Plugging In & Backsolving
Key strategies for using PSAT answer choices to shortcut heavy algebra.
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Questions Covered in This Set
10 cards to master
Backsolving
Substituting the numeric answer choices back into the problem until one works.
Plugging In
Choosing your own easy number for a variable, computing a target, then testing each answer choice.
Which choice should you test first when backsolving?
Start with B or C (a middle value), since choices are usually in numerical order — one test can eliminate several options.
When is Plugging In the right tool?
When the answer choices contain variables (expressions like 2x+3) or the question says 'in terms of'.
Which numbers should you avoid when plugging in?
Avoid 0 and 1 (they make different expressions collapse to the same value) and numbers already used in the problem.
Best number to plug in for percent problems?
100 — percent increases and decreases become easy arithmetic.
Best number to plug in for fraction problems?
A common multiple of the denominators (e.g., x = 12 if you see x/2 and x/3).
What if two answer choices both hit your target?
Plug in a second, different number to break the tie.
When should you NOT use these strategies?
When direct algebra is obvious (3x = 21), on systems needing both equations checked, or on grid-ins with no choices.
How to handle 'must be true' questions?
Pick a legal value (e.g., n = 4 for an even integer), test each choice, and retest survivors with a second value like n = 10.
