GRE Quantitative Comparison: How the Four Answers Work

Each question presents Quantity A and Quantity B, sometimes with information above them that applies to both. You decide which of four statements describes the relationship. ETS lists them as: Quantity A is greater; Quantity B is greater; the two quantities are equal; the relationship cannot be determined from the information given.

Because the four statements never change, you should know them cold. ETS specifically warns against reversing the first two choices once you have decided which quantity is larger, an error that is easy to make when you are moving quickly. Quantitative Comparison is one of the four Quant formats ETS describes, alongside two kinds of multiple choice and Numeric Entry.

Choosing A, B or equal is a claim that the relationship holds in every case the given information allows. Choosing the fourth answer is a claim that different allowed cases produce different relationships. That framing is the heart of the format.

It follows that if both quantities are fixed numbers you can compute, the fourth answer cannot be correct. ETS makes the same point: never pick cannot be determined when computation settles the values. Conversely, when variables appear, a single test case is never enough to justify A, B or equal. You need either an algebraic argument or confidence that you have tried the cases most likely to break the pattern.

ETS advises avoiding needless computation and simplifying or estimating only as far as the comparison requires. Often you can match pieces of the two quantities and compare what is left.

Original example. Quantity A: 5n + 12. Quantity B: 5n + 9. Both contain 5n, whatever n is, so the comparison reduces to 12 against 9. Quantity A is greater for every value of n. No substitution needed.

Original example. Quantity A: 3/7. Quantity B: 0.43. Multiply 0.43 by 7 to get 3.01, which is larger than 3. So 0.43 is slightly more than 3/7, and Quantity B is greater. Converting 3/7 to 0.4286 on the calculator also works, but the multiplication is quicker and avoids a rounding judgment.

When variables are involved, ETS recommends substituting easy numbers and deliberately trying different kinds: zero, positives and negatives, small and large values, fractions. If one substitution makes A larger and another makes B larger, the answer is that the relationship cannot be determined.

Original example. Given that x is an integer. Quantity A: x squared. Quantity B: x cubed. Try x = 2: A is 4 and B is 8, so B is greater. Try x = 0: both are 0, so they are equal. Try x = -1: A is 1 and B is -1, so A is greater. Three different outcomes, so the relationship cannot be determined.

Notice that a student who tried only 2 and 3 would have confidently chosen B. The integers most likely to break a pattern are 0, 1, -1 and a negative number with a larger absolute value. For non-integers, add a fraction between 0 and 1.

The information above the quantities narrows the cases you need to test, and sometimes settles the question outright.

Original example. Given that 0 < y < 1. Quantity A: y squared. Quantity B: the square root of y. For a number between 0 and 1, squaring makes it smaller and taking the square root makes it larger. With y = 0.25, A is 0.0625 and B is 0.5. Since this holds for every y in the interval, Quantity B is greater.

Original example. The average of four numbers is 20. Quantity A: the sum of the four numbers. Quantity B: 80. The sum equals the average times the count, 20 times 4, which is 80. The quantities are equal, even though you do not know any individual number.

ETS states that geometric figures are not necessarily drawn to scale and suggests redrawing a figure, keeping fixed what the information determines and varying what it does not. If the relationship changes as you redraw, the answer is that it cannot be determined.

Original example. A triangle has sides of length 5 and 8, and its third side has length c. Quantity A: c. Quantity B: 13. By the triangle inequality, any side must be shorter than the sum of the other two, so c is less than 5 + 8 = 13. However the triangle is drawn, Quantity B is greater.

A subtle error is finding one case where the quantities match and stopping there. Equal, like A or B, is a claim about every allowed case.

Original example. Given that x > 0. Quantity A: x divided by 2. Quantity B: 2 divided by x. With x = 2, both quantities are 1, so they look equal. With x = 4, A is 2 and B is 0.5, so A is greater. With x = 1, A is 0.5 and B is 2, so B is greater. The relationship cannot be determined. Whenever your first substitution produces a tie, treat it as a signal to test at least one value above and one below it.

In review, this error is worth tracking separately from arithmetic slips. It reflects a reasoning habit, stopping at the first confirming case, and it tends to recur until you deliberately build the extra check into your routine.

ETS describes treating the relationship between the quantities as an unknown symbol and simplifying both sides step by step, as you would when solving an inequality. You may add or subtract the same value on both sides, and multiply or divide by the same positive value, without changing the relationship.

The trap is multiplying or dividing by a quantity whose sign you do not know, since a negative multiplier reverses an inequality. If you are about to divide both sides by x and nothing tells you x is positive, stop and test cases instead.

When you practice, keep a short log of the Quantitative Comparison items you miss and note which strategy would have caught the error. RetakePrep's review set, which collects every question you have missed, is one convenient place to do that kind of rework before a retake.