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

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

What does data sufficiency ask you to determine?

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

How do you form a passage's main idea?

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

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

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

What makes information sufficient for a value question?

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

How do you identify the passage's primary purpose?

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

How do you find p percent of a quantity q?

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

How can two valid cases prove insufficiency?

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

How do you determine a paragraph's role?

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

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

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

Why can an integer restriction change sufficiency?

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

When is a product of signed factors negative?

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.

How should two data-sufficiency statements be tested initially?

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

What makes an integer greater than 1 prime?

It has exactly two positive divisors: 1 and itself.

What should you do first on a detail question?

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

What is the divisibility rule for 2?

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

How do you test whether a fact is relevant?

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

How far may a reading inference go beyond the text?

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

Why is prime factorization useful in GMAT arithmetic?

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

What must happen before quantities with different units are combined?

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

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

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

Which relationship connects distance, rate, and time?

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

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

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

How do you multiply powers with the same base?

Add the exponents: aᵐ × aⁿ = aᵐ⁺ⁿ.

How is a weighted average computed?

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

What should a quick passage map record?

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

What does the principal square root symbol √x return?

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

When can bounds replace exact arithmetic?

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

How do you keep viewpoints separate?

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

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

They mean addition, multiplication, and division, respectively.

How do you reduce a fraction to lowest terms?

Divide the numerator and denominator by their greatest common factor.

What evidence should determine the author's tone?

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

When should rounding usually occur?

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

How do you convert a terminating decimal to a fraction?

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

When should you stop calculating in a sufficiency problem?

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

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

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

What is the percent-change formula?

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

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

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

What preserves a ratio when its quantities are scaled?

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

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

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

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

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

How do you simplify subtraction of a negative number?

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

Whose purpose matters in a primary-purpose question?

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

When is the on-screen calculator most useful?

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

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

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

What is the divisibility rule for 3?

The sum of the digits must be divisible by 3.

What does a transition paragraph often do?

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

When is a proxy measure useful?

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.

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

Take each shared prime to the smaller exponent.

What is the arithmetic mean?

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

What units should a rate have?

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

GMAT Flashcards: Quant, Verbal & Data Insights Decisions

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

Автор Open Study Contributor

Про цю колоду

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.

