Koydo
CDLNCLEXIELTSOpen Koydo

GRE · 8% of test plan

Quantitative: Algebra for the GRE Exam

Algebra is tested across all GRE Quantitative question types: problem solving, Quantitative Comparison, and data interpretation. Key sub-areas include setting up and solving linear equations from word problems, working with inequalities (especially when multiplying or dividing by a negative), simplifying algebraic expressions, solving quadratics by factoring, and evaluating functions. GRE algebra questions are typically not computationally difficult — they test careful setup and awareness of edge cases like negative multipliers and undefined expressions.

ETS GRE General Test Preparation — Quantitative Reasoning content specifications.

Locale-specific study guides

Pass-rate data, regulatory context, and study tips for Quantitative: Algebra all change by candidate locale. Pick your context:

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.

  • !Flipping the inequality sign when multiplying or dividing by a negative — a consistent GRE trap in Quantitative Comparison items
  • !Incorrectly FOIL-ing or factoring quadratics — especially (a − b)² ≠ a² − b²
  • !Ignoring domain restrictions: dividing by a variable without checking that the variable ≠ 0
  • !Setting up a word problem incorrectly — spending algebra time on the wrong equation

Study tips

  • 1Always flip the inequality sign when multiplying or dividing both sides by a negative number. Practice this deliberately on 10 inequality problems in a row to build automaticity.
  • 2Memorize the three special factoring patterns: (a+b)² = a²+2ab+b², (a−b)² = a²−2ab+b², (a+b)(a−b) = a²−b². These save time and prevent common errors.
  • 3On word problems, translate to algebra systematically: assign variables to the unknown quantities, write an equation based on the relationship described, then solve.
  • 4For Quantitative Comparison items involving variables, test edge cases: x = 0, x = 1, x = −1, x = a fraction. If the comparison changes, the answer is "cannot be determined."

Sample GRE Quantitative: Algebra 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

    If 3x − 7 > 2x + 1, which of the following must be true?

    • Ax > −6
    • Bx > 8Correct
    • Cx < 8
    • Dx > 6
    Why this answer?

    3x − 7 > 2x + 1 → 3x − 2x > 1 + 7 → x > 8. The solution is x > 8. This is a straightforward linear inequality — no sign flip because we subtracted (not divided by) a negative. (Illustrative.)

  2. 2

    Quantity A: (x + 3)² where x = −5. Quantity B: (x − 3)² where x = 5. Which is greater?

    • 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: (−5 + 3)² = (−2)² = 4. Quantity B: (5 − 3)² = (2)² = 4. The quantities are equal. This tests the GRE skill of noticing that (−2)² = (2)² = 4 — the squaring removes the sign difference.

Practice GRE Verbal & Quant free with Koydo.

Adaptive practice, 4,000+ questions, AWA scoring built-in.

Start free GRE practice →