data/question_support_bank.jsonl

{"question_id": "EQUANT01", "topic": "algebra", "stem": "If x is an integer and 3x+2 is divisible by 5, which value could x be?", "choices": ["1", "2", "3", "4", "6"], "correct_option": 3, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: If x is an integer and 3x+2 is divisible by 5, whi...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "EQUANT02", "topic": "percent", "stem": "A price is increased by 20% and then decreased by 20%. The final price is what percent of the original?", "choices": ["96%", "100%", "104%", "108%", "120%"], "correct_option": 0, "first_step": "Treat the original value as 100 unless a specific number is easier.", "hint_1": "Focus on how the percentage is applied — is it increase, decrease, or part of a whole?", "hint_2": "Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).", "hint_3": "Apply each percentage step in order — don’t combine them directly.", "walkthrough_steps": ["Start with an easy base value (like 100).", "Apply the first percentage change.", "Apply the second change to the new value.", "Compare the result with the original."], "method_explanation": ["Percent changes are multiplicative, not additive.", "Each change affects the updated value.", "Using 100 simplifies calculations."], "common_trap": "Adding/subtracting percentages directly instead of applying sequential changes."}
{"question_id": "EQUANT03", "topic": "algebra", "stem": "If a and b are positive and a/b = 3/4, what is (a+b)/b?", "choices": ["1.25", "1.5", "1.75", "2", "2.5"], "correct_option": 2, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: If a and b are positive and a/b = 3/4, what is (a+...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "EQUANT04", "topic": "algebra", "stem": "If 5y - 3 = 22, what is y?", "choices": ["3", "4", "5", "6", "7"], "correct_option": 2, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: If 5y - 3 = 22, what is y?...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "EQUANT05", "topic": "probability", "stem": "A box contains 3 red and 5 blue balls. If one ball is chosen at random, what is the probability it is red?", "choices": ["3/5", "3/8", "5/8", "1/3", "1/5"], "correct_option": 1, "first_step": "Count total outcomes and favorable outcomes.", "hint_1": "How many total possibilities are there?", "hint_2": "How many meet the condition?", "hint_3": "Probability = favorable / total.", "walkthrough_steps": ["Count total outcomes.", "Count favorable outcomes.", "Divide favorable by total."], "method_explanation": ["Probability is a ratio.", "Clear counting is essential."], "common_trap": "Incorrect counting of outcomes."}
{"question_id": "EQUANT06", "topic": "algebra", "stem": "If (x/3) = 5, what is 2x?", "choices": ["10", "15", "20", "25", "30"], "correct_option": 2, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: If (x/3) = 5, what is 2x?...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "EQUANT07", "topic": "general", "stem": "The sum of two consecutive integers is 41. What is the larger integer?", "choices": ["19", "20", "21", "22", "23"], "correct_option": 2, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "EQUANT08", "topic": "geometry", "stem": "If a rectangle has perimeter 30 and length 9, what is its width?", "choices": ["3", "4", "5", "6", "7"], "correct_option": 1, "first_step": "Identify the shape and formula needed.", "hint_1": "Recall the relevant formula.", "hint_2": "Substitute values carefully.", "hint_3": "Solve step by step.", "walkthrough_steps": ["Identify formula.", "Substitute values.", "Compute result."], "method_explanation": ["Geometry relies on standard formulas.", "Careful substitution avoids mistakes."], "common_trap": "Using the wrong formula."}
{"question_id": "EQUANT09", "topic": "general", "stem": "What is the smallest prime factor of 91?", "choices": ["7", "11", "13", "17", "19"], "correct_option": 0, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "EQUANT10", "topic": "general", "stem": "If 0.06 = 6/k, what is k?", "choices": ["10", "50", "60", "100", "600"], "correct_option": 3, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "EVERBAL01", "topic": "general", "stem": "The committee based its decision not only on cost but also ___ the long term impact.", "choices": ["consider", "considered", "considering", "to consider", "on considering"], "correct_option": 4, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "EVERBAL02", "topic": "general", "stem": "Which sentence is grammatically correct?", "choices": ["Neither the managers nor the director were informed.", "Neither the managers nor the director was informed.", "Neither the manager nor the directors was informed.", "Neither the managers or the director was informed.", "Neither manager nor director were informed."], "correct_option": 1, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "EVERBAL03", "topic": "ratio", "stem": "In the passage, the study is mentioned primarily to:", "choices": ["refute the author’s main claim", "introduce a new topic unrelated to the argument", "illustrate a broader trend", "dismiss earlier research entirely", "prove causation beyond doubt"], "correct_option": 2, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "EVERBAL04", "topic": "statistics", "stem": "Choose the word closest in meaning to 'mitigate'.", "choices": ["worsen", "reduce", "predict", "separate", "repeat"], "correct_option": 1, "first_step": "Identify what measure is being asked (mean, median, etc.).", "hint_1": "Write out the numbers clearly.", "hint_2": "Apply the correct formula.", "hint_3": "Check your calculation.", "walkthrough_steps": ["List values.", "Apply formula (mean, median, etc.).", "Compute carefully."], "method_explanation": ["Different measures describe data differently.", "Mean = sum / count."], "common_trap": "Using the wrong measure."}