Картки в цій колоді

Картка 1
Питання
Which numerator-and-denominator operation creates an equivalent fraction?
Відповідь
Multiply or divide the numerator and denominator by the same nonzero number. The fraction's value stays unchanged.
Картка 2
Питання
What does data sufficiency ask you to determine?
Відповідь
Whether the information guarantees one answer. You usually don’t need to calculate that answer.
Картка 3
Питання
How do you form a passage's main idea?
Відповідь
Combine the passage's central topic with its main claim about that topic. The answer should cover the whole passage at the right level.
Картка 4
Питання
What does multiplying a decimal by 10ⁿ do when n is a positive integer?
Відповідь
It moves the decimal point n places to the right. Dividing by 10ⁿ moves it n places left.
Картка 5
Питання
What makes information sufficient for a value question?
Відповідь
It forces exactly one value for the target. Different values that satisfy all conditions make it insufficient.
Картка 6
Питання
How do you identify the passage's primary purpose?
Відповідь
Name what the author is doing with the topic: explaining, comparing, challenging, defending, or proposing. Keep content and action together.
Картка 7
Питання
How do you find p percent of a quantity q?
Відповідь
Compute (p/100) × q. Translate “of” as multiplication.
Картка 8
Питання
How can two valid cases prove insufficiency?
Відповідь
Make the cases produce different answers to the question. One clean counterexample pair is enough.
Картка 9
Питання
How do you determine a paragraph's role?
Відповідь
Connect the paragraph to what comes before and after it. Decide whether it introduces, supports, qualifies, contrasts, applies, or concludes the larger discussion.
Картка 10
Питання
A total of 45 is split in the ratio 2:3. What are the two parts?
Відповідь
18 and 27. The five ratio units are worth 45 ÷ 5 = 9 each.
Картка 11
Питання
Why can an integer restriction change sufficiency?
Відповідь
It removes noninteger possibilities. A range containing many real numbers may contain only one integer.
Картка 12
Питання
When is a product of signed factors negative?
Відповідь
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.
Картка 13
Питання
How should two data-sufficiency statements be tested initially?
Відповідь
Test each statement independently against the stem. Do not carry information from one statement into the other.
Картка 14
Питання
What makes an integer greater than 1 prime?
Відповідь
It has exactly two positive divisors: 1 and itself.
Картка 15
Питання
What should you do first on a detail question?
Відповідь
Return to the relevant lines and read their local context. Memory tends to preserve the topic while blurring qualifications.
Картка 16
Питання
What is the divisibility rule for 2?
Відповідь
The last digit must be even: 0, 2, 4, 6, or 8.
Картка 17
Питання
How do you test whether a fact is relevant?
Відповідь
Connect it to the requested target. A true fact that does not narrow the target adds no decision value.
Картка 18
Питання
How far may a reading inference go beyond the text?
Відповідь
Only as far as the text strongly supports. Prefer the smallest justified step and reject claims needing outside knowledge.
Картка 19
Питання
Why is prime factorization useful in GMAT arithmetic?
Відповідь
It exposes divisibility, factors, greatest common factors, least common multiples, and perfect powers.
Картка 20
Питання
What must happen before quantities with different units are combined?
Відповідь
First confirm that their dimensions are compatible, then convert them to a common unit. Keep the unit attached through the calculation to catch mismatches.
Картка 21
Питання
How do you apply a passage principle to a new case?
Відповідь
Extract the principle's required conditions, then test whether the new case has them. Surface similarity isn't enough.
Картка 22
Питання
Which relationship connects distance, rate, and time?
Відповідь
Distance = rate × time. Rearrange only after the units are compatible.
Картка 23
Питання
How do you find a least common multiple from prime factorizations?
Відповідь
Take every prime that appears, using the largest exponent present.
Картка 24
Питання
How do you multiply powers with the same base?
Відповідь
Add the exponents: aᵐ × aⁿ = aᵐ⁺ⁿ.
Картка 25
Питання
How is a weighted average computed?
Відповідь
Divide the total weighted value by the total weight. For groups, use group size as the weight unless another weight is given.
Картка 26
Питання
What should a quick passage map record?
Відповідь
Each paragraph's role and major viewpoint, plus the passage's overall direction. Record structure, not a sentence-by-sentence summary.
Картка 27
Питання
What does the principal square root symbol √x return?
Відповідь
For real x ≥ 0, it is the nonnegative number whose square is x. For example, √9 = 3, not ±3.
Картка 28
Питання
When can bounds replace exact arithmetic?
Відповідь
When the bounds separate the viable decisions. Stop once every value in the interval leads to the same choice.
Картка 29
Питання
How do you keep viewpoints separate?
Відповідь
Attach each claim to its speaker: author, critic, researcher, or group. Track agreement, disagreement, and any later qualification.
Картка 30
Питання
How do “sum,” “product,” and “quotient” translate into algebra?
Відповідь
They mean addition, multiplication, and division, respectively.
Картка 31
Питання
How do you reduce a fraction to lowest terms?
Відповідь
Divide the numerator and denominator by their greatest common factor.
Картка 32
Питання
What evidence should determine the author's tone?
Відповідь
Evaluative words, qualifications, and the treatment of competing views. Topic alone doesn't establish approval, concern, or skepticism.
Картка 33
Питання
When should rounding usually occur?
Відповідь
At the end, unless estimation already settles the decision. Early rounding can move a result across a cutoff.
Картка 34
Питання
How do you convert a terminating decimal to a fraction?
Відповідь
Write the digits over the matching power of 10, then reduce. For example, 0.375 = 375/1000 = 3/8.
Картка 35
Питання
When should you stop calculating in a sufficiency problem?
Відповідь
As soon as uniqueness is proved or disproved. More arithmetic cannot change the sufficiency decision.
Картка 36
Питання
How do you spot an out-of-scope answer?
Відповідь
It introduces a person, period, cause, or consequence the passage doesn't address. Being reasonable doesn't make it textually supported.
Картка 37
Питання
What is the percent-change formula?
Відповідь
For original > 0, percent change = (new − original) / original × 100%. Percent change from zero is undefined; negative baselines require context-specific interpretation.
Картка 38
Питання
What makes information sufficient for a yes-or-no question?
Відповідь
It forces the same yes-or-no answer in every valid case. The underlying value may still vary.
Картка 39
Питання
What preserves a ratio when its quantities are scaled?
Відповідь
Multiplying or dividing both terms by the same nonzero factor preserves the ratio.
Картка 40
Питання
How do you reject a main-idea answer with the wrong scope?
Відповідь
Compare it with the whole passage. A detail-only answer is too narrow; a claim extending beyond the passage is too broad.
Картка 41
Питання
Why should you track whether a variable is positive, negative, or zero?
Відповідь
Sign controls valid cases and operations. Squaring can hide sign, and division requires a nonzero denominator.
Картка 42
Питання
How do you simplify subtraction of a negative number?
Відповідь
Change it to addition: a − (−b) = a + b.
Картка 43
Питання
Whose purpose matters in a primary-purpose question?
Відповідь
The passage author's purpose. A theory or researcher may be described at length without representing what the author ultimately wants to do.
