Quantitative: Quantitative Comparison for the GRE Exam

Common failure modes

These are the patterns that cause most candidates to lose marks on this topic. Recognising them in advance is half the work.

• !Computing both quantities fully when simplification would determine the relationship in seconds
• !Trying only one substitution value (often x = 2) when testing variables — always test x = 0, x = 1, x = −1, and a fraction
• !Forgetting that if two different substitution values give different comparison results, the answer is automatically D (cannot be determined)
• !Not cancelling equal quantities from both sides — any quantity that appears identically on both sides can be subtracted or divided out

Study tips

• 1Learn the four QC simplification techniques: (1) add/subtract the same value from both sides, (2) multiply/divide by the same positive value, (3) substitute numbers, (4) use algebraic simplification. Apply them in this priority order.
• 2Always test at least four values when a variable is present: 0, 1, −1, and 1/2. These cover cases where the comparison changes direction.
• 3If the relationship between two quantities depends on a constraint not given (e.g., "x > 0" is not stated when x is a variable), the answer is likely D.
• 4Practice 20 QC problems per session to build pattern recognition — certain algebraic structures recur frequently (absolute values, squares of variables, expressions with fractions).

Sample GRE Quantitative: Quantitative Comparison questions

These sample items mirror the format and difficulty of real GRE questions. Practice with thousands more on the free Koydo question bank.

1. 1

   Quantity A: x² + 2x + 1. Quantity B: (x + 1)². (x is any real number)

   • AQuantity A is greater
   • BQuantity B is greater
   • CThe two quantities are equalCorrect
   • DThe relationship cannot be determined from the information given
   Why this answer?

   Quantity A: x² + 2x + 1 is the expanded form of (x+1)² by the binomial square formula. Quantity B is (x+1)². Therefore A = B for all real values of x. The answer is C. This tests recognizing the special binomial identity — no calculation needed. (Illustrative.)

2. 2

   Quantity A: |x − 3| when x = −2. Quantity B: |x + 3| when x = 2.

   • AQuantity A is greater
   • BQuantity B is greater
   • CThe two quantities are equalCorrect
   • DThe relationship cannot be determined
   Why this answer?

   Quantity A: |−2 − 3| = |−5| = 5. Quantity B: |2 + 3| = |5| = 5. The quantities are equal. This tests absolute value evaluation with negative inputs — a common QC sub-type.