{"question_id": "EVERBAL05", "topic": "general", "stem": "Which sentence is most concise?", "choices": ["Due to the fact that the roads were icy, the match was canceled.", "Because the roads were icy, the match was canceled.", "The match was canceled due to the icy roads that existed.", "The match was canceled as a result of roads being icy.", "Icy roads were the reason that the match was canceled."], "correct_option": 1, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "EVERBAL06", "topic": "ratio", "stem": "Choose the correct verb form: Each of the reports ___ complete.", "choices": ["are", "were", "has", "is", "have"], "correct_option": 3, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "EVERBAL07", "topic": "ratio", "stem": "Choose the best transition: The hypothesis seemed plausible; ___, it lacked supporting data.", "choices": ["therefore", "however", "for example", "similarly", "in addition"], "correct_option": 1, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "EVERBAL08", "topic": "general", "stem": "Which choice best fixes the modifier error? 'Walking to the station, the rain soaked Maria.'", "choices": ["Walking to the station, the rain soaked Maria.", "Walking to the station, Maria was soaked by the rain.", "Walking to the station, soaking Maria was the rain.", "Walking to the station, the station soaked Maria with rain.", "Walking to the station, Maria soaked the rain."], "correct_option": 1, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "EVERBAL09", "topic": "general", "stem": "Choose the correctly spelled word.", "choices": ["definately", "seperate", "receive", "enviroment", "occassion"], "correct_option": 2, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "EVERBAL10", "topic": "general", "stem": "Which option is a complete sentence?", "choices": ["Because the deadline was moved.", "Although working late.", "The deadline was moved.", "While in the office.", "After the meeting."], "correct_option": 2, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "EDATA01", "topic": "percent", "stem": "Revenue increased from 80000 to 92000. What was the percent increase?", "choices": ["10%", "12%", "15%", "18%", "20%"], "correct_option": 2, "first_step": "Treat the original value as 100 unless a specific number is easier.", "hint_1": "Focus on how the percentage is applied — is it increase, decrease, or part of a whole?", "hint_2": "Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).", "hint_3": "Apply each percentage step in order — don’t combine them directly.", "walkthrough_steps": ["Start with an easy base value (like 100).", "Apply the first percentage change.", "Apply the second change to the new value.", "Compare the result with the original."], "method_explanation": ["Percent changes are multiplicative, not additive.", "Each change affects the updated value.", "Using 100 simplifies calculations."], "common_trap": "Adding/subtracting percentages directly instead of applying sequential changes."}
{"question_id": "EDATA02", "topic": "statistics", "stem": "Which dataset has the greatest variability?", "choices": ["10,12,14", "8,12,16", "11,12,13", "9,12,15", "10,11,12"], "correct_option": 1, "first_step": "Identify what measure is being asked (mean, median, etc.).", "hint_1": "Write out the numbers clearly.", "hint_2": "Apply the correct formula.", "hint_3": "Check your calculation.", "walkthrough_steps": ["List values.", "Apply formula (mean, median, etc.).", "Compute carefully."], "method_explanation": ["Different measures describe data differently.", "Mean = sum / count."], "common_trap": "Using the wrong measure."}
{"question_id": "EDATA03", "topic": "ratio", "stem": "If the median is greater than the mean, the distribution is most likely:", "choices": ["symmetric", "uniform", "skewed right", "skewed left", "bimodal"], "correct_option": 3, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "EDATA04", "topic": "statistics", "stem": "A table shows values 6, 9, 15, 20. What is the mean?", "choices": ["10", "11.5", "12.5", "13", "14"], "correct_option": 1, "first_step": "Identify what measure is being asked (mean, median, etc.).", "hint_1": "Write out the numbers clearly.", "hint_2": "Apply the correct formula.", "hint_3": "Check your calculation.", "walkthrough_steps": ["List values.", "Apply formula (mean, median, etc.).", "Compute carefully."], "method_explanation": ["Different measures describe data differently.", "Mean = sum / count."], "common_trap": "Using the wrong measure."}