Картка 44
Питання
When is the on-screen calculator most useful?
Відповідь
For tedious arithmetic after the setup is clear. It does not replace choosing the right relationship or denominator.
Картка 45
Питання
In Data Sufficiency, what stem information applies when testing either statement?
Відповідь
Everything in the question stem. Stem facts remain active for each statement and for the combination.
Картка 46
Питання
What is the divisibility rule for 3?
Відповідь
The sum of the digits must be divisible by 3.
Картка 47
Питання
What does a transition paragraph often do?
Відповідь
It closes one line of thought and sets up the next. Its role depends on both sides, not only on its first sentence.
Картка 48
Питання
When is a proxy measure useful?
Відповідь
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.
Картка 49
Питання
How do you find a greatest common factor from prime factorizations?
Відповідь
Take each shared prime to the smaller exponent.
Картка 50
Питання
What is the arithmetic mean?
Відповідь
The sum of the values divided by the number of values.
Картка 51
Питання
What units should a rate have?
Відповідь
One quantity per another, such as kilometers per hour. The denominator tells you what the rate is measured against.
Картка 52
Питання
How do you divide powers with the same nonzero base?
Відповідь
Subtract the exponents: aᵐ ÷ aⁿ = aᵐ⁻ⁿ.
Картка 53
Питання
What makes a paraphrase faithful to a passage detail?
Відповідь
It preserves the original meaning, scope, and certainty in different words. Shared keywords alone don't make it accurate.
Картка 54
Питання
How do you recover a total from an average?
Відповідь
Total = average × number of values.
Картка 55
Питання
How do you choose between two plausible reading inferences?
Відповідь
Choose the one with the tighter textual chain and fewer assumptions. Plausibility in the real world is secondary.
Картка 56
Питання
What quick check can catch a calculator-entry error?
Відповідь
Estimate the order of magnitude and direction first. An exact result far outside that range deserves another look.
Картка 57
Питання
How do you simplify a square root with a perfect-square factor?
Відповідь
Factor out the perfect square. For example, √72 = √(36 × 2) = 6√2.
Картка 58
Питання
What makes a new example parallel to one in the passage?
Відповідь
The same logical relationship. Match cause, contrast, exception, or function rather than shared subject matter.
Картка 59
Питання
When can work rates be added?
Відповідь
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.
Картка 60
Питання
What is the denominator in a percent comparison?
Відповідь
The stated reference value. “A as a percent of B” means A divided by B, then multiplied by 100.
Картка 61
Питання
How do you translate “5 less than x”?
Відповідь
x − 5. The phrase “less than” reverses the spoken order.
Картка 62
Питання
In Data Sufficiency, what should you check before testing values?
Відповідь
The full domain. Honor stated restrictions and implicit ones such as positive lengths or nonzero divisors before judging sufficiency.
Картка 63
Питання
How do you add fractions with different denominators?
Відповідь
Rewrite them with a common denominator, then add the numerators. For example, 2/3 + 1/4 = 8/12 + 3/12 = 11/12.
Картка 64
Питання
How do you distinguish description from argument in a passage?
Відповідь
Description presents what happened or what a view says; argument gives reasons to accept, reject, or revise a claim.
Картка 65
Питання
How should you compare decimals with different lengths?
Відповідь
Append trailing zeros and compare place by place. For example, compare 0.47 with 0.4700, which are equal.
Картка 66
Питання
How should combined statements be evaluated?
Відповідь
Intersect their constraints with the stem. The combination is sufficient only if every remaining case gives one answer.
Картка 67
Питання
How do you find common ground between two viewpoints?
Відповідь
Look for the narrow claim both accept, even if they disagree about its cause, importance, or implications.
Картка 68
Питання
How do you solve a proportion such as a/b = c/d?
Відповідь
Cross-multiply to get ad = bc, provided b and d are nonzero.
Картка 69
Питання
How is average speed computed?
Відповідь
Total distance divided by total time. It is not usually the simple mean of the segment speeds.
Картка 70
Питання
What does |x| represent?
Відповідь
The nonnegative distance from x to 0 on the number line.
Картка 71
Питання
Why are strongly emotional tone descriptions often wrong?
Відповідь
They overstate measured academic prose. Match the answer's intensity to the author's actual language.
Картка 72
Питання
What is the divisibility rule for 4?
Відповідь
The number formed by the last two digits must be divisible by 4.
Картка 73
Питання
Can the ordinary percent-change formula be applied directly when the original value is zero or negative?
Відповідь
No. The ordinary GMAT rule assumes original > 0. Change from zero is undefined, and a negative baseline requires context-specific interpretation.
Картка 74
Питання
Why can a true statement still be a wrong answer?
Відповідь
It may not answer the question asked. Check the task—main idea, detail, inference, role, or purpose—before checking truth.
Картка 75
Питання
When must a weighted average lie between its component values?
Відповідь
When every weight is nonnegative and the total weight is positive. The average then lies between the smallest and largest component values.
Картка 76
Питання
How do you express an integer n divided by d with remainder r?
Відповідь
n = dq + r, where q is an integer and 0 ≤ r < d for positive d.
Картка 77
Питання
What does an inequality usually provide?
Відповідь
A range, not a unique value. It can still be sufficient if the question asks whether a threshold is crossed.
Картка 78
Питання
How should you handle an EXCEPT detail prompt?
Відповідь
Verify four statements against the passage and select the one that isn't supported. Keep the reversed task visible while checking each choice.
Картка 79
Питання
How should you set up a unit conversion?
Відповідь
Multiply by a conversion factor equal to 1, placing units so the unwanted unit cancels.
Картка 80
Питання
Can two individually insufficient statements remain insufficient together?
Відповідь
Yes. They may repeat the same limitation or still leave multiple valid answers.
Картка 81
Питання
For a positive base, how do you simplify a power raised to another power?
Відповідь
Multiply the exponents: (aᵐ)ⁿ = a^(mn).
Картка 82
Питання
When can you infer that an author accepts a claim?
Відповідь
When the author endorses it directly or relies on it without distancing language. Merely reporting another person's view isn't endorsement.
Картка 83
Питання
How should successive percentage changes be combined?
Відповідь
Multiply their factors. A 10% rise followed by a 10% fall gives 1.10 × 0.90 = 0.99, a 1% net fall.
Картка 84
Питання
What are compatible numbers in estimation?
Відповідь
Nearby numbers chosen to make mental arithmetic easy, such as 203 ÷ 9.9 ≈ 200 ÷ 10 = 20.
Картка 85
Питання
Which constraints are easy to overlook in a word problem?
Відповідь
Countability, positivity, distinctness, and capacity limits. Translate each noun and rule into a usable constraint.
Картка 86
Питання
How do you state the exact disagreement between two viewpoints?
Відповідь
Identify one claim that one side accepts and the other rejects. Don't substitute a topic that only one side discusses.
Картка 87
Питання
How do you represent three consecutive integers?
Відповідь
n, n + 1, and n + 2 for an integer n.
Картка 88
Питання
How do percentage points differ from percent change?
Відповідь
Percentage points are the direct difference between percentages. Moving from 20% to 25% is 5 points and a 25% relative increase.
