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.

Tác giả Open Study Contributor

Về bộ thẻ này

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.

Thẻ trong bộ này

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

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GMAT Flashcards: Quant, Verbal & Data Insights Decisions

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