GMAT Flashcards: Quant, Verbal & Data Insights Decisions

300 original flashcards for current-format GMAT Quant, Verbal, and Data Insights concepts, cues, and reusable decisions.

Über dieses Lernkartenset

GMAT Flashcards: Quant, Verbal & Data Insights Decisions

Build quick recall for the current GMAT with 300 original cards across Quantitative Reasoning, Verbal Reasoning, and Data Insights. The deck focuses on reusable concepts and decisions; full-length practice belongs in official or properly licensed question banks.

What the cards map

  • Quant maps numeric forms, terms, rules, and formulas to their meaning, conditions, or use. Short scenarios ask for the operation, equation, or answer check that fits.
  • Verbal maps passage and argument cues to purpose, scope, evidence, inference, reasoning flaws, and evaluation moves.
  • Data Insights maps targets, constraints, source and display cues, metrics, and evidence states to the interpretation or decision they support. It covers Data Sufficiency, Multi-Source Reasoning, Table Analysis, Graphics Interpretation, and Two-Part Analysis.

Learning order

The mixed sequence keeps all three sections in rotation. Quant foundations come before algebra, models, and strategy checks; passage reading comes before argument evaluation; shared data literacy comes before the five Data Insights formats. Closely related prompts are spaced apart so one card does not cue the next.

Current-format boundary

This deck has no geometry lessons or formula drills, Sentence Correction, or the retired Integrated Reasoning section. It also excludes timing, scoring, test-center policy, full passages, large data sets, and response-pattern tricks.

Every card is an original compact concept or decision prompt. No official or competitor questions, answer choices, explanations, mark schemes, curriculum text, logos, or trade dress were copied or adapted. See the official GMAT exam content and Data Insights preparation guidance for the current exam boundary.

This is an independent, unofficial study resource. It is not affiliated with, endorsed by, or sponsored by the Graduate Management Admission Council (GMAC). GMAT is used only to identify the exam.

Karten in diesem Lernkartenset

  1. Karte 1

    Frage

    Which numerator-and-denominator operation creates an equivalent fraction?

    Antwort

    Multiply or divide the numerator and denominator by the same nonzero number. The fraction's value stays unchanged.

  2. Karte 2

    Frage

    What does data sufficiency ask you to determine?

    Antwort

    Whether the information guarantees one answer. You usually don’t need to calculate that answer.

  3. Karte 3

    Frage

    How do you form a passage's main idea?

    Antwort

    Combine the passage's central topic with its main claim about that topic. The answer should cover the whole passage at the right level.

  4. Karte 4

    Frage

    What does multiplying a decimal by 10ⁿ do when n is a positive integer?

    Antwort

    It moves the decimal point n places to the right. Dividing by 10ⁿ moves it n places left.

  5. Karte 5

    Frage

    What makes information sufficient for a value question?

    Antwort

    It forces exactly one value for the target. Different values that satisfy all conditions make it insufficient.

  6. Karte 6

    Frage

    How do you identify the passage's primary purpose?

    Antwort

    Name what the author is doing with the topic: explaining, comparing, challenging, defending, or proposing. Keep content and action together.

  7. Karte 7

    Frage

    How do you find p percent of a quantity q?

    Antwort

    Compute (p/100) × q. Translate “of” as multiplication.

  8. Karte 8

    Frage

    How can two valid cases prove insufficiency?

    Antwort

    Make the cases produce different answers to the question. One clean counterexample pair is enough.

  9. Karte 9

    Frage

    How do you determine a paragraph's role?

    Antwort

    Connect the paragraph to what comes before and after it. Decide whether it introduces, supports, qualifies, contrasts, applies, or concludes the larger discussion.

  10. Karte 10

    Frage

    A total of 45 is split in the ratio 2:3. What are the two parts?

    Antwort

    18 and 27. The five ratio units are worth 45 ÷ 5 = 9 each.

  11. Karte 11

    Frage

    Why can an integer restriction change sufficiency?

    Antwort

    It removes noninteger possibilities. A range containing many real numbers may contain only one integer.

  12. Karte 12

    Frage

    When is a product of signed factors negative?

    Antwort

    Provided no factor is zero, an odd number of negative factors gives a negative product, while an even number gives a positive product. If any factor is zero, the product is zero.

  13. Karte 13

    Frage

    How should two data-sufficiency statements be tested initially?

    Antwort

    Test each statement independently against the stem. Do not carry information from one statement into the other.

  14. Karte 14

    Frage

    What makes an integer greater than 1 prime?

    Antwort

    It has exactly two positive divisors: 1 and itself.

  15. Karte 15

    Frage

    What should you do first on a detail question?

    Antwort

    Return to the relevant lines and read their local context. Memory tends to preserve the topic while blurring qualifications.

  16. Karte 16

    Frage

    What is the divisibility rule for 2?

    Antwort

    The last digit must be even: 0, 2, 4, 6, or 8.

  17. Karte 17

    Frage

    How do you test whether a fact is relevant?

    Antwort

    Connect it to the requested target. A true fact that does not narrow the target adds no decision value.

  18. Karte 18

    Frage

    How far may a reading inference go beyond the text?

    Antwort

    Only as far as the text strongly supports. Prefer the smallest justified step and reject claims needing outside knowledge.

  19. Karte 19

    Frage

    Why is prime factorization useful in GMAT arithmetic?

    Antwort

    It exposes divisibility, factors, greatest common factors, least common multiples, and perfect powers.

  20. Karte 20

    Frage

    What must happen before quantities with different units are combined?

    Antwort

    First confirm that their dimensions are compatible, then convert them to a common unit. Keep the unit attached through the calculation to catch mismatches.

  21. Karte 21

    Frage

    How do you apply a passage principle to a new case?

    Antwort

    Extract the principle's required conditions, then test whether the new case has them. Surface similarity isn't enough.

  22. Karte 22

    Frage

    Which relationship connects distance, rate, and time?

    Antwort

    Distance = rate × time. Rearrange only after the units are compatible.

  23. Karte 23

    Frage

    How do you find a least common multiple from prime factorizations?

    Antwort

    Take every prime that appears, using the largest exponent present.

  24. Karte 24

    Frage

    How do you multiply powers with the same base?

    Antwort

    Add the exponents: aᵐ × aⁿ = aᵐ⁺ⁿ.

  25. Karte 25

    Frage

    How is a weighted average computed?

    Antwort

    Divide the total weighted value by the total weight. For groups, use group size as the weight unless another weight is given.

  26. Karte 26

    Frage

    What should a quick passage map record?

    Antwort

    Each paragraph's role and major viewpoint, plus the passage's overall direction. Record structure, not a sentence-by-sentence summary.

  27. Karte 27

    Frage

    What does the principal square root symbol √x return?

    Antwort

    For real x ≥ 0, it is the nonnegative number whose square is x. For example, √9 = 3, not ±3.

  28. Karte 28

    Frage

    When can bounds replace exact arithmetic?

    Antwort

    When the bounds separate the viable decisions. Stop once every value in the interval leads to the same choice.

  29. Karte 29

    Frage

    How do you keep viewpoints separate?

