 - 3816\n(A) 476  (B) 486  (C) 456  (D) 466",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 1890 + 2392 - 3816\n(A) 476  (B) 486  (C) 456  (D) 466"
  },
  {
    "task_id": "J1_landmark_comparison_000655_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "strong_shortcut",
    "problem": "Is 26% of 60670 greater than 16769?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.99,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 26% of 60670 greater than 16769?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_option_elimination_000792_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 3210 × 3880?\n(A) 12454780  (B) 12454799  (C) 12454801  (D) 12454800",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 3210 × 3880?\n(A) 12454780  (B) 12454799  (C) 12454801  (D) 12454800"
  },
  {
    "task_id": "J1_compatible_numbers_000608_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "strong_shortcut",
    "problem": "Estimate 5009 × 1968.\n(A) 9857722  (B) 9857702  (C) 9857732  (D) 9857712",
    "ground_truth": "YES",
    "shortcut_strength": 0.9911,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 5009 × 1968.\n(A) 9857722  (B) 9857702  (C) 9857732  (D) 9857712"
  },
  {
    "task_id": "J1_option_elimination_000754_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 7810 × 8136?\n(A) 63542159  (B) 63542160  (C) 63542170  (D) 63542161",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 7810 × 8136?\n(A) 63542159  (B) 63542160  (C) 63542170  (D) 63542161"
  },
  {
    "task_id": "J1_landmark_comparison_000682_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 5% of 52750 greater than 15517?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.95,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 5% of 52750 greater than 15517?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_option_elimination_000757_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "control",
    "problem": "What is 8927 × 2827?\n(A) 21436629  (B) 29656629  (C) 25236629  (D) 26726629",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 8927 × 2827?\n(A) 21436629  (B) 29656629  (C) 25236629  (D) 26726629"
  },
  {
    "task_id": "J1_relative_distance_000533_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "control",
    "problem": "Which is larger: 3952/7184 or 830/1431?\n(A) 3952/7184  (B) 1189/1886  (C) 3511/7958  (D) 830/1431",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 3952/7184 or 830/1431?\n(A) 3952/7184  (B) 1189/1886  (C) 3511/7958  (D) 830/1431"
  },
  {
    "task_id": "J1_cancellation_identity_000554_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 6105 + 3719 - 5618\n(A) 4206  (B) 4196  (C) 4226  (D) 4216",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 6105 + 3719 - 5618\n(A) 4206  (B) 4196  (C) 4226  (D) 4216"
  },
  {
    "task_id": "J1_option_elimination_000753_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 7335 × 4896?\n(A) 35912161  (B) 35912140  (C) 35912159  (D) 35912160",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 7335 × 4896?\n(A) 35912161  (B) 35912140  (C) 35912159  (D) 35912160"
  },
  {
    "task_id": "J1_compatible_numbers_000607_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "strong_shortcut",
    "problem": "Estimate 1274 × 8785.\n(A) 11192110  (B) 11192090  (C) 11192080  (D) 11192100",
    "ground_truth": "YES",
    "shortcut_strength": 0.9413375,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1274 × 8785.\n(A) 11192110  (B) 11192090  (C) 11192080  (D) 11192100"
  },
  {
    "task_id": "J1_equation_reasoning_000721_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  6468 × (2099 + 2237) = 6468 × ___ + 6468 × 2237\n(A) 2109  (B) 2089  (C) 2119  (D) 2099",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  6468 × (2099 + 2237) = 6468 × ___ + 6468 × 2237\n(A) 2109  (B) 2089  (C) 2119  (D) 2099"
  },
  {
    "task_id": "J1_landmark_comparison_000685_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "strong_shortcut",
    "problem": "Is 52% of 76710 greater than 22129?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.98,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 52% of 76710 greater than 22129?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_structural_shortcuts_000493_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 9996 * 5407?\n(A) 54048372  (B) 54048362  (C) 54048392  (D) 54048382",
    "ground_truth": "YES",
    "shortcut_strength": 0.9996,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9996 * 5407?\n(A) 54048372  (B) 54048362  (C) 54048392  (D) 54048382"
  },
  {
    "task_id": "J1_magnitude_estimation_000442_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "weak_shortcut",
