GRE · Quantitative: Algebra · United States

Quantitative: Algebra for the GRE Exam — U.S. candidates

8% of the GRE test plan. GRE Algebra covers linear equations, systems of equations, inequalities, absolute value, and quadratic functions with an emphasis on reasoning over calculation. Calibrated for American candidates.

Examiners do not award marks for content alone — they award them for the ability to demonstrate competency in the precise format the test demands. Quantitative: Algebra sits at roughly 8% of the Graduate Record Examinations content distribution — 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. In 2024, the published overall rate for GRE candidates in United States was 50% (ETS — GRE General Test Snapshot Report 2023–24 (V+Q ≥ 310 cohort threshold)). For U.S. candidates preparing for GRE, the calibration of study to local context matters: U.S. licensure exams are governed at the state level (CDL, NCLEX) or by national boards (MCAT, GRE). Pearson VUE and PSI are the dominant test-delivery vendors.

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."
5If you are testing in the U.S., expect GRE delivery via Pearson VUE or PSI test centres — register through the official board portal at least 30 days in advance.

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
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
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.

Frequently asked questions

Do I need to know quadratic formula for the GRE?

The quadratic formula (x = [−b ± √(b²−4ac)] / 2a) is useful but rarely required on the GRE, since most GRE quadratics are designed to factor nicely. Knowing how to factor quadratics (FOIL in reverse) is the primary skill. The quadratic formula is a backup for non-factorable cases.

Does the GRE test logarithms or exponential functions?

The GRE tests basic exponent rules (product rule, power rule, negative exponents) and simple exponential growth/decay scenarios. Advanced logarithm problems (change of base, log equations) are rare but possible at the highest Quant difficulty levels.

What is the GRE Quantitative: Algebra pass rate for American candidates?

The published overall rate for GRE candidates in United States in 2024 was 50%, according to ETS — GRE General Test Snapshot Report 2023–24 (V+Q ≥ 310 cohort threshold). Pass rates within specific topics like Quantitative: Algebra are not separately published, but the topic represents roughly 8% of the exam.

How long should American candidates study Quantitative: Algebra for the GRE?

For most candidates, focused mastery of Quantitative: Algebra requires 20–40 hours of deliberate practice — drilling sample questions, reviewing failure modes, and timing yourself against exam conditions. U.S. licensure exams are governed at the state level (CDL, NCLEX) or by national boards (MCAT, GRE). Pearson VUE and PSI are the dominant test-delivery vendors. Combine Quantitative: Algebra study with full-length mock exams in the final two weeks before your test date.

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Related study guides

Regulatory citation: ETS GRE General Test Preparation — Quantitative Reasoning content specifications.