SAT Math · Problem Solving & Data Analysis
Percentages and percent change
Percent of, percent change, and successive percent changes.
What's tested in this subtopic
Items test percent of a quantity ("what is 18% of 250"), percent change ("the price rose from 80 to 92, what is the percent increase"), reverse percent ("after a 15% discount, the item costs $51 — what was the original price"), and successive percent changes ("a 10% raise then a 5% raise — what is the net percent change").
Tactics that actually move your score
For percent change, the formula is (new − old)/old × 100%. For successive percents, multiply the multipliers (1.10 × 1.05 = 1.155, so 15.5% net increase) — never add the percentages. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy The price of an item increased from $197 to $260. What was the percent change?
- Easy The price of an item increased from $48 to $62. What was the percent change?
- Medium The price of an item increased from $59 to $78. What was the percent change?
- Medium The price of an item increased from $179 to $224. What was the percent change?
- Medium The price of an item decreased from $72 to $55. What was the percent change?
- Hard The price of an item decreased from $171 to $128. What was the percent change?
- Easy The price of an item decreased from $151 to $139. What was the percent change?
- Easy The price of an item increased from $61 to $64. What was the percent change?
- Medium The price of an item increased from $114 to $149. What was the percent change?
- Medium The price of an item decreased from $155 to $133. What was the percent change?
- Medium The price of an item decreased from $189 to $161. What was the percent change?
- Hard The price of an item increased from $85 to $99. What was the percent change?
- Easy The price of an item decreased from $117 to $81. What was the percent change?
- Easy The price of an item decreased from $197 to $167. What was the percent change?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in SAT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.