    "problem": "Which of the following is the best estimate for 9800 * 10225?\n(A) 100205020  (B) 100204990  (C) 100205000  (D) 100205010",
    "ground_truth": "YES",
    "shortcut_strength": 0.97875,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 9800 * 10225?\n(A) 100205020  (B) 100204990  (C) 100205000  (D) 100205010"
  },
  {
    "task_id": "J1_relative_distance_000520_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 4625/9376 or 2049/4061?\n(A) 1260/2884  (B) 2049/4061  (C) 3020/5052  (D) 4625/9376",
    "ground_truth": "YES",
    "shortcut_strength": 0.011274811471476298,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4625/9376 or 2049/4061?\n(A) 1260/2884  (B) 2049/4061  (C) 3020/5052  (D) 4625/9376"
  },
  {
    "task_id": "J1_landmark_comparison_000676_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 20% of 41260 greater than 11171?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.95,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 20% of 41260 greater than 11171?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_equation_reasoning_000723_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "weak_shortcut",
    "problem": "What value fills the blank?  6054 + 3975 + ___ = 3975 + 2653 + 1429\n(A) -1958  (B) -1968  (C) -1988  (D) -1972",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  6054 + 3975 + ___ = 3975 + 2653 + 1429\n(A) -1958  (B) -1968  (C) -1988  (D) -1972"
  },
  {
    "task_id": "J1_magnitude_estimation_000434_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 5516 * 4789?\n(A) 26416134  (B) 26416144  (C) 26416124  (D) 26416114",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 5516 * 4789?\n(A) 26416134  (B) 26416144  (C) 26416124  (D) 26416114"
  },
  {
    "task_id": "J1_compatible_numbers_000610_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 1226 × 9734.\n(A) 11933904  (B) 11933894  (C) 11933874  (D) 11933884",
    "ground_truth": "YES",
    "shortcut_strength": 0.8820250000000001,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1226 × 9734.\n(A) 11933904  (B) 11933894  (C) 11933874  (D) 11933884"
  },
  {
    "task_id": "J1_cancellation_identity_000586_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "strong_shortcut",
    "problem": "Evaluate: 3507 + 2988 - 2990\n(A) 3495  (B) 3525  (C) 3505  (D) 3515",
    "ground_truth": "YES",
    "shortcut_strength": 0.999330655957162,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 3507 + 2988 - 2990\n(A) 3495  (B) 3525  (C) 3505  (D) 3515"
  },
  {
    "task_id": "J1_option_elimination_000776_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "strong_shortcut",
    "problem": "What is 6135 × 7717?\n(A) 47343795  (B) 47343796  (C) 47343798  (D) 47343794",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 6135 × 7717?\n(A) 47343795  (B) 47343796  (C) 47343798  (D) 47343794"
  },
  {
    "task_id": "J1_equation_reasoning_000741_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "control",
    "problem": "What value fills the blank?  7752 + 1464 + ___ = 8481 + 5153\n(A) 4418  (B) 4428  (C) 4408  (D) 4438",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  7752 + 1464 + ___ = 8481 + 5153\n(A) 4418  (B) 4428  (C) 4408  (D) 4438"
  },
  {
    "task_id": "J1_structural_shortcuts_000478_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 4870 * 5878?\n(A) 28625880  (B) 28625850  (C) 28625860  (D) 28625870",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 4870 * 5878?\n(A) 28625880  (B) 28625850  (C) 28625860  (D) 28625870"
  },
  {
    "task_id": "J1_magnitude_estimation_000433_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 10200 * 9800?\n(A) 99960010  (B) 99959990  (C) 99960020  (D) 99960000",
    "ground_truth": "YES",
    "shortcut_strength": 0.98,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10200 * 9800?\n(A) 99960010  (B) 99959990  (C) 99960020  (D) 99960000"
  },
  {
    "task_id": "J1_cancellation_identity_000587_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 4015 + 4854 - 1874\n(A) 6985  (B) 6995  (C) 7015  (D) 7005",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 4015 + 4854 - 1874\n(A) 6985  (B) 6995  (C) 7015  (D) 7005"
  },
  {
    "task_id": "J1_landmark_comparison_000665_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 67% of 34690 greater than 11606?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 67% of 34690 greater than 11606?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_landmark_comparison_000699_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 7% of 57250 greater than 11559?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.97,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 7% of 57250 greater than 11559?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_equation_reasoning_000736_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "weak_shortcut",