    Antwort

    Attach each claim to its speaker: author, critic, researcher, or group. Track agreement, disagreement, and any later qualification.

  30. Karte 30

    Frage

    How do “sum,” “product,” and “quotient” translate into algebra?

    Antwort

    They mean addition, multiplication, and division, respectively.

  31. Karte 31

    Frage

    How do you reduce a fraction to lowest terms?

    Antwort

    Divide the numerator and denominator by their greatest common factor.

  32. Karte 32

    Frage

    What evidence should determine the author's tone?

    Antwort

    Evaluative words, qualifications, and the treatment of competing views. Topic alone doesn't establish approval, concern, or skepticism.

  33. Karte 33

    Frage

    When should rounding usually occur?

    Antwort

    At the end, unless estimation already settles the decision. Early rounding can move a result across a cutoff.

  34. Karte 34

    Frage

    How do you convert a terminating decimal to a fraction?

    Antwort

    Write the digits over the matching power of 10, then reduce. For example, 0.375 = 375/1000 = 3/8.

  35. Karte 35

    Frage

    When should you stop calculating in a sufficiency problem?

    Antwort

    As soon as uniqueness is proved or disproved. More arithmetic cannot change the sufficiency decision.

  36. Karte 36

    Frage

    How do you spot an out-of-scope answer?

    Antwort

    It introduces a person, period, cause, or consequence the passage doesn't address. Being reasonable doesn't make it textually supported.

  37. Karte 37

    Frage

    What is the percent-change formula?

    Antwort

    For original > 0, percent change = (new − original) / original × 100%. Percent change from zero is undefined; negative baselines require context-specific interpretation.

  38. Karte 38

    Frage

    What makes information sufficient for a yes-or-no question?

    Antwort

    It forces the same yes-or-no answer in every valid case. The underlying value may still vary.

  39. Karte 39

    Frage

    What preserves a ratio when its quantities are scaled?

    Antwort

    Multiplying or dividing both terms by the same nonzero factor preserves the ratio.

  40. Karte 40

    Frage

    How do you reject a main-idea answer with the wrong scope?

    Antwort

    Compare it with the whole passage. A detail-only answer is too narrow; a claim extending beyond the passage is too broad.

  41. Karte 41

    Frage

    Why should you track whether a variable is positive, negative, or zero?

    Antwort

    Sign controls valid cases and operations. Squaring can hide sign, and division requires a nonzero denominator.

  42. Karte 42

    Frage

    How do you simplify subtraction of a negative number?

    Antwort

    Change it to addition: a − (−b) = a + b.

  43. Karte 43

    Frage

    Whose purpose matters in a primary-purpose question?

    Antwort

    The passage author's purpose. A theory or researcher may be described at length without representing what the author ultimately wants to do.

  44. Karte 44

    Frage

    When is the on-screen calculator most useful?

    Antwort

    For tedious arithmetic after the setup is clear. It does not replace choosing the right relationship or denominator.

  45. Karte 45

    Frage

    In Data Sufficiency, what stem information applies when testing either statement?

    Antwort

    Everything in the question stem. Stem facts remain active for each statement and for the combination.

  46. Karte 46

    Frage

    What is the divisibility rule for 3?

    Antwort

    The sum of the digits must be divisible by 3.

  47. Karte 47

    Frage

    What does a transition paragraph often do?

    Antwort

    It closes one line of thought and sets up the next. Its role depends on both sides, not only on its first sentence.

  48. Karte 48

    Frage

    When is a proxy measure useful?

    Antwort

    When evidence shows it reliably tracks the target for the intended decision. Correlation may support prediction, but it proves neither causation nor suitability on its own.

  49. Karte 49

    Frage

    How do you find a greatest common factor from prime factorizations?

    Antwort

    Take each shared prime to the smaller exponent.

  50. Karte 50

    Frage

    What is the arithmetic mean?

    Antwort

    The sum of the values divided by the number of values.

  51. Karte 51

    Frage

    What units should a rate have?

    Antwort

    One quantity per another, such as kilometers per hour. The denominator tells you what the rate is measured against.

  52. Karte 52

    Frage

    How do you divide powers with the same nonzero base?

    Antwort

    Subtract the exponents: aᵐ ÷ aⁿ = aᵐ⁻ⁿ.

  53. Karte 53

    Frage

    What makes a paraphrase faithful to a passage detail?

    Antwort

    It preserves the original meaning, scope, and certainty in different words. Shared keywords alone don't make it accurate.

  54. Karte 54

    Frage

    How do you recover a total from an average?

    Antwort

    Total = average × number of values.

  55. Karte 55

    Frage

    How do you choose between two plausible reading inferences?

    Antwort

    Choose the one with the tighter textual chain and fewer assumptions. Plausibility in the real world is secondary.

  56. Karte 56

    Frage

    What quick check can catch a calculator-entry error?

    Antwort

    Estimate the order of magnitude and direction first. An exact result far outside that range deserves another look.

  57. Karte 57

    Frage

    How do you simplify a square root with a perfect-square factor?

    Antwort

    Factor out the perfect square. For example, √72 = √(36 × 2) = 6√2.

  58. Karte 58

    Frage

    What makes a new example parallel to one in the passage?

    Antwort

    The same logical relationship. Match cause, contrast, exception, or function rather than shared subject matter.

  59. Karte 59

    Frage

    When can work rates be added?

    Antwort

    Add the stated constant rates when the workers operate simultaneously without interfering with one another. At 1/4 and 1/6 job per hour, together they complete 5/12 job per hour.

  60. Karte 60

    Frage

    What is the denominator in a percent comparison?

    Antwort

    The stated reference value. “A as a percent of B” means A divided by B, then multiplied by 100.

  61. Karte 61

    Frage

    How do you translate “5 less than x”?

    Antwort

    x − 5. The phrase “less than” reverses the spoken order.

  62. Karte 62

    Frage

    In Data Sufficiency, what should you check before testing values?

    Antwort

    The full domain. Honor stated restrictions and implicit ones such as positive lengths or nonzero divisors before judging sufficiency.

  63. Karte 63

    Frage

    How do you add fractions with different denominators?

    Antwort

    Rewrite them with a common denominator, then add the numerators. For example, 2/3 + 1/4 = 8/12 + 3/12 = 11/12.

  64. Karte 64

    Frage

    How do you distinguish description from argument in a passage?

    Antwort

    Description presents what happened or what a view says; argument gives reasons to accept, reject, or revise a claim.

  65. Karte 65

    Frage

    How should you compare decimals with different lengths?

    Antwort

    Append trailing zeros and compare place by place. For example, compare 0.47 with 0.4700, which are equal.

  66. Karte 66

    Frage

    How should combined statements be evaluated?

    Antwort

    Intersect their constraints with the stem. The combination is sufficient only if every remaining case gives one answer.

  67. Karte 67

    Frage

    How do you find common ground between two viewpoints?

    Antwort

    Look for the narrow claim both accept, even if they disagree about its cause, importance, or implications.

  68. Karte 68

    Frage

    How do you solve a proportion such as a/b = c/d?

    Antwort

    Cross-multiply to get ad = bc, provided b and d are nonzero.

