Backsolve
Concrete numerical answer choices.
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GMAT Strategy
Backsolving and Picking Numbers
Use answer choices or clean test values to replace unnecessary algebra when the structure allows it.
Backsolving
Backsolving uses the answer choices as candidate solutions.
It is especially useful when the choices are numerical and plugging a candidate is faster than solving the equation symbolically.
A reliable backsolving routine
- 01Start with the middle choice when choices are ordered.
- 02Plug it into the original condition.
- 03Decide whether the target needs a larger or smaller value.
- 04Move accordingly instead of testing every choice.
Picking numbers
Picking numbers replaces free variables with convenient values.
Use it when the question asks about a relationship and the variables are not fixed by the stem.
Useful values
Test values that expose common traps.
- 010, if allowed, for zero-related exceptions.
- 021 for multiplicative identities.
- 03Negative values for sign changes.
- 04Fractions for denominator and inequality traps.
- 05Small clean integers for speed.
Constraint
Do not pick numbers that violate the stem.
If the problem says positive integer, do not test 0, negatives, or fractions. The chosen values must satisfy every stated constraint.
Choose the tool based on what the question gives you.
Pick numbers
Free variables and a relationship that should hold generally.
Mini application
Try this: If x/y = 3/4 and the question asks for (x+y)/y, pick a clean pair.
Use the ratio itself to choose values.
Solution
Pick x = 3 and y = 4, so (x+y)/y = 7/4.
The clean values preserve the relationship and remove unnecessary algebra.
Remember this
Strategy replaces symbolic work only when the structure permits it.
Use answer choices when they are informative; use test values when variables are genuinely free.