{"question_id": "EDATA05", "topic": "percent", "stem": "If 18 out of 60 customers choose Option A, what percent choose A?", "choices": ["20%", "25%", "30%", "35%", "40%"], "correct_option": 2, "first_step": "Treat the original value as 100 unless a specific number is easier.", "hint_1": "Focus on how the percentage is applied — is it increase, decrease, or part of a whole?", "hint_2": "Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).", "hint_3": "Apply each percentage step in order — don’t combine them directly.", "walkthrough_steps": ["Start with an easy base value (like 100).", "Apply the first percentage change.", "Apply the second change to the new value.", "Compare the result with the original."], "method_explanation": ["Percent changes are multiplicative, not additive.", "Each change affects the updated value.", "Using 100 simplifies calculations."], "common_trap": "Adding/subtracting percentages directly instead of applying sequential changes."}
{"question_id": "EDATA06", "topic": "ratio", "stem": "Costs are 150 and revenue is 210. Profit is:", "choices": ["40", "50", "60", "70", "80"], "correct_option": 2, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "EDATA07", "topic": "percent", "stem": "A pie chart shows 25% for Segment X. This equals:", "choices": ["1/2", "1/3", "1/4", "2/5", "3/4"], "correct_option": 2, "first_step": "Treat the original value as 100 unless a specific number is easier.", "hint_1": "Focus on how the percentage is applied — is it increase, decrease, or part of a whole?", "hint_2": "Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).", "hint_3": "Apply each percentage step in order — don’t combine them directly.", "walkthrough_steps": ["Start with an easy base value (like 100).", "Apply the first percentage change.", "Apply the second change to the new value.", "Compare the result with the original."], "method_explanation": ["Percent changes are multiplicative, not additive.", "Each change affects the updated value.", "Using 100 simplifies calculations."], "common_trap": "Adding/subtracting percentages directly instead of applying sequential changes."}
{"question_id": "EDATA08", "topic": "statistics", "stem": "Which measure represents the middle value of an ordered dataset?", "choices": ["mean", "median", "mode", "range", "variance"], "correct_option": 1, "first_step": "Identify what measure is being asked (mean, median, etc.).", "hint_1": "Write out the numbers clearly.", "hint_2": "Apply the correct formula.", "hint_3": "Check your calculation.", "walkthrough_steps": ["List values.", "Apply formula (mean, median, etc.).", "Compute carefully."], "method_explanation": ["Different measures describe data differently.", "Mean = sum / count."], "common_trap": "Using the wrong measure."}
{"question_id": "EDATA09", "topic": "ratio", "stem": "If a value is far above most others, it is best described as a(n):", "choices": ["cluster", "outlier", "median", "trend", "index"], "correct_option": 1, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "EDATA10", "topic": "ratio", "stem": "If sales are 30 on Monday and 45 on Tuesday, Tuesday sales are higher by:", "choices": ["10", "12", "15", "18", "20"], "correct_option": 2, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "MQUANT01", "topic": "algebra", "stem": "If x and y are positive integers and x/y = 4/7 and x+y = 66, what is x?", "choices": ["24", "28", "32", "36", "40"], "correct_option": 1, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: If x and y are positive integers and x/y = 4/7 and...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "MQUANT02", "topic": "general", "stem": "Pipe A fills a tank in 6 hours and Pipe B in 12 hours. After 2 hours together, what fraction remains unfilled?", "choices": ["1/6", "1/4", "1/3", "5/12", "1/2"], "correct_option": 2, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "MQUANT03", "topic": "algebra", "stem": "If 2a - 3b = 7 and a = 5, what is b?", "choices": ["-1", "0", "1", "2", "3"], "correct_option": 3, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: If 2a - 3b = 7 and a = 5, what is b?...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "MQUANT04", "topic": "algebra", "stem": "If n is an integer, which value of n makes (n^2 + 5n + 6) divisible by 6?", "choices": ["-5", "-3", "-2", "1", "4"], "correct_option": 3, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: If n is an integer, which value of n makes (n^2 + ...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "MQUANT05", "topic": "percent", "stem": "A number is increased by 15% and then increased again by 20%. The final value is what percent of the original?", "choices": ["135%", "136%", "138%", "140%", "142%"], "correct_option": 2, "first_step": "Treat the original value as 100 unless a specific number is easier.", "hint_1": "Focus on how the percentage is applied — is it increase, decrease, or part of a whole?", "hint_2": "Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).", "hint_3": "Apply each percentage step in order — don’t combine them directly.", "walkthrough_steps": ["Start with an easy base value (like 100).", "Apply the first percentage change.", "Apply the second change to the new value.", "Compare the result with the original."], "method_explanation": ["Percent changes are multiplicative, not additive.", "Each change affects the updated value.", "Using 100 simplifies calculations."], "common_trap": "Adding/subtracting percentages directly instead of applying sequential changes."}