    "problem": "What value fills the blank?  4420 + 2094 + ___ = 2094 + 1970 + 7723\n(A) 5293  (B) 5263  (C) 5273  (D) 5283",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  4420 + 2094 + ___ = 2094 + 1970 + 7723\n(A) 5293  (B) 5263  (C) 5273  (D) 5283"
  },
  {
    "task_id": "J1_relative_distance_000541_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "control",
    "problem": "Which is larger: 1527/2775 or 4352/7503?\n(A) 3240/7578  (B) 2841/8096  (C) 1527/2775  (D) 4352/7503",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 1527/2775 or 4352/7503?\n(A) 3240/7578  (B) 2841/8096  (C) 1527/2775  (D) 4352/7503"
  },
  {
    "task_id": "J1_equation_reasoning_000706_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  5259 × 6610 × 5838 = ___ × 5838 × 5259\n(A) 6610  (B) 6630  (C) 6620  (D) 6600",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  5259 × 6610 × 5838 = ___ × 5838 × 5259\n(A) 6610  (B) 6630  (C) 6620  (D) 6600"
  },
  {
    "task_id": "J1_magnitude_estimation_000401_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 5835 * 6856?\n(A) 40004770  (B) 40004780  (C) 40004760  (D) 40004750",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 5835 * 6856?\n(A) 40004770  (B) 40004780  (C) 40004760  (D) 40004750"
  },
  {
    "task_id": "J1_equation_reasoning_000703_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "weak_shortcut",
    "problem": "What value fills the blank?  4963 + 3897 + ___ = 3897 + 8559 + 9195\n(A) 12781  (B) 12801  (C) 12811  (D) 12791",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  4963 + 3897 + ___ = 3897 + 8559 + 9195\n(A) 12781  (B) 12801  (C) 12811  (D) 12791"
  },
  {
    "task_id": "J1_cancellation_identity_000569_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "control",
    "problem": "Evaluate: 3894 + 5525 - 2035\n(A) 7394  (B) 7374  (C) 7384  (D) 7404",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 3894 + 5525 - 2035\n(A) 7394  (B) 7374  (C) 7384  (D) 7404"
  },
  {
    "task_id": "J1_equation_reasoning_000750_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  5076 × 3938 × 3969 = ___ × 3969 × 5076\n(A) 3928  (B) 3948  (C) 3958  (D) 3938",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  5076 × 3938 × 3969 = ___ × 3969 × 5076\n(A) 3928  (B) 3948  (C) 3958  (D) 3938"
  },
  {
    "task_id": "J1_option_elimination_000778_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 7810 × 8136?\n(A) 63542159  (B) 63542160  (C) 63542170  (D) 63542161",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 7810 × 8136?\n(A) 63542159  (B) 63542160  (C) 63542170  (D) 63542161"
  },
  {
    "task_id": "J1_option_elimination_000793_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "control",
    "problem": "What is 2251 × 9459?\n(A) 25332209  (B) 23342209  (C) 21292209  (D) 23812209",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 2251 × 9459?\n(A) 25332209  (B) 23342209  (C) 21292209  (D) 23812209"
  },
  {
    "task_id": "J1_magnitude_estimation_000427_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "strong_shortcut",
    "problem": "Which of the following is the best estimate for 10100 * 10200?\n(A) 103020010  (B) 103020020  (C) 103019990  (D) 103020000",
    "ground_truth": "YES",
    "shortcut_strength": 0.985,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10100 * 10200?\n(A) 103020010  (B) 103020020  (C) 103019990  (D) 103020000"
  },
  {
    "task_id": "J1_option_elimination_000783_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "weak_shortcut",
    "problem": "What is 3345 × 2034?\n(A) 6803750  (B) 6803730  (C) 6803731  (D) 6803729",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 3345 × 2034?\n(A) 6803750  (B) 6803730  (C) 6803731  (D) 6803729"
  },
  {
    "task_id": "J1_option_elimination_000755_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "option_elimination",
    "variant": "strong_shortcut",
    "problem": "What is 4893 × 1523?\n(A) 7452040  (B) 7452042  (C) 7452038  (D) 7452039",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 4893 × 1523?\n(A) 7452040  (B) 7452042  (C) 7452038  (D) 7452039"
  },
  {
    "task_id": "J1_compatible_numbers_000644_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "strong_shortcut",
    "problem": "Estimate 2510 × 3724.\n(A) 9347260  (B) 9347250  (C) 9347230  (D) 9347240",
    "ground_truth": "YES",
    "shortcut_strength": 0.9635,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 2510 × 3724.\n(A) 9347260  (B) 9347250  (C) 9347230  (D) 9347240"
  },
  {
    "task_id": "J1_structural_shortcuts_000494_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "strong_shortcut",