  69. Karte 69

    Frage

    How is average speed computed?

    Antwort

    Total distance divided by total time. It is not usually the simple mean of the segment speeds.

  70. Karte 70

    Frage

    What does |x| represent?

    Antwort

    The nonnegative distance from x to 0 on the number line.

  71. Karte 71

    Frage

    Why are strongly emotional tone descriptions often wrong?

    Antwort

    They overstate measured academic prose. Match the answer's intensity to the author's actual language.

  72. Karte 72

    Frage

    What is the divisibility rule for 4?

    Antwort

    The number formed by the last two digits must be divisible by 4.

  73. Karte 73

    Frage

    Can the ordinary percent-change formula be applied directly when the original value is zero or negative?

    Antwort

    No. The ordinary GMAT rule assumes original > 0. Change from zero is undefined, and a negative baseline requires context-specific interpretation.

  74. Karte 74

    Frage

    Why can a true statement still be a wrong answer?

    Antwort

    It may not answer the question asked. Check the task—main idea, detail, inference, role, or purpose—before checking truth.

  75. Karte 75

    Frage

    When must a weighted average lie between its component values?

    Antwort

    When every weight is nonnegative and the total weight is positive. The average then lies between the smallest and largest component values.

  76. Karte 76

    Frage

    How do you express an integer n divided by d with remainder r?

    Antwort

    n = dq + r, where q is an integer and 0 ≤ r < d for positive d.

  77. Karte 77

    Frage

    What does an inequality usually provide?

    Antwort

    A range, not a unique value. It can still be sufficient if the question asks whether a threshold is crossed.

  78. Karte 78

    Frage

    How should you handle an EXCEPT detail prompt?

    Antwort

    Verify four statements against the passage and select the one that isn't supported. Keep the reversed task visible while checking each choice.

  79. Karte 79

    Frage

    How should you set up a unit conversion?

    Antwort

    Multiply by a conversion factor equal to 1, placing units so the unwanted unit cancels.

  80. Karte 80

    Frage

    Can two individually insufficient statements remain insufficient together?

    Antwort

    Yes. They may repeat the same limitation or still leave multiple valid answers.

  81. Karte 81

    Frage

    For a positive base, how do you simplify a power raised to another power?

    Antwort

    Multiply the exponents: (aᵐ)ⁿ = a^(mn).

  82. Karte 82

    Frage

    When can you infer that an author accepts a claim?

    Antwort

    When the author endorses it directly or relies on it without distancing language. Merely reporting another person's view isn't endorsement.

  83. Karte 83

    Frage

    How should successive percentage changes be combined?

    Antwort

    Multiply their factors. A 10% rise followed by a 10% fall gives 1.10 × 0.90 = 0.99, a 1% net fall.

  84. Karte 84

    Frage

    What are compatible numbers in estimation?

    Antwort

    Nearby numbers chosen to make mental arithmetic easy, such as 203 ÷ 9.9 ≈ 200 ÷ 10 = 20.

  85. Karte 85

    Frage

    Which constraints are easy to overlook in a word problem?

    Antwort

    Countability, positivity, distinctness, and capacity limits. Translate each noun and rule into a usable constraint.

  86. Karte 86

    Frage

    How do you state the exact disagreement between two viewpoints?

    Antwort

    Identify one claim that one side accepts and the other rejects. Don't substitute a topic that only one side discusses.

  87. Karte 87

    Frage

    How do you represent three consecutive integers?

    Antwort

    n, n + 1, and n + 2 for an integer n.

  88. Karte 88

    Frage

    How do percentage points differ from percent change?

    Antwort

    Percentage points are the direct difference between percentages. Moving from 20% to 25% is 5 points and a 25% relative increase.

  89. Karte 89

    Frage

    What is a reversed-relationship trap?

    Antwort

    It swaps cause and effect, support and conclusion, or the positions of two viewpoints while reusing familiar passage language.

  90. Karte 90

    Frage

    How do you multiply two fractions?

    Antwort

    Multiply numerator by numerator and denominator by denominator, canceling common factors when convenient.

  91. Karte 91

    Frage

    How do direct and inverse proportion differ?

    Antwort

    Direct: y = kx; inverse: y = k/x for x ≠ 0.

  92. Karte 92

    Frage

    How do you recover an original value after a percentage increase?

    Antwort

    Divide the new value by the growth factor. After a 20% increase, original = new ÷ 1.20.

  93. Karte 93

    Frage

    When should absolute wording raise suspicion?

    Antwort

    When the passage is qualified. Words such as always, never, entirely, and impossible require equally strong textual support.

  94. Karte 94

    Frage

    What should you identify first in Data Sufficiency?

    Antwort

    The exact target and answer type. Decide whether the stem asks for a value, a comparison, or a yes-or-no result.

  95. Karte 95

    Frage

    What ending makes an integer divisible by 5 or by 10?

    Antwort

    A last digit of 0 or 5 gives divisibility by 5; a last digit of 0 gives divisibility by 10.

  96. Karte 96

    Frage

    How should a Data Sufficiency condition be handled?

    Antwort

    Translate it into a precise constraint before testing sufficiency. Keep it separate from the conclusion you want.

  97. Karte 97

    Frage

    How do you reject a half-right answer?

    Antwort

    Test every part of it. One accurate clause can't rescue a second clause that distorts the passage or exceeds its scope.

  98. Karte 98

    Frage

    When you convert a positive measurement to a smaller linear unit, what happens to its numerical value?

    Antwort

    It increases. Multiply by the number of smaller units in one larger unit.

  99. Karte 99

    Frage

    DS example: Is x > 5? Statement: x > 3. Is the statement sufficient?

    Antwort

    No. Both x = 4 and x = 6 satisfy the statement, but they answer the stem differently.

  100. Karte 100

    Frage

    What is a⁰ when a is nonzero?

    Antwort

    1. The nonzero-base condition matters because 0⁰ is not assigned this rule.
  101. Karte 101

    Frage

    Which claim is the argument trying to establish?

    Antwort

    The main conclusion. Find the claim supported by the other statements, then check that it answers the argument's central issue.

  102. Karte 102

    Frage

    When should the two statements be combined?

    Antwort

    When neither statement is sufficient alone. Use both constraints at once and test the remaining possibilities.

  103. Karte 103

    Frage

    A positive number rounds to 8.2 to the nearest tenth. What interval contains it?

    Antwort

    8.15 ≤ x < 8.25. The lower endpoint rounds up to 8.2; the upper endpoint rounds to 8.3.

  104. Karte 104

    Frage

    What should you check when the conclusion changes populations?

    Antwort

    Whether the evidence applies to the new population. Results from volunteers, specialists, or one age group may not transfer to everyone.

  105. Karte 105

    Frage

    How should test values be chosen in Data Sufficiency?

    Antwort

    Choose valid values that probe boundaries, signs, and distinct outcomes. Random easy values can miss the deciding case.

  106. Karte 106

    Frage

    How do you translate “A is 30% more than B”?

    Antwort

    A = 1.30B. The percentage is based on B.

  107. Karte 107

    Frage

    When can one equation involving two variables be sufficient for a target?

