1996 AJHSME Problems/Problem 18

Problem

Ana's monthly salary was $$2000$ in May. In June she received a 20% raise. In July she received a 20% pay cut. After the two changes in June and July, Ana's monthly salary was

$\text{(A)}\ 1920\text{ dollars} \qquad \text{(B)}\ 1980\text{ dollars} \qquad \text{(C)}\ 2000\text{ dollars} \qquad \text{(D)}\ 2020\text{ dollars} \qquad \text{(E)}\ 2040\text{ dollars}$

Solution

Notice that a 20% raise translates to Ana's monthly salary multiplied by $(100 + 10)\% = 120\%$ , and a 20% pay cut translates to her salary multiplied by $100\% - 20\% = 80\%$ , so

$2000 \cdot 120\% = 2400$ $2400 \cdot 80\% = 1920 \rightarrow \boxed{\textbf{A}}$

~SpeedCuber7

1996 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 17	Followed by Problem 19
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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1996 AJHSME Problems/Problem 18

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