Picking Numbers When the Choices Contain Variables

The move works because an algebraic expression has to be true for every value of the variable, including the one you invent. So if a question describes a relationship in words, or gives answer choices full of x's and k's, you assign the variable a concrete number, work out what the correct result should be using that number, then plug the same number into each answer choice. Whichever choice spits out your target number survives. The others get eliminated because they fail for a number that was supposed to work for all numbers.

The trap is choosing 0 or 1. Those two numbers are special: 1 squared is still 1, 1 times anything is that thing, and 0 wipes out whole terms. That means expressions that are genuinely different algebraically can accidentally produce the same output at x = 1 or x = 0, so two or more choices survive and you learn nothing. A number like 2, 5, or 10 keeps powers, products, and sums distinct, so it actually discriminates between choices.

This is the second half of a two-part pacing strategy, alongside backsolving from the choices when the question asks for a specific unknown rather than a general expression. Both tricks exist to dodge slow symbolic algebra under a tight clock, trading it for arithmetic you can do fast and check twice if a number ties.