Картка 89
Питання
What is a reversed-relationship trap?
Відповідь
It swaps cause and effect, support and conclusion, or the positions of two viewpoints while reusing familiar passage language.
Картка 90
Питання
How do you multiply two fractions?
Відповідь
Multiply numerator by numerator and denominator by denominator, canceling common factors when convenient.
Картка 91
Питання
How do direct and inverse proportion differ?
Відповідь
Direct: y = kx; inverse: y = k/x for x ≠ 0.
Картка 92
Питання
How do you recover an original value after a percentage increase?
Відповідь
Divide the new value by the growth factor. After a 20% increase, original = new ÷ 1.20.
Картка 93
Питання
When should absolute wording raise suspicion?
Відповідь
When the passage is qualified. Words such as always, never, entirely, and impossible require equally strong textual support.
Картка 94
Питання
What should you identify first in Data Sufficiency?
Відповідь
The exact target and answer type. Decide whether the stem asks for a value, a comparison, or a yes-or-no result.
Картка 95
Питання
What ending makes an integer divisible by 5 or by 10?
Відповідь
A last digit of 0 or 5 gives divisibility by 5; a last digit of 0 gives divisibility by 10.
Картка 96
Питання
How should a Data Sufficiency condition be handled?
Відповідь
Translate it into a precise constraint before testing sufficiency. Keep it separate from the conclusion you want.
Картка 97
Питання
How do you reject a half-right answer?
Відповідь
Test every part of it. One accurate clause can't rescue a second clause that distorts the passage or exceeds its scope.
Картка 98
Питання
When you convert a positive measurement to a smaller linear unit, what happens to its numerical value?
Відповідь
It increases. Multiply by the number of smaller units in one larger unit.
Картка 99
Питання
DS example: Is x > 5? Statement: x > 3. Is the statement sufficient?
Відповідь
No. Both x = 4 and x = 6 satisfy the statement, but they answer the stem differently.
Картка 100
Питання
What is a⁰ when a is nonzero?
Відповідь
The nonzero-base condition matters because 0⁰ is not assigned this rule.
Картка 101
Питання
Which claim is the argument trying to establish?
Відповідь
The main conclusion. Find the claim supported by the other statements, then check that it answers the argument's central issue.
Картка 102
Питання
When should the two statements be combined?
Відповідь
When neither statement is sufficient alone. Use both constraints at once and test the remaining possibilities.
Картка 103
Питання
A positive number rounds to 8.2 to the nearest tenth. What interval contains it?
Відповідь
8.15 ≤ x < 8.25. The lower endpoint rounds up to 8.2; the upper endpoint rounds to 8.3.
Картка 104
Питання
What should you check when the conclusion changes populations?
Відповідь
Whether the evidence applies to the new population. Results from volunteers, specialists, or one age group may not transfer to everyone.
Картка 105
Питання
How should test values be chosen in Data Sufficiency?
Відповідь
Choose valid values that probe boundaries, signs, and distinct outcomes. Random easy values can miss the deciding case.
Картка 106
Питання
How do you translate “A is 30% more than B”?
Відповідь
A = 1.30B. The percentage is based on B.
Картка 107
Питання
When can one equation involving two variables be sufficient for a target?
Відповідь
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.
Картка 108
Питання
What does a correlation establish by itself?
Відповідь
Only that two things vary together. It doesn't establish which one causes the other or whether a third factor causes both.
Картка 109
Питання
How do you divide by a nonzero fraction?
Відповідь
Multiply by its reciprocal. For example, 3/5 ÷ 2/7 = 3/5 × 7/2.
Картка 110
Питання
Why is a ratio often insufficient for an absolute value?
Відповідь
A ratio fixes relative size but usually leaves the scale free. Many proportional pairs can share the same ratio.
Картка 111
Питання
What is the divisibility rule for 9?
Відповідь
The sum of the digits must be divisible by 9.
Картка 112
Питання
What matters most when applying a sample result to a population?
Відповідь
Representativeness. The sample must resemble the target population on traits that could affect the result.
Картка 113
Питання
What should you check after solving a squared equation?
Відповідь
Check every allowed root. If positive and negative roots produce different target answers, the information is insufficient.
Картка 114
Питання
What does a negative exponent mean?
Відповідь
It takes the reciprocal: a⁻ⁿ = 1/aⁿ for nonzero a.
Картка 115
Питання
Which baseline makes a comparison informative?
Відповідь
The baseline relevant to the claim. Compare the outcome with what would otherwise have happened, not merely with an unrelated earlier figure.
Картка 116
Питання
What risk appears when an equation factors into multiple branches?
Відповідь
Each branch may create valid cases. Test all branches against the stem before deciding sufficiency.
Картка 117
Питання
How can you compare two positive fractions quickly?
Відповідь
Compare their cross-products. For a/b and c/d with positive denominators, compare ad with bc.
Картка 118
Питання
What may be assumed from a Data Sufficiency diagram?
Відповідь
Only marked or stated facts. Do not infer scale, equality, perpendicularity, or midpoint status from appearance.
Картка 119
Питання
What multiplier represents a p percent increase or decrease?
Відповідь
Use 1 + p/100 for an increase and 1 − p/100 for a decrease.
Картка 120
Питання
Which statements count as evidence?
Відповідь
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.
Картка 121
Питання
Can a mean determine an individual observation?
Відповідь
Not by itself. A mean fixes the total, but different sets can have that total unless more constraints apply.
Картка 122
Питання
What weakens a move from past evidence to a present claim?
Відповідь
A relevant change over time. New technology, prices, rules, or behavior can make the earlier evidence a poor guide.
Картка 123
Питання
A value becomes 96 after a 20% increase. What was the original value?
Відповідь
Divide the final value by the growth multiplier: 96 ÷ 1.2 = 80.
Картка 124
Питання
How do extreme valid cases help in Data Sufficiency?
Відповідь
They expose whether the target can change. Test the smallest, largest, or boundary cases allowed by the conditions.
Картка 125
Питання
How do you test for reverse causation?
Відповідь
Ask whether the alleged effect could instead cause the alleged cause. Productive teams may meet more because they are productive, not the reverse.
Картка 126
Питання
Must a sufficient statement make every variable unique?
Відповідь
No. It only needs to make the requested target unique, even if other variables remain undetermined.
Картка 127
Питання
A price rises 20% and then falls 20%. Does it return to its original value?
Відповідь
No. The multipliers give 1.20 × 0.80 = 0.96, so the final price is 4% below the original.
Картка 128
Питання
Why can a voluntary survey be biased?
Відповідь
People who choose to respond may differ from those who don't. Strong opinions or extra interest can distort the sample.
Картка 129
Питання
How do you expand a(b + c)?
Відповідь
ab + ac. The outside factor multiplies every term inside the parentheses.
Картка 130
Питання
What should the final Data Sufficiency decision describe?
Відповідь
Which information set guarantees an answer. It should not report the target’s numerical value.
Картка 131
Питання
What is the goal when solving a linear equation?
Відповідь
Isolate the variable by applying equivalent operations to both sides.
Картка 132
Питання
DS example: Is integer n even? Statement: n = 7. Is the statement sufficient?
Відповідь