    Antwort

    When every valid solution gives the same target value, even if neither variable is unique. For example, x + y = 10 is sufficient to determine x + y.

  108. Karte 108

    Frage

    What does a correlation establish by itself?

    Antwort

    Only that two things vary together. It doesn't establish which one causes the other or whether a third factor causes both.

  109. Karte 109

    Frage

    How do you divide by a nonzero fraction?

    Antwort

    Multiply by its reciprocal. For example, 3/5 ÷ 2/7 = 3/5 × 7/2.

  110. Karte 110

    Frage

    Why is a ratio often insufficient for an absolute value?

    Antwort

    A ratio fixes relative size but usually leaves the scale free. Many proportional pairs can share the same ratio.

  111. Karte 111

    Frage

    What is the divisibility rule for 9?

    Antwort

    The sum of the digits must be divisible by 9.

  112. Karte 112

    Frage

    What matters most when applying a sample result to a population?

    Antwort

    Representativeness. The sample must resemble the target population on traits that could affect the result.

  113. Karte 113

    Frage

    What should you check after solving a squared equation?

    Antwort

    Check every allowed root. If positive and negative roots produce different target answers, the information is insufficient.

  114. Karte 114

    Frage

    What does a negative exponent mean?

    Antwort

    It takes the reciprocal: a⁻ⁿ = 1/aⁿ for nonzero a.

  115. Karte 115

    Frage

    Which baseline makes a comparison informative?

    Antwort

    The baseline relevant to the claim. Compare the outcome with what would otherwise have happened, not merely with an unrelated earlier figure.

  116. Karte 116

    Frage

    What risk appears when an equation factors into multiple branches?

    Antwort

    Each branch may create valid cases. Test all branches against the stem before deciding sufficiency.

  117. Karte 117

    Frage

    How can you compare two positive fractions quickly?

    Antwort

    Compare their cross-products. For a/b and c/d with positive denominators, compare ad with bc.

  118. Karte 118

    Frage

    What may be assumed from a Data Sufficiency diagram?

    Antwort

    Only marked or stated facts. Do not infer scale, equality, perpendicularity, or midpoint status from appearance.

  119. Karte 119

    Frage

    What multiplier represents a p percent increase or decrease?

    Antwort

    Use 1 + p/100 for an increase and 1 − p/100 for a decrease.

  120. Karte 120

    Frage

    Which statements count as evidence?

    Antwort

    The statements offered as reasons to accept another claim. Evidence may be factual or assumed for the argument, even if it isn't proven in real life.

  121. Karte 121

    Frage

    Can a mean determine an individual observation?

    Antwort

    Not by itself. A mean fixes the total, but different sets can have that total unless more constraints apply.

  122. Karte 122

    Frage

    What weakens a move from past evidence to a present claim?

    Antwort

    A relevant change over time. New technology, prices, rules, or behavior can make the earlier evidence a poor guide.

  123. Karte 123

    Frage

    A value becomes 96 after a 20% increase. What was the original value?

    Antwort

    1. Divide the final value by the growth multiplier: 96 ÷ 1.2 = 80.
  124. Karte 124

    Frage

    How do extreme valid cases help in Data Sufficiency?

    Antwort

    They expose whether the target can change. Test the smallest, largest, or boundary cases allowed by the conditions.

  125. Karte 125

    Frage

    How do you test for reverse causation?

    Antwort

    Ask whether the alleged effect could instead cause the alleged cause. Productive teams may meet more because they are productive, not the reverse.

  126. Karte 126

    Frage

    Must a sufficient statement make every variable unique?

    Antwort

    No. It only needs to make the requested target unique, even if other variables remain undetermined.

  127. Karte 127

    Frage

    A price rises 20% and then falls 20%. Does it return to its original value?

    Antwort

    No. The multipliers give 1.20 × 0.80 = 0.96, so the final price is 4% below the original.

  128. Karte 128

    Frage

    Why can a voluntary survey be biased?

    Antwort

    People who choose to respond may differ from those who don't. Strong opinions or extra interest can distort the sample.

  129. Karte 129

    Frage

    How do you expand a(b + c)?

    Antwort

    ab + ac. The outside factor multiplies every term inside the parentheses.

  130. Karte 130

    Frage

    What should the final Data Sufficiency decision describe?

    Antwort

    Which information set guarantees an answer. It should not report the target’s numerical value.

  131. Karte 131

    Frage

    What is the goal when solving a linear equation?

    Antwort

    Isolate the variable by applying equivalent operations to both sides.

  132. Karte 132

    Frage

    DS example: Is integer n even? Statement: n = 7. Is the statement sufficient?

    Antwort

    Yes. It guarantees one answer—no. A statement can be sufficient even when that answer is negative.

  133. Karte 133

    Frage

    When must an inequality sign reverse?

    Antwort

    When both sides are multiplied or divided by a negative number.

  134. Karte 134

    Frage

    What must be checked before comparing two groups?

    Antwort

    Whether they differ in other relevant ways. Age, experience, starting level, or incentives may explain the outcome instead.

  135. Karte 135

    Frage

    When is substitution preferable to elimination in a two-equation system?

    Antwort

    Use substitution when one variable is already isolated or easy to isolate; use elimination when coefficients cancel easily.

  136. Karte 136

    Frage

    What should you build before analyzing Multi-Source Reasoning material?

    Antwort

    A quick source map. Note what each tab or document contains, who produced it, and the relevant date or scope.

  137. Karte 137

    Frage

    How do you separate background from evidence?

    Antwort

    Ask whether the statement supports a claim. Background sets context; evidence does logical work in moving the argument toward a conclusion.

  138. Karte 138

    Frage

    Which algebraic terms can be combined?

    Antwort

    Terms with the same variable part and exponents. For example, 3x² and −5x² combine, but 3x² and 3x do not.

  139. Karte 139

    Frage

    When should you read the Multi-Source Reasoning question?

    Antwort

    Before a deep read of every source. The question tells you which details deserve attention.

  140. Karte 140

    Frage

    What is a reliable first step for an equation containing several fractions?

    Antwort

    Multiply every term by the least common denominator, then solve the simpler equation.

  141. Karte 141

    Frage

    Why does source provenance matter?

    Antwort

    It defines what a claim can support. An internal forecast and an audited result do not carry the same evidentiary weight.

  142. Karte 142

    Frage

    What should you test when evidence comes from a different setting?

    Antwort

    Whether the settings differ in a way that affects the result. A finding from one market, school, or climate may not carry over unchanged.

  143. Karte 143

    Frage

    What does an “and” compound inequality require?

    Antwort

    The overlap of both solution sets. A value must satisfy both conditions.

  144. Karte 144

    Frage

    What should you compare before combining claims from two sources?

    Antwort

    Their population, period, units, and definitions. Matching labels can hide different scopes.

  145. Karte 145

    Frage

    How can a third factor undermine a causal claim?

    Antwort

    It may explain both events, so their correlation no longer establishes a direct causal link by itself. Hot weather can raise both cold-drink sales and pool attendance.

  146. Karte 146

    Frage

    What do one, zero, or infinitely many solutions mean for two linear equations in two variables?

