Question 1
From last year to this year, a store's weekly sales decreased from 250 to 125. By what percent did it change?
- A.
55%
- B.
100%
- C.
50%
- D.
125%
Answer: C. 50%
Percent change = |new - old|/old × 100 = 125/250 × 100 = 50%.
SAT · Math · Problem-Solving and Data Analysis
Percentages
Percentages is part of Problem-Solving and Data Analysis in the SAT Math section. The questions below are written in the style of the real test, each with the answer and a worked explanation.
Question types you will see here include find a percent of a quantity, percent increase or decrease, successive percent changes and work back to the original.
Common traps: treating 15% as 1.5; dividing by the part instead of the whole; rounding an intermediate value before the final step.
Sample questions
Question 2
From last year to this year, the number of volunteers at a food bank increased from 120 to 144. By what percent did it change?
- A.
24%
- B.
120%
- C.
16.7%
- D.
20%
Answer: D. 20%
Percent change = |new - old|/old × 100 = 24/120 × 100 = 20%.
- A.
Question 3
A poll of 900 randomly selected voters found that 46% support building a new metro line, with a margin of error of 3.5 percentage points. Based on the poll, what is the greatest plausible percent of all voters who support building the new metro line?
Enter your own answer.
Answer: 49.5
The plausible values run from 46 − 3.5 to 46 + 3.5 percent, so the greatest plausible percent is 46 + 3.5 = 49.5. Subtracting gives 42.5, which is the least plausible value, and treating 3.5 as a percent of 46 would give only about 47.6.
Question 4
A commuter can buy a monthly travel pass for $92 or pay $2.50 per ride. Last month the commuter took 46 rides. The price of the pass is what percent of what the 46 rides would cost at the pay-per-ride fare?
- A.
20
- B.
23
- C.
80
- D.
125
Answer: C. 80
The rides would cost 46 × 2.50 = $115, and 92/115 = 0.8, or 80% (C). A is the percent saved, not the percent the pass costs; B reports the $23 saving as if it were a percent; D divides 115 by 92, using the pass as the base.
- A.
Question 5
A sprinter's best 100-meter time decreased by 4% after a season of training. Her new best time is 11.52 seconds. What was her best time, in seconds, before the season?
- A.
11.06
- B.
11.98
- C.
12
- D.
15.52
Answer: C. 12
The new time is 96% of the old time, so the old time was 11.52 ÷ 0.96 = 12 seconds (C). 11.98 adds 4% of the new time instead of dividing, 11.06 takes another 4% off, and 15.52 adds 4 seconds instead of 4%.
- A.
Find your real gaps
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