Yes. It guarantees one answer—no. A statement can be sufficient even when that answer is negative.
Картка 133
Питання
When must an inequality sign reverse?
Відповідь
When both sides are multiplied or divided by a negative number.
Картка 134
Питання
What must be checked before comparing two groups?
Відповідь
Whether they differ in other relevant ways. Age, experience, starting level, or incentives may explain the outcome instead.
Картка 135
Питання
When is substitution preferable to elimination in a two-equation system?
Відповідь
Use substitution when one variable is already isolated or easy to isolate; use elimination when coefficients cancel easily.
Картка 136
Питання
What should you build before analyzing Multi-Source Reasoning material?
Відповідь
A quick source map. Note what each tab or document contains, who produced it, and the relevant date or scope.
Картка 137
Питання
How do you separate background from evidence?
Відповідь
Ask whether the statement supports a claim. Background sets context; evidence does logical work in moving the argument toward a conclusion.
Картка 138
Питання
Which algebraic terms can be combined?
Відповідь
Terms with the same variable part and exponents. For example, 3x² and −5x² combine, but 3x² and 3x do not.
Картка 139
Питання
When should you read the Multi-Source Reasoning question?
Відповідь
Before a deep read of every source. The question tells you which details deserve attention.
Картка 140
Питання
What is a reliable first step for an equation containing several fractions?
Відповідь
Multiply every term by the least common denominator, then solve the simpler equation.
Картка 141
Питання
Why does source provenance matter?
Відповідь
It defines what a claim can support. An internal forecast and an audited result do not carry the same evidentiary weight.
Картка 142
Питання
What should you test when evidence comes from a different setting?
Відповідь
Whether the settings differ in a way that affects the result. A finding from one market, school, or climate may not carry over unchanged.
Картка 143
Питання
What does an “and” compound inequality require?
Відповідь
The overlap of both solution sets. A value must satisfy both conditions.
Картка 144
Питання
What should you compare before combining claims from two sources?
Відповідь
Their population, period, units, and definitions. Matching labels can hide different scopes.
Картка 145
Питання
How can a third factor undermine a causal claim?
Відповідь
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.
Картка 146
Питання
What do one, zero, or infinitely many solutions mean for two linear equations in two variables?
Відповідь
The lines intersect once, are parallel and distinct, or are the same line, respectively.
Картка 147
Питання
How should records from separate sources be linked?
Відповідь
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.
Картка 148
Питання
How do you factor 6x + 9?
Відповідь
3(2x + 3). Pull out the greatest common factor.
Картка 149
Питання
When does nonresponse threaten a survey result?
Відповідь
When nonrespondents may answer differently from respondents. A high response count doesn't fix a systematic missing group.
Картка 150
Питання
What is the first step when two sources seem inconsistent?
Відповідь
Compare definitions, dates, units, and aggregation levels. Many apparent conflicts come from mismatched frames.
300 карток
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Картка 151
Питання
When can you use the zero-product property?
Відповідь
After rewriting a product equal to zero. If (x − 2)(x + 5) = 0, then x = 2 or x = −5.
Картка 152
Питання
How does an inference differ from a stated fact?
Відповідь
A fact appears directly in a source; an inference must follow from the sources without an extra assumption.
Картка 153
Питання
Does a higher percentage by itself prove a higher count?
Відповідь
No. The underlying totals matter. Twenty percent of 1,000 is more than fifty percent of 100.
Картка 154
Питання
What does an “or” compound inequality require?
Відповідь
The union of the solution sets. A value may satisfy either condition or both.
Картка 155
Питання
What does a blank or omitted value establish?
Відповідь
Only that the value is not provided. It does not establish zero, no change, or failure.
Картка 156
Питання
How do you recognize an intermediate conclusion?
Відповідь
It is supported by one claim and supports another. It acts as both a conclusion and a premise in the same argument.
Картка 157
Питання
What should you do before writing equations for a two-quantity word problem?
Відповідь
Define each variable with its unit, then translate one independent relationship per equation.
Картка 158
Питання
Why should cross-source events be placed in time order?
Відповідь
Sequence separates prior conditions from later outcomes and prevents using future information as an earlier cause.
Картка 159
Питання
When should candidate solutions be checked in the original equation?
Відповідь
Always after a step that may introduce solutions, especially squaring both sides or clearing variable denominators.
Картка 160
Питання
How can switching from one measured outcome to another create a gap?
Відповідь
Evidence about one metric may not support a conclusion about another. More website visits, for example, don't by themselves mean more sales.
Картка 161
Питання
What makes a source relevant to a claim?
Відповідь
It supplies evidence for a required link in the claim. Related background alone is not enough.
Картка 162
Питання
How do you solve a factored polynomial inequality reliably?
Відповідь
Find the zeros, split the number line into intervals, and test each interval's sign. Include a zero only when equality is allowed.
Картка 163
Питання
Does happening first prove causation?
Відповідь
No. The timing may fit a causal story, but coincidence or another cause can still explain the later event.
Картка 164
Питання
How can you spot an unsupported cross-source conclusion?
Відповідь
Identify the bridge between evidence and conclusion. If the sources never establish that bridge, the conclusion needs an assumption.
Картка 165
Питання
What do 0 = 0 and 0 = 5 mean after simplifying an equation?
Відповідь
0 = 0 means every allowed value is a solution; 0 = 5 means there is no solution.
Картка 166
Питання
What should you verify before comparing figures from different sources?
Відповідь
Common units and denominators. Convert first, then compare the same quantity on the same basis.
Картка 167
Питання
How do you interpret |x − a| < r when r is positive?
Відповідь
x is within r units of a: a − r < x < a + r.
Картка 168
Питання
What can a larger sample improve?
Відповідь
Precision, if the sampling method is sound. A huge biased sample can still give a confidently wrong picture of the population.
Картка 169
Питання
How should a cross-source recommendation be evaluated?
Відповідь
Apply the stated decision rule to the combined evidence. Do not substitute a personal preference for the rule.
Картка 170
Питання
If a worker finishes one job in t hours, what is the worker's hourly rate?
Відповідь
1/t of the job per hour.
Картка 171
Питання
What can an average hide?
Відповідь
The distribution. Two groups can share an average while differing sharply in range, concentration, or the number of extreme values.
Картка 172
Питання
What should you confirm before submitting a Multi-Source Reasoning answer?
Відповідь
That every required part is supported by the correct source and scope. One unsupported component can invalidate the whole decision.
Картка 173
Питання
How do you find the amount of a pure component in a mixture?
Відповідь
Concentration × total mixture amount. A 30% solution with volume 20 contains 0.30 × 20 = 6 units of the component.
Картка 174
Питання
What role does a concession usually play?