    Antwort

    The lines intersect once, are parallel and distinct, or are the same line, respectively.

  147. Karte 147

    Frage

    How should records from separate sources be linked?

    Antwort

    Use a shared key with the same meaning in both sources, such as product code and month. Do not join on a vague label alone.

  148. Karte 148

    Frage

    How do you factor 6x + 9?

    Antwort

    3(2x + 3). Pull out the greatest common factor.

  149. Karte 149

    Frage

    When does nonresponse threaten a survey result?

    Antwort

    When nonrespondents may answer differently from respondents. A high response count doesn't fix a systematic missing group.

  150. Karte 150

    Frage

    What is the first step when two sources seem inconsistent?

    Antwort

    Compare definitions, dates, units, and aggregation levels. Many apparent conflicts come from mismatched frames.

    Abstract study workspace with blue number blocks, amber argument notes, and teal charts around a central light.

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  151. Karte 151

    Frage

    When can you use the zero-product property?

    Antwort

    After rewriting a product equal to zero. If (x − 2)(x + 5) = 0, then x = 2 or x = −5.

  152. Karte 152

    Frage

    How does an inference differ from a stated fact?

    Antwort

    A fact appears directly in a source; an inference must follow from the sources without an extra assumption.

  153. Karte 153

    Frage

    Does a higher percentage by itself prove a higher count?

    Antwort

    No. The underlying totals matter. Twenty percent of 1,000 is more than fifty percent of 100.

  154. Karte 154

    Frage

    What does an “or” compound inequality require?

    Antwort

    The union of the solution sets. A value may satisfy either condition or both.

  155. Karte 155

    Frage

    What does a blank or omitted value establish?

    Antwort

    Only that the value is not provided. It does not establish zero, no change, or failure.

  156. Karte 156

    Frage

    How do you recognize an intermediate conclusion?

    Antwort

    It is supported by one claim and supports another. It acts as both a conclusion and a premise in the same argument.

  157. Karte 157

    Frage

    What should you do before writing equations for a two-quantity word problem?

    Antwort

    Define each variable with its unit, then translate one independent relationship per equation.

  158. Karte 158

    Frage

    Why should cross-source events be placed in time order?

    Antwort

    Sequence separates prior conditions from later outcomes and prevents using future information as an earlier cause.

  159. Karte 159

    Frage

    When should candidate solutions be checked in the original equation?

    Antwort

    Always after a step that may introduce solutions, especially squaring both sides or clearing variable denominators.

  160. Karte 160

    Frage

    How can switching from one measured outcome to another create a gap?

    Antwort

    Evidence about one metric may not support a conclusion about another. More website visits, for example, don't by themselves mean more sales.

  161. Karte 161

    Frage

    What makes a source relevant to a claim?

    Antwort

    It supplies evidence for a required link in the claim. Related background alone is not enough.

  162. Karte 162

    Frage

    How do you solve a factored polynomial inequality reliably?

    Antwort

    Find the zeros, split the number line into intervals, and test each interval's sign. Include a zero only when equality is allowed.

  163. Karte 163

    Frage

    Does happening first prove causation?

    Antwort

    No. The timing may fit a causal story, but coincidence or another cause can still explain the later event.

  164. Karte 164

    Frage

    How can you spot an unsupported cross-source conclusion?

    Antwort

    Identify the bridge between evidence and conclusion. If the sources never establish that bridge, the conclusion needs an assumption.

  165. Karte 165

    Frage

    What do 0 = 0 and 0 = 5 mean after simplifying an equation?

    Antwort

    0 = 0 means every allowed value is a solution; 0 = 5 means there is no solution.

  166. Karte 166

    Frage

    What should you verify before comparing figures from different sources?

    Antwort

    Common units and denominators. Convert first, then compare the same quantity on the same basis.

  167. Karte 167

    Frage

    How do you interpret |x − a| < r when r is positive?

    Antwort

    x is within r units of a: a − r < x < a + r.

  168. Karte 168

    Frage

    What can a larger sample improve?

    Antwort

    Precision, if the sampling method is sound. A huge biased sample can still give a confidently wrong picture of the population.

  169. Karte 169

    Frage

    How should a cross-source recommendation be evaluated?

    Antwort

    Apply the stated decision rule to the combined evidence. Do not substitute a personal preference for the rule.

  170. Karte 170

    Frage

    If a worker finishes one job in t hours, what is the worker's hourly rate?

    Antwort

    1/t of the job per hour.

  171. Karte 171

    Frage

    What can an average hide?

    Antwort

    The distribution. Two groups can share an average while differing sharply in range, concentration, or the number of extreme values.

  172. Karte 172

    Frage

    What should you confirm before submitting a Multi-Source Reasoning answer?

    Antwort

    That every required part is supported by the correct source and scope. One unsupported component can invalidate the whole decision.

  173. Karte 173

    Frage

    How do you find the amount of a pure component in a mixture?

    Antwort

    Concentration × total mixture amount. A 30% solution with volume 20 contains 0.30 × 20 = 6 units of the component.

  174. Karte 174

    Frage

    What role does a concession usually play?

    Antwort

    It acknowledges a point that weighs against the conclusion, then answers that point or limits its relevance. Don't mistake the conceded claim for the argument's main conclusion.

  175. Karte 175

    Frage

    When can an apparent cross-source discrepancy be resolved?

    Antwort

    When a stated difference in scope or method explains both figures. If no bridge is given, keep the conflict open.

  176. Karte 176

    Frage

    What is the two-set overlap formula?

    Antwort

    In A or B = in A + in B − in both. Subtract the overlap because it was counted twice.

  177. Karte 177

    Frage

    What should you identify first in Table Analysis?

    Antwort

    The row unit, column definitions, and any notes. This establishes what one record and each value represent.

  178. Karte 178

    Frage

    What is the fundamental counting principle?

    Antwort

    Multiply the choices at successive stages when each stage has a fixed number of available choices.

  179. Karte 179

    Frage

    Why distinguish relative change from absolute change?

    Antwort

    Relative change is the percentage change; absolute change is the amount added or lost. A 50% rise from 2 adds 1, while a 10% rise from 1,000 adds 100.

  180. Karte 180

    Frage

    How should a table filter be translated?

    Antwort

    Turn it into an exact inclusion rule. Apply every condition before counting or comparing rows.

  181. Karte 181

    Frage

    For equally likely outcomes, what is the basic probability formula?

    Antwort

    Favorable outcomes divided by total possible outcomes.

  182. Karte 182

    Frage

    What makes a proposed causal mechanism useful?

    Antwort

    It explains how the cause could produce the effect. A plausible, evidence-backed mechanism strengthens the causal link.

  183. Karte 183

    Frage

    How do you find the median?

    Antwort

    Order the values and take the middle value; for an even count, average the two middle values.

  184. Karte 184

    Frage

    How should numeric values be sorted?

    Antwort

    By numerical value, not digit order. For example, 12 comes after 9 in ascending order.

  185. Karte 185

    Frage

    What is missed when evidence includes only successful cases?

    Antwort

    The failures. Studying only surviving firms can make a strategy look safer or more effective than it is.

