1996 AMC 8 Problem 18

Attempt Problem 18 of the 1996 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1996 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

18.

Ana’s monthly salary was $2000\$2000 in May. In June she received a 20%20\% raise. In July she received a 20%20\% pay cut. After the two changes in June and July, Ana’s monthly salary was
$1920\$1920
$1980\$1980
$2000\$2000
$2020\$2020
$2040\$2040
Answer: A
Concepts:percentage
Small hint:
A 20%20\% raise multiplies by 1.2;1.2; a 20%20\% cut multiplies by 0.80.8
Big hint:
Apply both factors in turn: 2000⋅1.2⋅0.82000 \cdot 1.2 \cdot 0.8
Solution:
After the raise, the salary is 2000⋅1.2=2400.2000 \cdot 1.2 = 2400.
After the cut, it is 2400⋅0.8=1920.2400 \cdot 0.8 = 1920.
Thus, the correct answer is A .
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