Відповідь
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.
Картка 175
Питання
When can an apparent cross-source discrepancy be resolved?
Відповідь
When a stated difference in scope or method explains both figures. If no bridge is given, keep the conflict open.
Картка 176
Питання
What is the two-set overlap formula?
Відповідь
In A or B = in A + in B − in both. Subtract the overlap because it was counted twice.
Картка 177
Питання
What should you identify first in Table Analysis?
Відповідь
The row unit, column definitions, and any notes. This establishes what one record and each value represent.
Картка 178
Питання
What is the fundamental counting principle?
Відповідь
Multiply the choices at successive stages when each stage has a fixed number of available choices.
Картка 179
Питання
Why distinguish relative change from absolute change?
Відповідь
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.
Картка 180
Питання
How should a table filter be translated?
Відповідь
Turn it into an exact inclusion rule. Apply every condition before counting or comparing rows.
Картка 181
Питання
For equally likely outcomes, what is the basic probability formula?
Відповідь
Favorable outcomes divided by total possible outcomes.
Картка 182
Питання
What makes a proposed causal mechanism useful?
Відповідь
It explains how the cause could produce the effect. A plausible, evidence-backed mechanism strengthens the causal link.
Картка 183
Питання
How do you find the median?
Відповідь
Order the values and take the middle value; for an even count, average the two middle values.
Картка 184
Питання
How should numeric values be sorted?
Відповідь
By numerical value, not digit order. For example, 12 comes after 9 in ascending order.
Картка 185
Питання
What is missed when evidence includes only successful cases?
Відповідь
The failures. Studying only surviving firms can make a strategy look safer or more effective than it is.
Картка 186
Питання
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?
Відповідь
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.
Картка 187
Питання
How should a table ratio be built when filters are involved?
Відповідь
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.
Картка 188
Питання
What quantity is conserved when two solutions are mixed without loss?
Відповідь
The amount of the pure component. Set the sum of the starting component amounts equal to the final component amount.
Картка 189
Питання
When may table rows be added directly?
Відповідь
Only when they are disjoint parts of the same measure and use compatible units. Overlapping groups would be double-counted.
Картка 190
Питання
What does n! mean for a positive integer n?
Відповідь
The product of the positive integers from 1 through n.
Картка 191
Питання
Where is the argument's logical gap?
Відповідь
Between the evidence and the conclusion. State what must connect them without merely repeating either side.
Картка 192
Питання
How do you find the number in neither of two sets?
Відповідь
Subtract the number in the union from the total population.
Картка 193
Питання
How should rates from table groups be combined?
Відповідь
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.
Картка 194
Питання
What is wrong with moving from some cases to all cases?
Відповідь
The conclusion is broader than the evidence. Evidence that some members have a trait doesn't show that every member does.
Картка 195
Питання
When should you use a permutation?
Відповідь
When selecting and arranging items and order matters. The number of ordered selections of r from n distinct items is n!/(n − r)!.
Картка 196
Питання
Why does table granularity matter?
Відповідь
A row-level fact may disappear or change after aggregation. Match the claim to the table’s level of detail.
Картка 197
Питання
How do you find the probability that an event does not occur?
Відповідь
1 − P(event). This is often the quickest route for “at least one” questions.
Картка 198
Питання
Why does a comparable control group help test causation?
Відповідь
It shows what happened without the suspected cause. If the groups differ mainly in that factor, the result is harder to explain another way.
Картка 199
Питання
How should missing table entries be treated?
Відповідь
As unknown unless the notes define another meaning. Exclude or include them only as the question directs.
Картка 200
Питання
What is the mode of a data set?
Відповідь
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.
Картка 201
Питання
What makes a table comparison valid?
Відповідь
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.
Картка 202
Питання
What should you check when a prediction extends a past pattern?
Відповідь
Whether the conditions behind the past pattern will continue. A trend alone doesn't show that its causes will remain in place.
Картка 203
Питання
How should a drain or other undoing process enter a work-rate equation?
Відповідь
As a negative rate. Add productive rates and subtract rates that reverse the work.
Картка 204
Питання
How can you avoid losing your place while scanning a table?
Відповідь
Evaluate one condition at a time and mark qualifying rows mentally or on the scratchpad. Count only after the final filter.
Картка 205
Питання
Can evidence that an outcome is possible show it is likely?
Відповідь
No. Possibility only shows that an outcome can occur; probability requires evidence about how likely it is.
Картка 206
Питання
What correction is needed when counting the union of three sets?
Відповідь
Add the three individual counts, subtract all three pairwise overlaps, then add the triple overlap back once.
Картка 207
Питання
When does a filtered table support a decision?
Відповідь
When the qualifying rows satisfy the stated rule. Keep filtering, calculation, and decision as separate steps.
Картка 208
Питання
When should you use a combination?
Відповідь
When selecting items and order does not matter. The number of selections of r from n distinct items is n!/[r!(n − r)!].
Картка 209
Питання
What must support a recommendation?
Відповідь
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.
Картка 210
Питання
How do AND and OR change a table filter?
Відповідь
AND requires every condition; OR requires at least one. Parenthesize mixed rules before scanning rows.
Картка 211
Питання
How do you find the probability that independent events both occur?
Відповідь
Multiply their probabilities: P(A and B) = P(A) × P(B).
Картка 212
Питання
What can make an alphabetical sort misleading?
Відповідь
Labels may contain categories or embedded numbers. Confirm whether the column is text, numeric, or chronological.
Картка 213
Питання
What kind of fact most directly strengthens an argument?
Відповідь
A fact that supports the missing link between evidence and conclusion. Merely repeating a premise adds little.
Картка 214
Питання
What is the range of a data set?
Відповідь
Maximum value minus minimum value.
Картка 215
Питання
What should you check at a filter cutoff?
Відповідь
Whether the boundary is inclusive. “At least 40” includes 40; “more than 40” does not.
Картка 216
Питання
A train covers 150 miles in 3 hours at a constant rate. What is its rate?
Відповідь
50 miles per hour. Rearrange distance = rate × time to get rate = 150 ÷ 3.
Картка 217
Питання
What is the most direct way to weaken an argument?
Відповідь
Undermine a necessary assumption connecting the evidence to the conclusion. The premises can remain true while the conclusion loses support.
Картка 218
Питання
What does a tie in the sorted column imply?
Відповідь
The tied rows share rank on that measure. Their display order does not create a performance difference.
Картка 219
Питання
How do you identify a useful evaluation question?
Відповідь
Test whether opposite answers would push the argument in opposite directions. If both answers leave the conclusion unchanged, the question isn't useful.