  186. Karte 186

    Frage

    Two machines have stated constant rates of 1/3 and 1/5 job per hour and operate simultaneously without interference. May their rates be added?

    Antwort

    Yes. The stated rates are constant and the machines do not interfere, so their combined rate is 1/3 + 1/5 = 8/15 job per hour.

  187. Karte 187

    Frage

    How should a table ratio be built when filters are involved?

    Antwort

    Derive the numerator and denominator separately from the question, then apply each filter only where it is relevant. Do not automatically filter both quantities or default to all rows.

  188. Karte 188

    Frage

    What quantity is conserved when two solutions are mixed without loss?

    Antwort

    The amount of the pure component. Set the sum of the starting component amounts equal to the final component amount.

  189. Karte 189

    Frage

    When may table rows be added directly?

    Antwort

    Only when they are disjoint parts of the same measure and use compatible units. Overlapping groups would be double-counted.

  190. Karte 190

    Frage

    What does n! mean for a positive integer n?

    Antwort

    The product of the positive integers from 1 through n.

  191. Karte 191

    Frage

    Where is the argument's logical gap?

    Antwort

    Between the evidence and the conclusion. State what must connect them without merely repeating either side.

  192. Karte 192

    Frage

    How do you find the number in neither of two sets?

    Antwort

    Subtract the number in the union from the total population.

  193. Karte 193

    Frage

    How should rates from table groups be combined?

    Antwort

    Divide the total numerator by the total denominator. Weight a group rate by its group size only when that size is the rate's denominator.

  194. Karte 194

    Frage

    What is wrong with moving from some cases to all cases?

    Antwort

    The conclusion is broader than the evidence. Evidence that some members have a trait doesn't show that every member does.

  195. Karte 195

    Frage

    When should you use a permutation?

    Antwort

    When selecting and arranging items and order matters. The number of ordered selections of r from n distinct items is n!/(n − r)!.

  196. Karte 196

    Frage

    Why does table granularity matter?

    Antwort

    A row-level fact may disappear or change after aggregation. Match the claim to the table’s level of detail.

  197. Karte 197

    Frage

    How do you find the probability that an event does not occur?

    Antwort

    1 − P(event). This is often the quickest route for “at least one” questions.

  198. Karte 198

    Frage

    Why does a comparable control group help test causation?

    Antwort

    It shows what happened without the suspected cause. If the groups differ mainly in that factor, the result is harder to explain another way.

  199. Karte 199

    Frage

    How should missing table entries be treated?

    Antwort

    As unknown unless the notes define another meaning. Exclude or include them only as the question directs.

  200. Karte 200

    Frage

    What is the mode of a data set?

    Antwort

    A mode is any value with the greatest frequency. Under the no-mode convention, there is no mode only when at least two distinct values all have equal frequency.

  201. Karte 201

    Frage

    What makes a table comparison valid?

    Antwort

    The values must have compatible measures, units, periods, populations, and definitions. Normalize only validly convertible differences; reject differences in population, period, or definition that cannot be reconciled.

  202. Karte 202

    Frage

    What should you check when a prediction extends a past pattern?

    Antwort

    Whether the conditions behind the past pattern will continue. A trend alone doesn't show that its causes will remain in place.

  203. Karte 203

    Frage

    How should a drain or other undoing process enter a work-rate equation?

    Antwort

    As a negative rate. Add productive rates and subtract rates that reverse the work.

  204. Karte 204

    Frage

    How can you avoid losing your place while scanning a table?

    Antwort

    Evaluate one condition at a time and mark qualifying rows mentally or on the scratchpad. Count only after the final filter.

  205. Karte 205

    Frage

    Can evidence that an outcome is possible show it is likely?

    Antwort

    No. Possibility only shows that an outcome can occur; probability requires evidence about how likely it is.

  206. Karte 206

    Frage

    What correction is needed when counting the union of three sets?

    Antwort

    Add the three individual counts, subtract all three pairwise overlaps, then add the triple overlap back once.

  207. Karte 207

    Frage

    When does a filtered table support a decision?

    Antwort

    When the qualifying rows satisfy the stated rule. Keep filtering, calculation, and decision as separate steps.

  208. Karte 208

    Frage

    When should you use a combination?

    Antwort

    When selecting items and order does not matter. The number of selections of r from n distinct items is n!/[r!(n − r)!].

  209. Karte 209

    Frage

    What must support a recommendation?

    Antwort

    A link from the proposed action to the stated goal. The argument also needs the action to be feasible and free of costs that defeat the goal.

  210. Karte 210

    Frage

    How do AND and OR change a table filter?

    Antwort

    AND requires every condition; OR requires at least one. Parenthesize mixed rules before scanning rows.

  211. Karte 211

    Frage

    How do you find the probability that independent events both occur?

    Antwort

    Multiply their probabilities: P(A and B) = P(A) × P(B).

  212. Karte 212

    Frage

    What can make an alphabetical sort misleading?

    Antwort

    Labels may contain categories or embedded numbers. Confirm whether the column is text, numeric, or chronological.

  213. Karte 213

    Frage

    What kind of fact most directly strengthens an argument?

    Antwort

    A fact that supports the missing link between evidence and conclusion. Merely repeating a premise adds little.

  214. Karte 214

    Frage

    What is the range of a data set?

    Antwort

    Maximum value minus minimum value.

  215. Karte 215

    Frage

    What should you check at a filter cutoff?

    Antwort

    Whether the boundary is inclusive. “At least 40” includes 40; “more than 40” does not.

  216. Karte 216

    Frage

    A train covers 150 miles in 3 hours at a constant rate. What is its rate?

    Antwort

    50 miles per hour. Rearrange distance = rate × time to get rate = 150 ÷ 3.

  217. Karte 217

    Frage

    What is the most direct way to weaken an argument?

    Antwort

    Undermine a necessary assumption connecting the evidence to the conclusion. The premises can remain true while the conclusion loses support.

  218. Karte 218

    Frage

    What does a tie in the sorted column imply?

    Antwort

    The tied rows share rank on that measure. Their display order does not create a performance difference.

  219. Karte 219

    Frage

    How do you identify a useful evaluation question?

    Antwort

    Test whether opposite answers would push the argument in opposite directions. If both answers leave the conclusion unchanged, the question isn't useful.

  220. Karte 220

    Frage

    What should you identify first in Graphics Interpretation?

    Antwort

    The chart type and what each visual encoding represents. Bars, lines, areas, and points support different readings.

  221. Karte 221

    Frage

    How do repeated identical items affect arrangement counts?

    Antwort

    For n total items, divide n! by the factorial of each repeated count. Identical items do not create new arrangements when swapped.

  222. Karte 222

    Frage

    What should you read before estimating a plotted value?

    Antwort

    Both axis labels, units, and category order. Position has meaning only after the axes are understood.

  223. Karte 223

    Frage

    How do you test whether a statement is a necessary assumption?

    Antwort

    Negate it. If that negation seriously damages the argument, the original statement was necessary.

  224. Karte 224

    Frage

    How do you find the probability that one of two mutually exclusive events occurs?

    Antwort

    Add their probabilities: P(A or B) = P(A) + P(B). Their overlap is zero.