{"question_id": "MQUANT06", "topic": "statistics", "stem": "If the average of 5 numbers is 12 and four of the numbers are 9, 10, 11, and 14, what is the fifth number?", "choices": ["12", "14", "16", "18", "20"], "correct_option": 1, "first_step": "Identify what measure is being asked (mean, median, etc.).", "hint_1": "Write out the numbers clearly.", "hint_2": "Apply the correct formula.", "hint_3": "Check your calculation.", "walkthrough_steps": ["List values.", "Apply formula (mean, median, etc.).", "Compute carefully."], "method_explanation": ["Different measures describe data differently.", "Mean = sum / count."], "common_trap": "Using the wrong measure."}
{"question_id": "MQUANT07", "topic": "geometry", "stem": "If a circle has circumference 18π, what is its area?", "choices": ["36π", "72π", "81π", "162π", "324π"], "correct_option": 2, "first_step": "Identify the shape and formula needed.", "hint_1": "Recall the relevant formula.", "hint_2": "Substitute values carefully.", "hint_3": "Solve step by step.", "walkthrough_steps": ["Identify formula.", "Substitute values.", "Compute result."], "method_explanation": ["Geometry relies on standard formulas.", "Careful substitution avoids mistakes."], "common_trap": "Using the wrong formula."}
{"question_id": "MQUANT08", "topic": "general", "stem": "A store sells pens at 3 for 5. If you buy 12 pens, what is the total cost?", "choices": ["15", "18", "20", "22", "25"], "correct_option": 2, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "MQUANT09", "topic": "general", "stem": "If x^2 - 9 = 0 and x is positive, what is x?", "choices": ["1", "2", "3", "6", "9"], "correct_option": 2, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "MQUANT10", "topic": "ratio", "stem": "If the ratio of apples to oranges is 5:3 and there are 64 fruits total, how many apples are there?", "choices": ["35", "40", "45", "50", "55"], "correct_option": 1, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "MVERBAL01", "topic": "general", "stem": "The scientist’s theory, once dismissed as implausible, is now regarded as ___ recent evidence.", "choices": ["validated by", "validation of", "validating", "to validate", "having validated"], "correct_option": 0, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "MVERBAL02", "topic": "ratio", "stem": "Which option best combines the sentences: 'The company expanded rapidly.' 'It underestimated logistical challenges.'", "choices": ["The company expanded rapidly but underestimated the logistical challenges.", "The company expanded rapidly, it underestimated the logistical challenges.", "Expanding rapidly, logistical challenges were underestimated.", "The company expanded rapidly; underestimated logistical challenges.", "Rapid expansion underestimated logistical challenges."], "correct_option": 0, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "MVERBAL03", "topic": "ratio", "stem": "The author’s discussion of early failures primarily serves to:", "choices": ["undermine later successes", "show that progress is inevitable", "illustrate the complexity of the process", "argue that results do not matter", "criticize modern views"], "correct_option": 2, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "MVERBAL04", "topic": "ratio", "stem": "Choose the best word: The report was praised for its ___ analysis.", "choices": ["thorough", "thoroughly", "thoroughness", "thoroughest", "thoroughen"], "correct_option": 0, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "MVERBAL05", "topic": "general", "stem": "Which sentence has correct subject verb agreement?", "choices": ["A list of items are on the desk.", "A list of items is on the desk.", "A list of items were on the desk.", "A list of item is on the desk.", "A list of items have on the desk."], "correct_option": 1, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "MVERBAL06", "topic": "ratio", "stem": "Choose the best revision: 'The policy is effective, it reduces costs.'", "choices": ["The policy is effective, and it reduces costs.", "The policy is effective it reduces costs.", "The policy is effective; reducing costs.", "The policy is effective, reducing costs.", "The policy is effective, which reducing costs."], "correct_option": 0, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "MVERBAL07", "topic": "statistics", "stem": "Choose the word closest in meaning to 'equivocal'.", "choices": ["certain", "ambiguous", "complete", "brief", "obvious"], "correct_option": 1, "first_step": "Identify what measure is being asked (mean, median, etc.).", "hint_1": "Write out the numbers clearly.", "hint_2": "Apply the correct formula.", "hint_3": "Check your calculation.", "walkthrough_steps": ["List values.", "Apply formula (mean, median, etc.).", "Compute carefully."], "method_explanation": ["Different measures describe data differently.", "Mean = sum / count."], "common_trap": "Using the wrong measure."}
