GRE Quantitative Comparison: When You Can't Tell Which Is Bigger

Quantitative Comparison gives you two quantities, A and B, and asks you to compare them. The four answer choices are always the same: A is greater, B is greater, the two are equal, or the relationship cannot be determined from the information given.

Because the answers are fixed, memorize them. The fourth option, cannot be determined, is the one students both overuse and underuse, so understanding exactly when it applies is central.

You rarely need an exact value; you only need the relationship. Treat the comparison like an inequality and do the same thing to both sides. You can add, subtract, multiply, or divide both quantities by the same positive number without changing which is larger.

One caution: never multiply or divide both sides by a variable that could be negative or zero, because that can flip or break the comparison. With positive numbers you are safe; with unknown signs you are not.

When variables are involved, plug in numbers. But do not only try friendly positives like 2 and 3. Deliberately test zero, one, a negative, and a fraction between zero and one, because these often change the outcome.

If one set of numbers makes A greater and another makes B greater, you are done: the answer is cannot be determined. A single counterexample to a fixed relationship settles it.

If every legitimate case you try gives the same relationship, that consistent result is your answer. If the quantities are always identical, choose equal. The test rewards recognizing forced outcomes.

Remember that cannot be determined means the relationship changes across allowed cases, not merely that you personally are unsure. If the math pins it down, one of the first three answers is correct, even when the numbers look intimidating.

Read both quantities and any shared information. Simplify both sides with legal moves. If variables appear, test zero, one, a negative, and a fraction. If results differ, answer cannot be determined; if they always agree, choose A greater, B greater, or equal accordingly.