Strategy: Quantitative Comparison and Plugging In

The Quantitative Comparison Format

About 8 of the 27 Quant questions per section are Quantitative Comparison (QC). Every QC question has the same four fixed answer choices, which are never shuffled:

• (A) Quantity A is greater
• (B) Quantity B is greater
• (C) The two quantities are equal
• (D) The relationship cannot be determined from the information given

Memorize this order. It is identical on every QC question, so you should recognize a QC question the instant you see two boxed quantities.

Strategy 1: Plug In Strategic Numbers — 0, 1, −1, and a Fraction

When a QC involves a variable with no (or loose) constraints, test values that expose different behavior. The essential set is 0, 1, −1, and a proper fraction such as $\tfrac12$ — these are precisely the numbers where algebraic intuition breaks down.

Quantity A: $x^2$ Quantity B: $x$ (no constraint on $x$)

• $x = 2$: $x^2 = 4 > 2$, so A is greater.
• $x = \tfrac12$: $x^2 = 0.25 < 0.5$, so B is greater.

Two different outcomes ⇒ the answer is (D). A student who only tries integers greater than 1 would wrongly pick (A).

Strategy 2: The "Cannot Be Determined" Trap Works Both Ways

(D) is correct only when the relationship can actually change. If the two quantities are always equal or always ordered — even though they contain variables — then (D) is wrong. Never pick (D) just because you see a variable; pick it only after finding two cases that disagree. Conversely, if you find even one case where they differ, you can stop immediately and choose (D).

Note: (D) can never be the answer when both quantities are pure numbers (no variables) — a fixed comparison always resolves to A, B, or C.

Strategy 3: Transform Both Quantities Identically

You may add, subtract, multiply, or divide both quantities by the same amount without changing their relationship — as long as you never multiply or divide by a negative or by something that could be zero. Use this to simplify:

Quantity A: $\dfrac{3}{7}$ Quantity B: $\dfrac{4}{9}$

Cross-multiply (both denominators positive): compare $3 \times 9 = 27$ against $4 \times 7 = 28$. Since $27 < 28$, Quantity B is greater — choice (B).

Strategy 4: Estimate Before You Compute on Multiple Choice

For ordinary five-choice questions and Numeric Entry, the calculator is a trap for time. Estimate first: round $19.6\%$ of $203$ to $20\%$ of $200 = 40$, then confirm the nearest choice. On the GRE, the answer choices themselves are a tool — if they are far apart, estimation alone decides the answer.

Strategy 5: Numeric Entry Demands Exact Form

Numeric Entry questions have no answer choices — you type the number into a box. Watch for:

• Fraction boxes (a numerator box over a denominator box): you need not reduce, but the value must be exact.
• Rounding instructions: "to the nearest 0.01" means give two decimals — a common careless-error source.
• Negative signs and decimal points must be entered explicitly.