Percentages
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Lesson overview
Percent change, discounts and percent-of problems — a top-tested SAT concept.
Go to lesson quiz →Exam guidance · Digital SAT Adaptive-Module Lens
Pacing
~71s per Reading/Writing item; ~95s per Math item with built-in Desmos graphing calculator.
How SAT marks this
Module 1 accuracy unlocks the higher-ceiling Module 2; graph intersections in Desmos often beat manual algebra.
Watch out for
Solving for x instead of the expression requested in the final clause of the stem.
Lesson content
Overview — Percentages
Percent change, discounts and percent-of problems — a top-tested SAT concept. This lesson is at the beginner level — by the end, you'll be able to recognise this question type, apply a reliable method, and avoid the traps that cost marks.
Key Concept
Percent problems on the SAT come in three main forms — finding a percent of a number, finding percent change, and working backward from a final value to an original one — each solved with a distinct but related formula.
Why It's Tested This Way
College Board tests percentages because they appear across real-world contexts (discounts, growth, statistics) that the Digital SAT deliberately favors in its word problems, testing practical numeracy rather than pure algebra.
Method
For percent-of, multiply by the decimal form; for percent change, use (new − old) / old × 100; for working backward from a final value after a percent change, divide by (1 ± the decimal rate) rather than simply reversing the multiplication.
Worked Example
A shirt's price increases from $40 to $50. Percent change = (50 − 40)/40 × 100 = 25%. A common error is dividing by the new price (50) instead of the original (40), which gives an incorrect 20%.
Second Worked Example
A jacket is on sale for $68 after a 15% discount; find the original price. Since $68 represents 85% of the original, divide: 68 / 0.85 = $80 — not 68 × 1.15 = $78.20, a frequent working-backward error.
Common Traps
The trap is applying percent change relative to the wrong base value (new instead of original) or reversing a discount by multiplying instead of dividing — always identify which value is the '100%' base before calculating.
Lesson Summary
Remember: (1) identify what is being asked, (2) apply the SAT strategy, (3) check against the traps. Complete the 10-question quiz below to unlock the next lesson — you need at least 60% to pass.
Mastery Check · Lesson Quiz · pass 60%
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