1985 AJHSME Problems/Problem 21

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Problem

Mr. Green receives a $10\%$ raise every year. His salary after four such raises has gone up by what percent?

$\text{(A)}\ \text{less than }40\% \qquad \text{(B)}\ 40\% \qquad \text{(C)}\ 44\% \qquad \text{(D)}\ 45\% \qquad \text{(E)}\ \text{more than }45\%$

Solution

If he gets a $10\%$ raise, then his new salary is $1.1$ of what it was before. He gets $4$ raises, so his new salary is $1.1^4$ of the previous salary. We want to know the percent of increase from $1$, so we just need $1.1^4-1$ as a percent.

If you know your powers of $11$ well, then you can just do $1.4641-1=.4641>45\%$, so the answer is $\boxed{\text{E}}$

If you don't know this, then first we note that $1.1^4$ clearly does not have a whole number percent representation, so the only possible choices are $\text{A}$ and $\text{E}$. We also have \[1.1^4=1.21^2>1.2^2=1.44\]

so the percent is greater than $40\%$ and the only choice left is $\boxed{\text{E}}$.

See Also

1985 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 20
Followed by
Problem 22
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All AJHSME/AMC 8 Problems and Solutions