{"question_id": "MVERBAL08", "topic": "general", "stem": "Which sentence avoids redundancy best?", "choices": ["Advance planning is necessary.", "Unexpected surprise occurred.", "Final outcome was unclear.", "Free gift was offered.", "Past history matters."], "correct_option": 0, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "MVERBAL09", "topic": "ratio", "stem": "In the argument, the author assumes that:", "choices": ["all variables are known", "past patterns will continue", "no alternatives exist", "correlation proves causation", "costs always exceed benefits"], "correct_option": 1, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "MVERBAL10", "topic": "general", "stem": "Choose the correct idiom.", "choices": ["capable to", "different than", "responsible for", "regard on", "concerned at"], "correct_option": 2, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "MDATA01", "topic": "percent", "stem": "Sales increase from 200 to 260. What is the percent increase?", "choices": ["20%", "25%", "30%", "35%", "40%"], "correct_option": 2, "first_step": "Treat the original value as 100 unless a specific number is easier.", "hint_1": "Focus on how the percentage is applied — is it increase, decrease, or part of a whole?", "hint_2": "Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).", "hint_3": "Apply each percentage step in order — don’t combine them directly.", "walkthrough_steps": ["Start with an easy base value (like 100).", "Apply the first percentage change.", "Apply the second change to the new value.", "Compare the result with the original."], "method_explanation": ["Percent changes are multiplicative, not additive.", "Each change affects the updated value.", "Using 100 simplifies calculations."], "common_trap": "Adding/subtracting percentages directly instead of applying sequential changes."}
{"question_id": "MDATA02", "topic": "statistics", "stem": "What is the weighted average of 60 with weight 2 and 80 with weight 3?", "choices": ["68", "70", "72", "74", "76"], "correct_option": 2, "first_step": "Identify what measure is being asked (mean, median, etc.).", "hint_1": "Write out the numbers clearly.", "hint_2": "Apply the correct formula.", "hint_3": "Check your calculation.", "walkthrough_steps": ["List values.", "Apply formula (mean, median, etc.).", "Compute carefully."], "method_explanation": ["Different measures describe data differently.", "Mean = sum / count."], "common_trap": "Using the wrong measure."}
{"question_id": "MDATA03", "topic": "statistics", "stem": "If the mean of five numbers is 20, what is their sum?", "choices": ["80", "90", "100", "110", "120"], "correct_option": 2, "first_step": "Identify what measure is being asked (mean, median, etc.).", "hint_1": "Write out the numbers clearly.", "hint_2": "Apply the correct formula.", "hint_3": "Check your calculation.", "walkthrough_steps": ["List values.", "Apply formula (mean, median, etc.).", "Compute carefully."], "method_explanation": ["Different measures describe data differently.", "Mean = sum / count."], "common_trap": "Using the wrong measure."}
{"question_id": "MDATA04", "topic": "general", "stem": "Quarterly profits are 40, 60, 50, 70. Which statement is true?", "choices": ["Mean exceeds median", "Median exceeds mean", "Mean equals median", "Range is 20", "No variability"], "correct_option": 1, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "MDATA05", "topic": "percent", "stem": "If price rises 25% and demand falls 10%, revenue will most likely:", "choices": ["increase significantly", "decrease significantly", "increase slightly", "stay about the same", "become zero"], "correct_option": 2, "first_step": "Treat the original value as 100 unless a specific number is easier.", "hint_1": "Focus on how the percentage is applied — is it increase, decrease, or part of a whole?", "hint_2": "Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).", "hint_3": "Apply each percentage step in order — don’t combine them directly.", "walkthrough_steps": ["Start with an easy base value (like 100).", "Apply the first percentage change.", "Apply the second change to the new value.", "Compare the result with the original."], "method_explanation": ["Percent changes are multiplicative, not additive.", "Each change affects the updated value.", "Using 100 simplifies calculations."], "common_trap": "Adding/subtracting percentages directly instead of applying sequential changes."}