Картка 220
Питання
What should you identify first in Graphics Interpretation?
Відповідь
The chart type and what each visual encoding represents. Bars, lines, areas, and points support different readings.
Картка 221
Питання
How do repeated identical items affect arrangement counts?
Відповідь
For n total items, divide n! by the factorial of each repeated count. Identical items do not create new arrangements when swapped.
Картка 222
Питання
What should you read before estimating a plotted value?
Відповідь
Both axis labels, units, and category order. Position has meaning only after the axes are understood.
Картка 223
Питання
How do you test whether a statement is a necessary assumption?
Відповідь
Negate it. If that negation seriously damages the argument, the original statement was necessary.
Картка 224
Питання
How do you find the probability that one of two mutually exclusive events occurs?
Відповідь
Add their probabilities: P(A or B) = P(A) + P(B). Their overlap is zero.
Картка 225
Питання
What should you verify in a chart legend?
Відповідь
Which color, shape, or line maps to each series. Similar styling can otherwise swap the groups in your interpretation.
Картка 226
Питання
What does standard deviation measure?
Відповідь
How spread out values are around the mean. Greater dispersion means a larger standard deviation.
Картка 227
Питання
What standard should an inference meet?
Відповідь
It must follow from the given statements, without extra assumptions. Choose the modest claim the evidence guarantees.
Картка 228
Питання
What does a segment’s share depend on?
Відповідь
The correct whole. A category’s share of one region may differ from its share of the full dataset.
Картка 229
Питання
For motion along the same line, when do you add or subtract two speeds to get relative speed?
Відповідь
Add the speeds for opposite directions; subtract the smaller speed from the larger for the same direction.
Картка 230
Питання
What must a paradox explanation accomplish?
Відповідь
Make both surprising facts plausible at the same time. Rejecting either stated fact doesn't resolve the tension.
Картка 231
Питання
How is a segment in a stacked bar measured?
Відповідь
Subtract its lower boundary from its upper boundary. The upper endpoint alone is cumulative, not the segment value.
Картка 232
Питання
Eight students average 70 and twelve students average 80. What is the combined mean?
Відповідь
The group sizes are the weights: (8 × 70 + 12 × 80) ÷ 20 = 76.
Картка 233
Питання
What is the difference between a graph’s level and its rate of change?
Відповідь
Level is the plotted value; rate of change is the slope. A high line can still be falling.
Картка 234
Питання
How should you describe a statement's role in an argument?
Відповідь
Describe what it does, not just what it says. It may support the conclusion, present an objection, answer that objection, or illustrate a principle.
Картка 235
Питання
What is P(A given B)?
Відповідь
P(A and B) / P(B), provided P(B) > 0. Restrict the sample space to outcomes in B.
Картка 236
Питання
How should slope be compared across a graph?
Відповідь
Use change in vertical value divided by change in horizontal value. Visual steepness is reliable only on the same scales.
Картка 237
Питання
A driver covers equal distances at 30 mph and 60 mph. Is the average speed 45 mph?
Відповідь
No. Using 60 miles for each leg gives 120 miles in 3 hours, so the average speed is 40 mph.
Картка 238
Питання
What should you identify first when evaluating a plan?
Відповідь
The plan's exact goal and success measure. A proposal can produce benefits yet still fail its stated objective.
Картка 239
Питання
What does a trend in a scatterplot establish?
Відповідь
An association in the displayed data. It does not by itself establish causation or predict every individual point.
Картка 240
Питання
How can you strengthen a causal explanation?
Відповідь
Rule out a credible alternative cause, support the proposed mechanism, or show the effect changes when the proposed cause changes.
Картка 241
Питання
How can an outlier affect a graphical trend?
Відповідь
It can pull a summary line or average away from the main cluster. Check whether the claim concerns all points or the typical pattern.
Картка 242
Питання
Why do probabilities usually change when sampling without replacement?
Відповідь
The sample space changes after each draw. Update both the favorable count and the total before multiplying conditional probabilities.
Картка 243
Питання
One value in an n-value set increases by d. How does the mean change?
Відповідь
It increases by d/n because the total rises by d while the count stays fixed.
Картка 244
Питання
When does a counterexample weaken a claim?
Відповідь
When the claim requires the counterexample not to exist. One genuine exception can defeat an absolute claim, but may barely affect a modest one.
Картка 245
Питання
What is the parity of the sum of two odd integers?
Відповідь
Even. Each odd integer is one more than an even integer, so the two extra ones add to 2.
Картка 246
Питання
What can an aggregate graph hide?
Відповідь
Differences among subgroups or periods. A stable total can coexist with large offsetting changes inside it.
Картка 247
Питання
When is interpolation reasonable on a graph?
Відповідь
When the graph implies continuity between nearby points. Do not interpolate across separate categories.
Картка 248
Питання
What makes information relevant to evaluating an argument?
Відповідь
It bears on the uncertain link the conclusion depends on. Interesting facts about the topic may still be logically irrelevant.
Картка 249
Питання
How precise should a value read from a graph be?
Відповідь
Only as precise as the scale supports. Use a defensible interval when the mark falls between ticks.
Картка 250
Питання
Must a necessary assumption prove the conclusion?
Відповідь
No. It only has to be required for the argument to work; it need not be enough to establish the conclusion on its own.
Картка 251
Питання
How do you multiply positive numbers written in scientific notation?
Відповідь
Multiply the coefficients, add the powers of 10, then adjust the coefficient to be at least 1 and less than 10.
Картка 252
Питання
How should a graph-based decision be made?
Відповідь
Translate the visual into values or bounds, then apply the stated rule. Do not decide from appearance alone.
Картка 253
Питання
When is backsolving from answer choices especially useful?
Відповідь
When the choices are concrete values and direct algebra is slower than testing them in the original conditions.
Картка 254
Питання
How can axis scale distort a visual impression?
Відповідь
Unequal intervals or a truncated baseline can magnify or compress differences. Use tick values, not apparent distance alone.
Картка 255
Питання
When should you combine two statements for an inference?
Відповідь
When they share a term or relationship that creates a guaranteed consequence. Don't combine them through an unstated causal or statistical link.
Картка 256
Питання
When is a product of integers odd?
Відповідь
Only when every factor is odd. One even factor makes the entire product even.
Картка 257
Питання
What often resolves two apparently conflicting results?
Відповідь
A hidden difference in group, time, measurement, or conditions. The results may describe different slices of the situation.
Картка 258
Питання
How should equal distances on a logarithmic axis be interpreted?
Відповідь
As equal multiplicative changes, not equal absolute changes. Read the labeled values before comparing gaps.
Картка 259
Питання
Why start with a middle answer choice when backsolving ordered options?
Відповідь
Its result often eliminates half the choices at once when the relationship is monotonic.