    "problem": "What is 9998 * 2587?\n(A) 25864816  (B) 25864836  (C) 25864846  (D) 25864826",
    "ground_truth": "YES",
    "shortcut_strength": 0.9998,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9998 * 2587?\n(A) 25864816  (B) 25864836  (C) 25864846  (D) 25864826"
  },
  {
    "task_id": "J1_structural_shortcuts_000488_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "strong_shortcut",
    "problem": "What is 10002 * 6011?\n(A) 60122022  (B) 60122042  (C) 60122032  (D) 60122012",
    "ground_truth": "YES",
    "shortcut_strength": 0.9998,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 10002 * 6011?\n(A) 60122022  (B) 60122042  (C) 60122032  (D) 60122012"
  },
  {
    "task_id": "J1_equation_reasoning_000737_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "weak_shortcut",
    "problem": "What value fills the blank?  3022 + 3487 + ___ = 3487 + 4372 + 8264\n(A) 9614  (B) 9604  (C) 9634  (D) 9624",
    "ground_truth": "YES",
    "shortcut_strength": 0.5,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  3022 + 3487 + ___ = 3487 + 4372 + 8264\n(A) 9614  (B) 9604  (C) 9634  (D) 9624"
  },
  {
    "task_id": "J1_landmark_comparison_000671_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 83% of 79470 greater than 33317?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 83% of 79470 greater than 33317?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_structural_shortcuts_000468_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 5883 * 5894?\n(A) 34674412  (B) 34674392  (C) 34674422  (D) 34674402",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 5883 * 5894?\n(A) 34674412  (B) 34674392  (C) 34674422  (D) 34674402"
  },
  {
    "task_id": "J1_structural_shortcuts_000488_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 6927 * 5921?\n(A) 41014757  (B) 41014787  (C) 41014767  (D) 41014777",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 6927 * 5921?\n(A) 41014757  (B) 41014787  (C) 41014767  (D) 41014777"
  },
  {
    "task_id": "J1_landmark_comparison_000700_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 37% of 26260 greater than 11086?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 37% of 26260 greater than 11086?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_equation_reasoning_000715_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "control",
    "problem": "What value fills the blank?  3375 + 6017 + ___ = 6467 + 6798\n(A) 3873  (B) 3863  (C) 3883  (D) 3893",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  3375 + 6017 + ___ = 6467 + 6798\n(A) 3873  (B) 3863  (C) 3883  (D) 3893"
  },
  {
    "task_id": "J1_landmark_comparison_000652_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "control",
    "problem": "Is 83% of 48380 greater than 22179?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 83% of 48380 greater than 22179?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_relative_distance_000503_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "control",
    "problem": "Which is larger: 4048/7359 or 4606/7941?\n(A) 3054/6237  (B) 1831/3069  (C) 4606/7941  (D) 4048/7359",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4048/7359 or 4606/7941?\n(A) 3054/6237  (B) 1831/3069  (C) 4606/7941  (D) 4048/7359"
  },
  {
    "task_id": "J1_equation_reasoning_000717_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  6336 + 4267 = ___ + 4522\n(A) 6101  (B) 6081  (C) 6091  (D) 6071",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  6336 + 4267 = ___ + 4522\n(A) 6101  (B) 6081  (C) 6091  (D) 6071"
  },
  {
    "task_id": "J1_equation_reasoning_000711_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "equation_reasoning",
    "variant": "strong_shortcut",
    "problem": "What value fills the blank?  4403 + 4728 + ___ = 4728 + 4996 + 4403\n(A) 5016  (B) 4996  (C) 5006  (D) 4986",
    "ground_truth": "YES",
    "shortcut_strength": 1.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What value fills the blank?  4403 + 4728 + ___ = 4728 + 4996 + 4403\n(A) 5016  (B) 4996  (C) 5006  (D) 4986"
  },
  {
    "task_id": "J1_magnitude_estimation_000447_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 6455 * 6835?\n(A) 44119925  (B) 44119935  (C) 44119915  (D) 44119945",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 6455 * 6835?\n(A) 44119925  (B) 44119935  (C) 44119915  (D) 44119945"
  },
  {
    "task_id": "J1_structural_shortcuts_000479_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "weak_shortcut",
    "problem": "What is 9997 * 9185?\n(A) 91822455  (B) 91822435  (C) 91822465  (D) 91822445",
    "ground_truth": "YES",