  225. Karte 225

    Frage

    What should you verify in a chart legend?

    Antwort

    Which color, shape, or line maps to each series. Similar styling can otherwise swap the groups in your interpretation.

  226. Karte 226

    Frage

    What does standard deviation measure?

    Antwort

    How spread out values are around the mean. Greater dispersion means a larger standard deviation.

  227. Karte 227

    Frage

    What standard should an inference meet?

    Antwort

    It must follow from the given statements, without extra assumptions. Choose the modest claim the evidence guarantees.

  228. Karte 228

    Frage

    What does a segment’s share depend on?

    Antwort

    The correct whole. A category’s share of one region may differ from its share of the full dataset.

  229. Karte 229

    Frage

    For motion along the same line, when do you add or subtract two speeds to get relative speed?

    Antwort

    Add the speeds for opposite directions; subtract the smaller speed from the larger for the same direction.

  230. Karte 230

    Frage

    What must a paradox explanation accomplish?

    Antwort

    Make both surprising facts plausible at the same time. Rejecting either stated fact doesn't resolve the tension.

  231. Karte 231

    Frage

    How is a segment in a stacked bar measured?

    Antwort

    Subtract its lower boundary from its upper boundary. The upper endpoint alone is cumulative, not the segment value.

  232. Karte 232

    Frage

    Eight students average 70 and twelve students average 80. What is the combined mean?

    Antwort

    1. The group sizes are the weights: (8 × 70 + 12 × 80) ÷ 20 = 76.
  233. Karte 233

    Frage

    What is the difference between a graph’s level and its rate of change?

    Antwort

    Level is the plotted value; rate of change is the slope. A high line can still be falling.

  234. Karte 234

    Frage

    How should you describe a statement's role in an argument?

    Antwort

    Describe what it does, not just what it says. It may support the conclusion, present an objection, answer that objection, or illustrate a principle.

  235. Karte 235

    Frage

    What is P(A given B)?

    Antwort

    P(A and B) / P(B), provided P(B) > 0. Restrict the sample space to outcomes in B.

  236. Karte 236

    Frage

    How should slope be compared across a graph?

    Antwort

    Use change in vertical value divided by change in horizontal value. Visual steepness is reliable only on the same scales.

  237. Karte 237

    Frage

    A driver covers equal distances at 30 mph and 60 mph. Is the average speed 45 mph?

    Antwort

    No. Using 60 miles for each leg gives 120 miles in 3 hours, so the average speed is 40 mph.

  238. Karte 238

    Frage

    What should you identify first when evaluating a plan?

    Antwort

    The plan's exact goal and success measure. A proposal can produce benefits yet still fail its stated objective.

  239. Karte 239

    Frage

    What does a trend in a scatterplot establish?

    Antwort

    An association in the displayed data. It does not by itself establish causation or predict every individual point.

  240. Karte 240

    Frage

    How can you strengthen a causal explanation?

    Antwort

    Rule out a credible alternative cause, support the proposed mechanism, or show the effect changes when the proposed cause changes.

  241. Karte 241

    Frage

    How can an outlier affect a graphical trend?

    Antwort

    It can pull a summary line or average away from the main cluster. Check whether the claim concerns all points or the typical pattern.

  242. Karte 242

    Frage

    Why do probabilities usually change when sampling without replacement?

    Antwort

    The sample space changes after each draw. Update both the favorable count and the total before multiplying conditional probabilities.

  243. Karte 243

    Frage

    One value in an n-value set increases by d. How does the mean change?

    Antwort

    It increases by d/n because the total rises by d while the count stays fixed.

  244. Karte 244

    Frage

    When does a counterexample weaken a claim?

    Antwort

    When the claim requires the counterexample not to exist. One genuine exception can defeat an absolute claim, but may barely affect a modest one.

  245. Karte 245

    Frage

    What is the parity of the sum of two odd integers?

    Antwort

    Even. Each odd integer is one more than an even integer, so the two extra ones add to 2.

  246. Karte 246

    Frage

    What can an aggregate graph hide?

    Antwort

    Differences among subgroups or periods. A stable total can coexist with large offsetting changes inside it.

  247. Karte 247

    Frage

    When is interpolation reasonable on a graph?

    Antwort

    When the graph implies continuity between nearby points. Do not interpolate across separate categories.

  248. Karte 248

    Frage

    What makes information relevant to evaluating an argument?

    Antwort

    It bears on the uncertain link the conclusion depends on. Interesting facts about the topic may still be logically irrelevant.

  249. Karte 249

    Frage

    How precise should a value read from a graph be?

    Antwort

    Only as precise as the scale supports. Use a defensible interval when the mark falls between ticks.

  250. Karte 250

    Frage

    Must a necessary assumption prove the conclusion?

    Antwort

    No. It only has to be required for the argument to work; it need not be enough to establish the conclusion on its own.

  251. Karte 251

    Frage

    How do you multiply positive numbers written in scientific notation?

    Antwort

    Multiply the coefficients, add the powers of 10, then adjust the coefficient to be at least 1 and less than 10.

  252. Karte 252

    Frage

    How should a graph-based decision be made?

    Antwort

    Translate the visual into values or bounds, then apply the stated rule. Do not decide from appearance alone.

  253. Karte 253

    Frage

    When is backsolving from answer choices especially useful?

    Antwort

    When the choices are concrete values and direct algebra is slower than testing them in the original conditions.

  254. Karte 254

    Frage

    How can axis scale distort a visual impression?

    Antwort

    Unequal intervals or a truncated baseline can magnify or compress differences. Use tick values, not apparent distance alone.

  255. Karte 255

    Frage

    When should you combine two statements for an inference?

    Antwort

    When they share a term or relationship that creates a guaranteed consequence. Don't combine them through an unstated causal or statistical link.

  256. Karte 256

    Frage

    When is a product of integers odd?

    Antwort

    Only when every factor is odd. One even factor makes the entire product even.

  257. Karte 257

    Frage

    What often resolves two apparently conflicting results?

    Antwort

    A hidden difference in group, time, measurement, or conditions. The results may describe different slices of the situation.

  258. Karte 258

    Frage

    How should equal distances on a logarithmic axis be interpreted?

    Antwort

    As equal multiplicative changes, not equal absolute changes. Read the labeled values before comparing gaps.

  259. Karte 259

    Frage

    Why start with a middle answer choice when backsolving ordered options?

    Antwort

    Its result often eliminates half the choices at once when the relationship is monotonic.

  260. Karte 260

    Frage

    What makes a Two-Part Analysis response complete?

    Antwort

    Both selections must satisfy their own column prompts under the same stem. Treat the pair as one submitted response.

  261. Karte 261

    Frage

    What is an analogy doing when it supports a claim?

    Antwort

    It argues that because two cases share relevant features, a result or principle from one likely applies to the other.

  262. Karte 262

    Frage

    How do you represent three consecutive odd integers?

    Antwort

    n, n + 2, and n + 4, where n is an odd integer.

  263. Karte 263

    Frage

    What should you identify before solving Two-Part Analysis?

    Antwort

    The role of each column. One may ask for a condition while the other asks for a consequence or decision.

