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.

Από τον συντάκτη Open Study Contributor

Σχετικά με αυτήν τη δέσμη

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.

Κάρτες σε αυτήν τη δέσμη

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