{"question_id": "MDATA06", "topic": "general", "stem": "Which measure is least affected by outliers?", "choices": ["mean", "median", "range", "maximum", "minimum"], "correct_option": 1, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "MDATA07", "topic": "ratio", "stem": "A dataset is skewed right if most values are:", "choices": ["high", "low", "evenly spread", "negative", "identical"], "correct_option": 1, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "MDATA08", "topic": "percent", "stem": "If 3 out of 8 customers return a product, what percent is that?", "choices": ["30%", "35%", "37.5%", "40%", "45%"], "correct_option": 2, "first_step": "Treat the original value as 100 unless a specific number is easier.", "hint_1": "Focus on how the percentage is applied — is it increase, decrease, or part of a whole?", "hint_2": "Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).", "hint_3": "Apply each percentage step in order — don’t combine them directly.", "walkthrough_steps": ["Start with an easy base value (like 100).", "Apply the first percentage change.", "Apply the second change to the new value.", "Compare the result with the original."], "method_explanation": ["Percent changes are multiplicative, not additive.", "Each change affects the updated value.", "Using 100 simplifies calculations."], "common_trap": "Adding/subtracting percentages directly instead of applying sequential changes."}
{"question_id": "MDATA09", "topic": "ratio", "stem": "If revenue is 500 and costs are 350, profit margin is:", "choices": ["20%", "25%", "30%", "35%", "40%"], "correct_option": 1, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "MDATA10", "topic": "general", "stem": "Which display is best for checking correlation between two variables?", "choices": ["pie chart", "bar chart", "histogram", "scatter plot", "stacked area chart"], "correct_option": 3, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "HQUANT01", "topic": "algebra", "stem": "If x + 1/x = 3, what is x^3 + 1/x^3?", "choices": ["9", "18", "21", "24", "27"], "correct_option": 2, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: If x + 1/x = 3, what is x^3 + 1/x^3?...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "HQUANT02", "topic": "general", "stem": "A positive integer n leaves remainder 1 when divided by 2 and remainder 2 when divided by 3. What could be the remainder when n is divided by 6?", "choices": ["0", "1", "2", "3", "5"], "correct_option": 4, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "HQUANT03", "topic": "general", "stem": "In a geometric sequence, each term is (2/3) times the previous term. If the 4th term is 16, what is the 1st term?", "choices": ["18", "24", "36", "54", "72"], "correct_option": 3, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "HQUANT04", "topic": "algebra", "stem": "If (x-2)(x-5)=0, and x is an integer greater than 3, what is x?", "choices": ["2", "3", "4", "5", "6"], "correct_option": 3, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: If (x-2)(x-5)=0, and x is an integer greater than ...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "HQUANT05", "topic": "algebra", "stem": "How many integers satisfy |x-5| ≤ 7?", "choices": ["12", "13", "14", "15", "16"], "correct_option": 3, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: How many integers satisfy |x-5| ≤ 7?...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "HQUANT06", "topic": "algebra", "stem": "If a^b = a^3 and a>0 and a≠1, what must be true?", "choices": ["b=0", "b=1", "b=3", "a=3", "a=b"], "correct_option": 2, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: If a^b = a^3 and a>0 and a≠1, what must be true?...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "HQUANT07", "topic": "general", "stem": "What is the remainder when 3^100 is divided by 4?", "choices": ["0", "1", "2", "3", "4"], "correct_option": 1, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "HQUANT08", "topic": "geometry", "stem": "If a triangle has sides 7 and 10 and included angle 60 degrees, what is the length of the third side?", "choices": ["3", "7", "9", "13", "17"], "correct_option": 2, "first_step": "Identify the shape and formula needed.", "hint_1": "Recall the relevant formula.", "hint_2": "Substitute values carefully.", "hint_3": "Solve step by step.", "walkthrough_steps": ["Identify formula.", "Substitute values.", "Compute result."], "method_explanation": ["Geometry relies on standard formulas.", "Careful substitution avoids mistakes."], "common_trap": "Using the wrong formula."}
{"question_id": "HQUANT09", "topic": "algebra", "stem": "If f(x)=x^2-4x+k has exactly one real root, what is k?", "choices": ["0", "2", "4", "8", "16"], "correct_option": 2, "first_step": "Write the equation clearly and identify the variable.", "hint_1": "Look at the structure: If f(x)=x^2-4x+k has exactly one real root, what i...", "hint_2": "Undo operations in reverse order.", "hint_3": "Keep both sides balanced while isolating the variable.", "walkthrough_steps": ["Identify the equation.", "Move constants to one side.", "Undo multiplication/division.", "Solve for the variable."], "method_explanation": ["Solve by isolating the variable step by step.", "Reverse operations carefully.", "Check your result by substitution."], "common_trap": "Forgetting to apply operations to both sides."}
{"question_id": "HQUANT10", "topic": "geometry", "stem": "If the area of a circle is 49π, what is its circumference?", "choices": ["7π", "14π", "21π", "28π", "49π"], "correct_option": 1, "first_step": "Identify the shape and formula needed.", "hint_1": "Recall the relevant formula.", "hint_2": "Substitute values carefully.", "hint_3": "Solve step by step.", "walkthrough_steps": ["Identify formula.", "Substitute values.", "Compute result."], "method_explanation": ["Geometry relies on standard formulas.", "Careful substitution avoids mistakes."], "common_trap": "Using the wrong formula."}
