Quantitative Reasoning: Quantitative Comparison Strategy

What you'll learn

Describe the Quantitative Comparison format and its four fixed answer choices
Apply the strategy of testing multiple values -- including negatives, fractions, and zero -- before concluding a relationship holds
Recognize when a relationship genuinely cannot be determined from the given information

Explanation

Quantitative Comparison (QC) is a format found only in the GRE's Quantitative Reasoning sections. You're given Quantity A and Quantity B -- numbers, expressions, or values described in a short scenario -- and must choose one of four fixed answer choices: Quantity A is greater; Quantity B is greater; the two quantities are equal; or the relationship cannot be determined from the information given. These same four options appear, in the same order, on every QC question.

When variables are involved, the reliable strategy is to test multiple different values, not just one convenient one -- try a positive integer, a negative number, a fraction between 0 and 1, and zero where it's permitted by the problem. If different test values produce different relationships between Quantity A and Quantity B, the correct answer is "cannot be determined," regardless of how confident a single test might have made you feel.

Worked original example: "Quantity A: x^2. Quantity B: x," with no constraint given on x. Testing x = 2 gives Quantity A = 4 and Quantity B = 2, so A is greater. Testing x = 0.5 gives Quantity A = 0.25 and Quantity B = 0.5, so B is greater instead. Since the relationship changes depending on which value of x is used, the correct answer is "cannot be determined" -- not a sign of an error, but the intended correct choice for a question built exactly this way.

If a question instead adds an explicit constraint (for example, "x > 1"), you must retest using only values consistent with that constraint, since it narrows the possibilities and can change which answer is correct -- never carry over an answer from an unconstrained version of a similar-looking question.

Common mistakes

Testing only one convenient value, such as a positive integer, and concluding a relationship holds universally without checking a fraction, zero, or a negative value.
Forgetting that 'cannot be determined' is a fully valid, and sometimes the intended correct, answer -- not a sign that you've made an error.
Ignoring an explicitly given constraint on a variable, such as 'x > 1', which narrows which test values are actually allowed and can change the correct answer.

Knowledge check

1. In Quantitative Comparison questions, which four answer choices are always available?

True, False, Not Given, Cannot be determinedQuantity A is greater; Quantity B is greater; the two quantities are equal; the relationship cannot be determined from the information givenYes, No, Maybe, Not applicableOnly two choices: Quantity A or Quantity B

2. For 'Quantity A: x^2, Quantity B: x' with no constraint on x, why is 'cannot be determined' the correct answer?

Because x^2 is always greater than x for every real numberBecause testing different values of x, such as 2 versus 0.5, produces different relationships between the two quantitiesBecause x is undefined in this scenarioBecause Quantitative Comparison questions never have a determinable answer

3. If a Quantitative Comparison question adds the constraint 'x > 1' to the same two quantities from above, what should you do?

Ignore the new constraint and reuse your original answerRetest using only values consistent with the new constraint, since it may change which answer is correctAutomatically select 'cannot be determined' whenever any constraint is addedAssume constraints never affect Quantitative Comparison answers

Takeaway

Test several different values -- positive, negative, fractional, and zero where allowed -- before concluding a Quantitative Comparison relationship holds, and treat 'cannot be determined' as a fully valid answer.

Summary

Quantitative Comparison always offers the same four fixed choices. Testing multiple values systematically, and respecting any given constraints, is the reliable way to reach the correct answer.

References

ETS GRE Quantitative Reasoning

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