  264. Karte 264

    Frage

    What values should you test first in a claim about an unspecified number?

    Antwort

    Test allowed categories that may behave differently: positive, negative, zero, fractional, and boundary values.

  265. Karte 265

    Frage

    How can an unchanged bottleneck defeat a plan?

    Antwort

    Improving a nonlimiting step won't improve the final outcome if another constraint still controls it. Faster ordering doesn't help when production is already full.

  266. Karte 266

    Frage

    How does the shared stem affect the two parts?

    Antwort

    Its definitions and constraints apply to both. Keep them fixed while testing each column’s requirement.

  267. Karte 267

    Frage

    How do you count the positive divisors of an integer greater than 1 from its prime factorization?

    Antwort

    Add 1 to each prime exponent, then multiply those results.

  268. Karte 268

    Frage

    In Two-Part Analysis, must the two selected entries be the same?

    Antwort

    In the current format, the two selected entries may be the same or different. A linkage in the stem determines whether you must reason through them jointly, not whether their values match.

  269. Karte 269

    Frage

    What makes evidence for a general claim strong?

    Antwort

    It should be relevant and reliable and, if case-based, come from representative cases. More evidence isn't automatically better evidence.

  270. Karte 270

    Frage

    How do you factor a difference of squares?

    Antwort

    Use x² − y² = (x − y)(x + y).

  271. Karte 271

    Frage

    When should the two Two-Part Analysis selections be solved together?

    Antwort

    When one shared relationship constrains both. Test candidate pairs against that relationship instead of solving isolated fragments.

  272. Karte 272

    Frage

    How can one counterexample evaluate a universal claim?

    Antwort

    One valid counterexample disproves a claim that is supposed to hold for every allowed value.

  273. Karte 273

    Frage

    How does an alternative explanation weaken a conclusion?

    Antwort

    It shows that the evidence can be true without the proposed explanation being true. The alternative must account for the same result.

  274. Karte 274

    Frage

    In Two-Part Analysis, how can one column help solve the other?

    Antwort

    A valid selection can narrow the remaining candidates when the parts share a constraint. Recheck the final pair in both columns.

  275. Karte 275

    Frage

    How do you test whether x² + bx + c factors into integer binomials?

    Antwort

    Look for integers r and s with r + s = b and rs = c. If they exist, the factorization is (x + r)(x + s).

  276. Karte 276

    Frage

    Which unknown should you evaluate first in a plan argument?

    Antwort

    A condition that could make the plan achieve or miss its goal. Focus on feasibility, response, costs, and side effects tied to that goal.

  277. Karte 277

    Frage

    How should a trade-off between two measures be evaluated?

    Antwort

    Apply the stated priorities or limits. An option is better only relative to the rule, not because one measure is largest.

  278. Karte 278

    Frage

    How can estimation screen answer choices before exact calculation?

    Antwort

    Approximate the expression's magnitude, then eliminate choices that are far too large or too small.

  279. Karte 279

    Frage

    In a constrained-decision Two-Part Analysis problem, what should you check before comparing candidates?

    Antwort

    Check every hard constraint first. Discard any option that breaks a required limit, then compare only the feasible candidates.

  280. Karte 280

    Frage

    What does a defensive assumption do?

    Antwort

    It rules out a threat that would break the argument. For example, a revenue plan may assume that its added costs won't exceed the new revenue.

  281. Karte 281

    Frage

    What restriction applies when a variable appears in a denominator?

    Antwort

    Exclude every value that makes the denominator zero.

  282. Karte 282

    Frage

    How does an objective differ from a constraint?

    Antwort

    A constraint determines what is allowed; an objective ranks the allowed options. Apply them in that order.

  283. Karte 283

    Frage

    Which quick checks catch many Quant answer errors?

    Antwort

    Check the sign, units, allowed range, and rough size against the question's conditions.

  284. Karte 284

    Frage

    What inference is safe from a statement about most members?

    Antwort

    More than half have the stated trait. You can't infer that all do, that any particular member does, or that most have another trait.

  285. Karte 285

    Frage

    How should a two-part threshold rule be handled?

    Antwort

    Translate each threshold with the correct inequality, including its boundary. Then test both selected values against it.

  286. Karte 286

    Frage

    Where can one negative sign appear in a fraction without changing its value?

    Antwort

    Before the fraction, in the numerator, or in the denominator: −(a/b) = (−a)/b = a/(−b), provided b ≠ 0.

  287. Karte 287

    Frage

    How does an argument choose between competing explanations?

    Antwort

    It presents evidence that one explanation handles better than the others, often by ruling out a rival prediction.

  288. Karte 288

    Frage

    What is an efficient way to handle two linked algebraic targets?

    Antwort

    Express both in terms of one variable or invariant. Evaluate candidate values only after the relationship is clear.

  289. Karte 289

    Frage

    How do you solve x² = c over the real numbers?

    Antwort

    If c > 0, x = ±√c; if c = 0, x = 0; if c < 0, there is no real solution.

  290. Karte 290

    Frage

    What should you check when two selected quantities form a ratio?

    Antwort

    Order and scale. The ratio A:B is not interchangeable with B:A, and proportional pairs may all fit.

  291. Karte 291

    Frage

    How does a positive proper fraction compare with 1?

    Antwort

    It is less than 1 because its numerator is smaller than its denominator.

  292. Karte 292

    Frage

    Which side effects matter when evaluating a plan?

    Antwort

    Effects that change the plan's net result or work against its goal. A small unrelated inconvenience usually doesn't matter.

  293. Karte 293

    Frage

    How should a two-part logical claim be tested?

    Antwort

    Separate the condition from the conclusion, then test whether each selected statement performs the requested role.

  294. Karte 294

    Frage

    What is the solution pattern for |x| = a over the real numbers?

    Antwort

    If a > 0, x = ±a; if a = 0, x = 0; if a < 0, there is no real solution.

  295. Karte 295

    Frage

    What unit check belongs in a two-part quantitative answer?

    Antwort

    Confirm that each selection has the unit requested by its column. Linked values may require different conversions.

  296. Karte 296

    Frage

    Why does user response matter to a plan?

    Antwort

    The plan may depend on people adopting, following, or not avoiding it. Availability alone doesn't guarantee the needed behavior.

  297. Karte 297

    Frage

    A response rate rises from 40% to 50%. What are the percentage-point change and the relative percent increase?

    Antwort

    The increase is 10 percentage points and 25% relative to the original rate: (50 − 40) ÷ 40 = 0.25.

  298. Karte 298

    Frage

    What is the final check for Two-Part Analysis?

    Antwort

    Read each column prompt with its chosen entry, then verify that the pair is jointly consistent with the stem.

  299. Karte 299

    Frage

    For real x and y, what two linear cases are equivalent to x² = y²?

    Antwort

    x = y or x = −y.

  300. Karte 300

    Frage

    How should benefits and costs be compared in a plan argument?

    Antwort

    By their net effect on the stated goal. A plan can create the intended benefit but still fail if its relevant costs are larger.

Abstract study workspace with blue number blocks, amber argument notes, and teal charts around a central light.

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