{"question_id": "HVERBAL01", "topic": "general", "stem": "Although the proposal appears straightforward, it depends on assumptions that are far from ___.", "choices": ["tenuous", "explicit", "unassailable", "redundant", "peripheral"], "correct_option": 2, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "HVERBAL02", "topic": "general", "stem": "Which sentence is grammatically correct and logically clear?", "choices": ["Having reviewed the data, the conclusions were revised by the analysts.", "Having reviewed the data, the analysts revised the conclusions.", "The analysts, having reviewed the data, the conclusions were revised.", "The data having been reviewed, revising the conclusions was done by the analysts.", "Reviewing the data, the conclusions revised the analysts."], "correct_option": 1, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "HVERBAL03", "topic": "ratio", "stem": "The argument is most vulnerable because it:", "choices": ["assumes what it sets out to prove", "uses a sample too small to justify any conclusion", "assumes one factor cannot influence another", "confuses a necessary condition with a sufficient one", "draws a conclusion that contradicts its evidence"], "correct_option": 3, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "HVERBAL04", "topic": "ratio", "stem": "Choose the best word: The results were not definitive but merely ___.", "choices": ["conclusive", "tentative", "certain", "mandatory", "literal"], "correct_option": 1, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "HVERBAL05", "topic": "general", "stem": "Which option has correct parallel structure?", "choices": ["She values integrity, working hard, and to be punctual.", "She values integrity, hard work, and punctuality.", "She values to be honest, working hard, and punctual.", "She values integrity, to work hard, and punctual.", "She values being honest, to work hard, and being punctual."], "correct_option": 1, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "HVERBAL06", "topic": "general", "stem": "Which option contains an idiom error?", "choices": ["regard as", "responsible for", "different from", "capable of", "capable to"], "correct_option": 4, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "HVERBAL07", "topic": "general", "stem": "Choose the most precise word.", "choices": ["thing", "stuff", "aspect", "kind", "lot"], "correct_option": 2, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "HVERBAL08", "topic": "ratio", "stem": "The passage’s primary purpose is to:", "choices": ["present a single example without analysis", "compare two competing explanations", "argue that all research is flawed", "describe a personal narrative", "list unrelated facts"], "correct_option": 1, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "HVERBAL09", "topic": "ratio", "stem": "The author implies that a policy change would be effective only if it:", "choices": ["is inexpensive", "is widely publicized", "addresses the underlying incentive", "is implemented gradually", "is approved unanimously"], "correct_option": 2, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "HVERBAL10", "topic": "ratio", "stem": "Choose the best completion: The theory was dismissed as ___ due to limited evidence.", "choices": ["speculative", "speculation", "speculate", "speculating", "speculated"], "correct_option": 0, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "HDATA01", "topic": "percent", "stem": "Option A returns +10% then -10%. Option B returns -5% then +5%. Starting at 100, which ends higher?", "choices": ["Both end at 100", "A ends higher", "B ends higher", "A and B end equal below 100", "Cannot be determined"], "correct_option": 2, "first_step": "Treat the original value as 100 unless a specific number is easier.", "hint_1": "Focus on how the percentage is applied — is it increase, decrease, or part of a whole?", "hint_2": "Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).", "hint_3": "Apply each percentage step in order — don’t combine them directly.", "walkthrough_steps": ["Start with an easy base value (like 100).", "Apply the first percentage change.", "Apply the second change to the new value.", "Compare the result with the original."], "method_explanation": ["Percent changes are multiplicative, not additive.", "Each change affects the updated value.", "Using 100 simplifies calculations."], "common_trap": "Adding/subtracting percentages directly instead of applying sequential changes."}
{"question_id": "HDATA02", "topic": "statistics", "stem": "Average weekly sales rise from 400 to 460 while stores rise from 8 to 10. Best supported conclusion?", "choices": ["Sales per store increased", "Sales per store decreased", "Sales per store stayed the same", "Campaign caused higher sales per store", "No comparison can be made"], "correct_option": 1, "first_step": "Identify what measure is being asked (mean, median, etc.).", "hint_1": "Write out the numbers clearly.", "hint_2": "Apply the correct formula.", "hint_3": "Check your calculation.", "walkthrough_steps": ["List values.", "Apply formula (mean, median, etc.).", "Compute carefully."], "method_explanation": ["Different measures describe data differently.", "Mean = sum / count."], "common_trap": "Using the wrong measure."}
