Rates
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SAT Math › Rates
A value is decreased by $p$ percent and then increased by $p$ percent, resulting in an overall decrease of 9%. What is $p$?
9
18
30
45
Explanation
The net factor is $(1 - p/100)(1 + p/100) = 1 - (p/100)^2 = 0.91$, so $p/100 = 0.3$ and $p = 30$. 9 and 18 treat the changes as additive or half of 9%, and 45 is an overcorrection.
After a 25% discount and then an 8% sales tax on the discounted price, a customer pays 162. What was the original price?
150
195.2
200
216
Explanation
Let $x$ be the original price: $x * 0.75 * 1.08 = 162$, so $x = 162/0.81 = 200$. 216 ignores the discount, 195.2 wrongly combines 25% off and 8% tax as a net 17% off, and 150 ignores the tax.
A city's recycling rate increased from 48% to 60%. By how many percentage points did it increase?
0.12
1.25
12
25
Explanation
Percentage-point change is 60 - 48 = 12. 25% is the percent increase relative to 48%, 0.12 is the decimal form, and 1.25 is the multiplier.
A gym membership fee increases from 80 to 92. What is the percent increase?
1.15
12
13
15
Explanation
Percent increase is (92 - 80)/80 * 100 = 15. 12 is the absolute difference, 13 uses the new price as the base, and 1.15 is the multiplier, not the percent.
A store charges 8% sales tax on a purchase of 75. What is the sales tax amount?
6
8
67
81
Explanation
Sales tax is 0.08 * 75 = 6. 8 treats the percent as dollars, 81 is the total with tax, and 67 subtracts 8 dollars instead of taking 8%.
A jacket is discounted 25% from an original price of 80. What is the sale price?
20
55
60
75
Explanation
25% of 80 is 20, so the sale price is 80 - 20 = 60. 20 is just the discount, 55 subtracts 25 dollars instead of 25%, and 75 reflects a 5% decrease, not 25%.
A stock price decreases by 30% one day and increases by 30% the next day. What is the net percent change relative to the original price?
-9%
-4%
0%
9%
Explanation
The overall factor is 0.70 × 1.30 = 0.91, which is a 9% decrease. The other choices assume the changes cancel, average the percents, or ignore direction.
A city's recycling rate increased from 32% to 40% in one year. By what percent did the rate increase?
8%
20%
25%
40%
Explanation
Percent increase = (40 − 32) ÷ 32 × 100 = 25%. The distractors confuse percentage points (8%), use the wrong base (20% from 8/40), or mistake the final rate for the change (40%).
In a class of 48 students, 18 are seniors. What percent of the class are seniors?
18%
37.50%
48%
62.50%
Explanation
18 ÷ 48 = 0.375 = 37.5%. The other options either use the wrong base or give the complement instead.
A thermometer reads 212°F when the actual temperature is 200°F. What is the percent error relative to the actual temperature?
5%
6%
10%
12%
Explanation
Percent error = |212 − 200| / 200 × 100 = 6%. The other choices use the wrong base or confuse the absolute difference with a percent.