    "shortcut_strength": 0.9997,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 9997 * 9185?\n(A) 91822455  (B) 91822435  (C) 91822465  (D) 91822445"
  },
  {
    "task_id": "J1_compatible_numbers_000614_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "weak_shortcut",
    "problem": "Estimate 1239 × 9766.\n(A) 12100084  (B) 12100094  (C) 12100074  (D) 12100064",
    "ground_truth": "YES",
    "shortcut_strength": 0.885225,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1239 × 9766.\n(A) 12100084  (B) 12100094  (C) 12100074  (D) 12100064"
  },
  {
    "task_id": "J1_landmark_comparison_000656_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 19% of 38290 greater than 9069?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.94,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 19% of 38290 greater than 9069?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_cancellation_identity_000564_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "cancellation_identity",
    "variant": "strong_shortcut",
    "problem": "Evaluate: 2356 + 6788 - 6789\n(A) 2345  (B) 2355  (C) 2375  (D) 2365",
    "ground_truth": "YES",
    "shortcut_strength": 0.9998526812021213,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Evaluate: 2356 + 6788 - 6789\n(A) 2345  (B) 2355  (C) 2375  (D) 2365"
  },
  {
    "task_id": "J1_magnitude_estimation_000443_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "control",
    "problem": "Which of the following is the best estimate for 5856 * 5571?\n(A) 32623796  (B) 32623776  (C) 32623786  (D) 32623766",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 5856 * 5571?\n(A) 32623796  (B) 32623776  (C) 32623786  (D) 32623766"
  },
  {
    "task_id": "J1_compatible_numbers_000640_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "compatible_numbers",
    "variant": "control",
    "problem": "Estimate 1554 × 1462.\n(A) 2271938  (B) 2271948  (C) 2271958  (D) 2271968",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Estimate 1554 × 1462.\n(A) 2271938  (B) 2271948  (C) 2271958  (D) 2271968"
  },
  {
    "task_id": "J1_structural_shortcuts_000466_control",
    "task_type": "J1_strategy_appropriateness",
    "category": "structural_shortcuts",
    "variant": "control",
    "problem": "What is 6196 * 5712?\n(A) 35391562  (B) 35391552  (C) 35391572  (D) 35391542",
    "ground_truth": "NO",
    "shortcut_strength": 0.0,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: What is 6196 * 5712?\n(A) 35391562  (B) 35391552  (C) 35391572  (D) 35391542"
  },
  {
    "task_id": "J1_magnitude_estimation_000412_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "weak_shortcut",
    "problem": "Which of the following is the best estimate for 10200 * 10224?\n(A) 104284820  (B) 104284800  (C) 104284790  (D) 104284810",
    "ground_truth": "YES",
    "shortcut_strength": 0.9788,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 10200 * 10224?\n(A) 104284820  (B) 104284800  (C) 104284790  (D) 104284810"
  },
  {
    "task_id": "J1_relative_distance_000525_strong_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "relative_distance",
    "variant": "strong_shortcut",
    "problem": "Which is larger: 4669/9401 or 4299/8461?\n(A) 4669/9401  (B) 4299/8461  (C) 2365/4609  (D) 2552/5240",
    "ground_truth": "YES",
    "shortcut_strength": 0.011446677115085346,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which is larger: 4669/9401 or 4299/8461?\n(A) 4669/9401  (B) 4299/8461  (C) 2365/4609  (D) 2552/5240"
  },
  {
    "task_id": "J1_landmark_comparison_000684_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "landmark_comparison",
    "variant": "weak_shortcut",
    "problem": "Is 30% of 17490 greater than 8451?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information",
    "ground_truth": "YES",
    "shortcut_strength": 0.95,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Is 30% of 17490 greater than 8451?\n(A) Yes  (B) No  (C) Cannot be determined  (D) Need more information"
  },
  {
    "task_id": "J1_magnitude_estimation_000439_weak_shortcut",
    "task_type": "J1_strategy_appropriateness",
    "category": "magnitude_estimation",
    "variant": "weak_shortcut",
    "problem": "Which of the following is the best estimate for 9900 * 10167?\n(A) 100653310  (B) 100653290  (C) 100653320  (D) 100653300",
    "ground_truth": "YES",
    "shortcut_strength": 0.98665,
    "prompt": "Consider this math problem. Could you solve it significantly faster using mental math or a clever observation, compared to computing it step by step? Answer YES or NO, then explain in one sentence why.\n\nProblem: Which of the following is the best estimate for 9900 * 10167?\n(A) 100653310  (B) 100653290  (C) 100653320  (D) 100653300"
  }
]