Percentages
A percent is just a fraction out of 100. The questions test four moves: finding a percent of a number, finding what percent one number is of another, percent change, and working backward from a percent to the original — the one students miss most.
What College Board tests
Computing a percent of a quantity, percent increase and decrease, reverse-percent problems (given the result after a change, find the original), and the difference between a change in percentage points and a relative percent change.
The translations
After a 20% increase, a quantity is times the original; after a 20% decrease, times. To undo a change, divide by that factor — don't add the percent back.
Four worked examples in SAT format. Read the approach, try it yourself, then tap Show the full solution.
1 · Find a percent of a number
A survey received 80 responses. If 35% of the respondents chose option A, how many respondents chose option A?
Approach "35% of 80" translates directly: turn the percent into a decimal and multiply. "Of" always means multiply.
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Answer: B
Why the other choices are wrong
A Uses 30% instead of 35%.
C Reads the percent itself as the count.
D Computes a larger percent (about 56%).
2 · Find a percent change
A store's daily sales rose from 40 units to 52 units. What was the percent increase in daily sales?
Approach Percent change is the size of the change divided by the original amount, times 100. The original is 40 — divide by that, not by 52.
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Answer: C
Why the other choices are wrong
A Reports the raw change (12) as if it were the percent.
B Divides by 52 (the new value) instead of 40.
D Uses the new total as the percent.
3 · Work backward from a percent
After a 25% discount, a jacket costs $60. What was the original price, in dollars?
Approach A 25% discount leaves 75% of the original. So $60 is 75% of the original price. Write that as an equation and divide — don't just add 25% back.
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Answer: C
Check: 25% of $80 is $20, and . ✓
Why the other choices are wrong
A Takes 25% of 60 and subtracts — discounting the sale price again.
B Adds 25% of 60 to 60, applying the percent to the wrong base.
D Adds a flat $25 instead of working from the percent.
4 · Percentage points vs. percent change
A candidate's approval rating rose from 20% to 30%. The increase of 10 percentage points represents what percent increase in the approval rating?
Approach Two different ideas hide here. The rating went up 10 percentage points (30 − 20). But the percent increase compares that change to the original 20 — a relative change. The question asks for the second.
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Answer: C
Going from 20 to 30 is a jump of half the original — a 50% relative increase, even though it's only 10 percentage points.
Why the other choices are wrong
A Reports the percentage-point change, not the percent increase.
B Uses the new value (30) as the answer.
D Divides by 15 (a midpoint) instead of the original 20.