GRE Algebra
Linear and quadratic equations, simultaneous equations, inequalities, absolute value, functions, sequences, and the word problems that turn into all of the above. No proofs and no calculus.
The two rules that cost the most
- Multiplying or dividing an inequality by a negative reverses it. This is the most frequently punished rule on the GRE, and it is punished mainly in Quantitative Comparison where the variable sign is unknown.
- Absolute value gives two cases. |x| = 5 means x = 5 or x = −5, and the question is almost always built on the case you did not write down.
Both have the same consequence: where a variable could be negative, you cannot treat it as though it is positive. That single habit decides a large share of Quant marks.
Worth knowing cold
| Pattern | Factors to |
|---|---|
| x² − y² | (x + y)(x − y) |
| x² + 2xy + y² | (x + y)² |
| x² − 2xy + y² | (x − y)² |
The difference of two squares is the one that turns an ugly-looking Quantitative Comparison into one line. Questions are written specifically to reward spotting it.
On word problems, define the variable in writing before setting up. Most errors here are not algebraic — they are the equation describing something slightly different from what was asked.
Algebra — FAQs
2 questions
Rarely. Most GRE quadratics factorise cleanly, which is a hint that you have set it up correctly.
Secondary-school level. The difficulty is in the wording and the clock rather than the technique.
More quantitative question types
Sources
Written from the test board's own published material and checked on 1 October 2026.