CramClub • Strategy: Plug In, Backsolve, and QC Algebra

Turning Algebra into Arithmetic

Two tactics let you sidestep messy algebra on the GRE, and both exploit the answer choices.

Strategy 1: Backsolving (Plug In the Answers)

When a multiple-choice question asks for a specific value and the algebra is tangled, test the answer choices. Because GRE numeric choices are listed in ascending order, start with the middle choice (C). If it's too big, go smaller; too small, go bigger. You will rarely need more than two tries.

If $\dfrac{x}{x - 2} = \dfrac{4}{x + 1}$ , which value could $x$ be? (Choices include 4.)

Testing $x = 4$ : left $= \frac{4}{2} = 2$ ; right $= \frac{4}{5} = 0.8$ . Not equal, so 4 is out — move on. Backsolving avoids clearing denominators and solving the resulting quadratic by hand.

Strategy 2: Plugging In Your Own Numbers (Variables in the Choices)

When the question and the answer choices are all in terms of variables, invent concrete values that satisfy the constraints, compute the target number, then see which choice matches.

If the width of a rectangle is $w$ and the length is 3 more than twice the width, the perimeter in terms of $w$ is …

Let $w = 5$ : length $= 2(5) + 3 = 13$ , perimeter $= 2(5) + 2(13) = 36$ . Now plug $w = 5$ into each choice; the one that yields 36 (namely $6w + 6$ ) is correct.

Strategy 3: QC Algebra — Simplify, Then Test Extremes

On Quantitative Comparison with variables, first simplify both quantities with legal moves (never multiply/divide both sides by a possibly-negative or possibly-zero expression). Then, if any freedom remains, plug in the critical values 0, 1, −1, and a fraction to look for two disagreeing cases.

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

$x = 2$ gives A greater; $x = \tfrac12$ gives B greater — the relationship changes, so the answer is (D). The trap is to try only $x = 2, 3, 4$ and conclude (A).

Strategy 4: Respect the Inequality Sign-Flip

The single most common GRE algebra error is forgetting to flip the inequality when dividing by a negative. $-3x > 12$ becomes $x < -4$ , not $x > -4$ . Whenever you multiply or divide an inequality by a negative, flip — every time.

Strategy 5: Don't Over-Solve

If a question asks for $x + y$ , $xy$ , or $x^2 - y^2$ , look for a way to produce that combination directly (add the equations, factor a difference of squares) instead of grinding out each variable. The GRE rewards recognizing the target.

Turning Algebra into Arithmetic

Two tactics let you sidestep messy algebra on the GRE, and both exploit the answer choices.

Strategy 1: Backsolving (Plug In the Answers)

If $\dfrac{x}{x - 2} = \dfrac{4}{x + 1}$ , which value could $x$ be? (Choices include 4.)

Testing

x = 4

: left

= \frac{4}{2} = 2

; right

= \frac{4}{5} = 0.8

. Not equal, so 4 is out — move on. Backsolving avoids clearing denominators and solving the resulting quadratic by hand.

Strategy 2: Plugging In Your Own Numbers (Variables in the Choices)

When the question and the answer choices are all in terms of variables, invent concrete values that satisfy the constraints, compute the target number, then see which choice matches.

If the width of a rectangle is $w$ and the length is 3 more than twice the width, the perimeter in terms of $w$ is …

Let

w = 5

: length

= 2(5) + 3 = 13

, perimeter

= 2(5) + 2(13) = 36

. Now plug

w = 5

into each choice; the one that yields 36 (namely

6w + 6

) is correct.

Strategy 3: QC Algebra — Simplify, Then Test Extremes

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

x = 2

gives A greater;

x = \tfrac12

gives B greater — the relationship changes, so the answer is (D). The trap is to try only

x = 2, 3, 4

and conclude (A).

Strategy 4: Respect the Inequality Sign-Flip

The single most common GRE algebra error is forgetting to flip the inequality when dividing by a negative.

-3x > 12

becomes

x < -4

, not

x > -4

. Whenever you multiply or divide an inequality by a negative, flip — every time.

Strategy 5: Don't Over-Solve

If a question asks for

x + y

xy

, or

x^2 - y^2

, look for a way to produce that combination directly (add the equations, factor a difference of squares) instead of grinding out each variable. The GRE rewards recognizing the target.