{"question_id": "HDATA03", "topic": "statistics", "stem": "A dataset has mean 50 and standard deviation 5 and is approximately normal. Which value is most likely?", "choices": ["35", "40", "45", "60", "70"], "correct_option": 2, "first_step": "Identify what measure is being asked (mean, median, etc.).", "hint_1": "Write out the numbers clearly.", "hint_2": "Apply the correct formula.", "hint_3": "Check your calculation.", "walkthrough_steps": ["List values.", "Apply formula (mean, median, etc.).", "Compute carefully."], "method_explanation": ["Different measures describe data differently.", "Mean = sum / count."], "common_trap": "Using the wrong measure."}
{"question_id": "HDATA04", "topic": "percent", "stem": "Compound interest at 10% annually on 100 for 2 years yields:", "choices": ["110", "115", "120", "121", "125"], "correct_option": 3, "first_step": "Treat the original value as 100 unless a specific number is easier.", "hint_1": "Focus on how the percentage is applied — is it increase, decrease, or part of a whole?", "hint_2": "Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).", "hint_3": "Apply each percentage step in order — don’t combine them directly.", "walkthrough_steps": ["Start with an easy base value (like 100).", "Apply the first percentage change.", "Apply the second change to the new value.", "Compare the result with the original."], "method_explanation": ["Percent changes are multiplicative, not additive.", "Each change affects the updated value.", "Using 100 simplifies calculations."], "common_trap": "Adding/subtracting percentages directly instead of applying sequential changes."}
{"question_id": "HDATA05", "topic": "ratio", "stem": "A regression model has R^2 = 0.81. This means:", "choices": ["81% of outcomes are predicted perfectly", "81% of variance is explained", "19% of variance is explained", "the model is invalid", "variables are independent"], "correct_option": 1, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "HDATA06", "topic": "percent", "stem": "If revenue grows 20% and costs grow 30%, profit will most likely:", "choices": ["increase", "decrease", "stay the same", "double", "become zero"], "correct_option": 1, "first_step": "Treat the original value as 100 unless a specific number is easier.", "hint_1": "Focus on how the percentage is applied — is it increase, decrease, or part of a whole?", "hint_2": "Convert the percentage into a multiplier (e.g. +20% → ×1.2, -20% → ×0.8).", "hint_3": "Apply each percentage step in order — don’t combine them directly.", "walkthrough_steps": ["Start with an easy base value (like 100).", "Apply the first percentage change.", "Apply the second change to the new value.", "Compare the result with the original."], "method_explanation": ["Percent changes are multiplicative, not additive.", "Each change affects the updated value.", "Using 100 simplifies calculations."], "common_trap": "Adding/subtracting percentages directly instead of applying sequential changes."}
{"question_id": "HDATA07", "topic": "general", "stem": "Which chart best displays the relationship between two quantitative variables?", "choices": ["bar chart", "pie chart", "histogram", "scatter plot", "stacked bar chart"], "correct_option": 3, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "HDATA08", "topic": "ratio", "stem": "If the median is greater than the mean, the distribution is:", "choices": ["symmetric", "uniform", "skewed right", "skewed left", "normal"], "correct_option": 3, "first_step": "Break the ratio into total parts.", "hint_1": "Add the ratio parts together.", "hint_2": "Find the value of one part.", "hint_3": "Scale up to get the required quantity.", "walkthrough_steps": ["Write ratio as parts.", "Sum the parts.", "Divide total by parts.", "Multiply by needed portion."], "method_explanation": ["Ratios represent proportional relationships.", "Breaking into equal units simplifies reasoning."], "common_trap": "Using ratio numbers directly instead of total parts."}
{"question_id": "HDATA09", "topic": "general", "stem": "Which metric best allows comparison across different scales?", "choices": ["raw total", "median", "percentage change", "maximum", "frequency"], "correct_option": 2, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}
{"question_id": "HDATA10", "topic": "general", "stem": "A statistically significant result best supports which conclusion?", "choices": ["Causation is proven", "Results occurred by chance", "There is evidence against the null hypothesis", "The sample is biased", "The model is perfect"], "correct_option": 2, "first_step": "Break the question into known and unknown parts.", "hint_1": "What is being asked?", "hint_2": "What information is given?", "hint_3": "How can you link them mathematically?", "walkthrough_steps": ["Understand the problem.", "Identify variables.", "Set up relationships.", "Solve step by step."], "method_explanation": ["Translate words into math.", "Solve systematically."], "common_trap": "Misinterpreting the question."}