Картка 260
Питання
What makes a Two-Part Analysis response complete?
Відповідь
Both selections must satisfy their own column prompts under the same stem. Treat the pair as one submitted response.
Картка 261
Питання
What is an analogy doing when it supports a claim?
Відповідь
It argues that because two cases share relevant features, a result or principle from one likely applies to the other.
Картка 262
Питання
How do you represent three consecutive odd integers?
Відповідь
n, n + 2, and n + 4, where n is an odd integer.
Картка 263
Питання
What should you identify before solving Two-Part Analysis?
Відповідь
The role of each column. One may ask for a condition while the other asks for a consequence or decision.
Картка 264
Питання
What values should you test first in a claim about an unspecified number?
Відповідь
Test allowed categories that may behave differently: positive, negative, zero, fractional, and boundary values.
Картка 265
Питання
How can an unchanged bottleneck defeat a plan?
Відповідь
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.
Картка 266
Питання
How does the shared stem affect the two parts?
Відповідь
Its definitions and constraints apply to both. Keep them fixed while testing each column’s requirement.
Картка 267
Питання
How do you count the positive divisors of an integer greater than 1 from its prime factorization?
Відповідь
Add 1 to each prime exponent, then multiply those results.
Картка 268
Питання
In Two-Part Analysis, must the two selected entries be the same?
Відповідь
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.
Картка 269
Питання
What makes evidence for a general claim strong?
Відповідь
It should be relevant and reliable and, if case-based, come from representative cases. More evidence isn't automatically better evidence.
Картка 270
Питання
How do you factor a difference of squares?
Відповідь
Use x² − y² = (x − y)(x + y).
Картка 271
Питання
When should the two Two-Part Analysis selections be solved together?
Відповідь
When one shared relationship constrains both. Test candidate pairs against that relationship instead of solving isolated fragments.
Картка 272
Питання
How can one counterexample evaluate a universal claim?
Відповідь
One valid counterexample disproves a claim that is supposed to hold for every allowed value.
Картка 273
Питання
How does an alternative explanation weaken a conclusion?
Відповідь
It shows that the evidence can be true without the proposed explanation being true. The alternative must account for the same result.
Картка 274
Питання
In Two-Part Analysis, how can one column help solve the other?
Відповідь
A valid selection can narrow the remaining candidates when the parts share a constraint. Recheck the final pair in both columns.
Картка 275
Питання
How do you test whether x² + bx + c factors into integer binomials?
Відповідь
Look for integers r and s with r + s = b and rs = c. If they exist, the factorization is (x + r)(x + s).
Картка 276
Питання
Which unknown should you evaluate first in a plan argument?
Відповідь
A condition that could make the plan achieve or miss its goal. Focus on feasibility, response, costs, and side effects tied to that goal.
Картка 277
Питання
How should a trade-off between two measures be evaluated?
Відповідь
Apply the stated priorities or limits. An option is better only relative to the rule, not because one measure is largest.
Картка 278
Питання
How can estimation screen answer choices before exact calculation?
Відповідь
Approximate the expression's magnitude, then eliminate choices that are far too large or too small.
Картка 279
Питання
In a constrained-decision Two-Part Analysis problem, what should you check before comparing candidates?
Відповідь
Check every hard constraint first. Discard any option that breaks a required limit, then compare only the feasible candidates.
Картка 280
Питання
What does a defensive assumption do?
Відповідь
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.
Картка 281
Питання
What restriction applies when a variable appears in a denominator?
Відповідь
Exclude every value that makes the denominator zero.
Картка 282
Питання
How does an objective differ from a constraint?
Відповідь
A constraint determines what is allowed; an objective ranks the allowed options. Apply them in that order.
Картка 283
Питання
Which quick checks catch many Quant answer errors?
Відповідь
Check the sign, units, allowed range, and rough size against the question's conditions.
Картка 284
Питання
What inference is safe from a statement about most members?
Відповідь
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.
Картка 285
Питання
How should a two-part threshold rule be handled?
Відповідь
Translate each threshold with the correct inequality, including its boundary. Then test both selected values against it.
Картка 286
Питання
Where can one negative sign appear in a fraction without changing its value?
Відповідь
Before the fraction, in the numerator, or in the denominator: −(a/b) = (−a)/b = a/(−b), provided b ≠ 0.
Картка 287
Питання
How does an argument choose between competing explanations?
Відповідь
It presents evidence that one explanation handles better than the others, often by ruling out a rival prediction.
Картка 288
Питання
What is an efficient way to handle two linked algebraic targets?
Відповідь
Express both in terms of one variable or invariant. Evaluate candidate values only after the relationship is clear.
Картка 289
Питання
How do you solve x² = c over the real numbers?
Відповідь
If c > 0, x = ±√c; if c = 0, x = 0; if c < 0, there is no real solution.
Картка 290
Питання
What should you check when two selected quantities form a ratio?
Відповідь
Order and scale. The ratio A:B is not interchangeable with B:A, and proportional pairs may all fit.
Картка 291
Питання
How does a positive proper fraction compare with 1?
Відповідь
It is less than 1 because its numerator is smaller than its denominator.
Картка 292
Питання
Which side effects matter when evaluating a plan?
Відповідь
Effects that change the plan's net result or work against its goal. A small unrelated inconvenience usually doesn't matter.
Картка 293
Питання
How should a two-part logical claim be tested?
Відповідь
Separate the condition from the conclusion, then test whether each selected statement performs the requested role.
Картка 294
Питання
What is the solution pattern for |x| = a over the real numbers?
Відповідь
If a > 0, x = ±a; if a = 0, x = 0; if a < 0, there is no real solution.
Картка 295
Питання
What unit check belongs in a two-part quantitative answer?
Відповідь
Confirm that each selection has the unit requested by its column. Linked values may require different conversions.
Картка 296
Питання
Why does user response matter to a plan?
Відповідь
The plan may depend on people adopting, following, or not avoiding it. Availability alone doesn't guarantee the needed behavior.
Картка 297
Питання
A response rate rises from 40% to 50%. What are the percentage-point change and the relative percent increase?
Відповідь
The increase is 10 percentage points and 25% relative to the original rate: (50 − 40) ÷ 40 = 0.25.
Картка 298
Питання
What is the final check for Two-Part Analysis?
Відповідь
Read each column prompt with its chosen entry, then verify that the pair is jointly consistent with the stem.
Картка 299
Питання
For real x and y, what two linear cases are equivalent to x² = y²?
Відповідь
x = y or x = −y.
Картка 300
Питання
How should benefits and costs be compared in a plan argument?
Відповідь
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.

300 карток

GMAT Flashcards: Quant, Verbal & Data Insights Decisions

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GMAT Flashcards: Quant, Verbal & Data Insights Decisions

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