1980 AHSME Problems/Problem 15

Problem

A store prices an item in dollars and cents so that when 4% sales tax is added, no rounding is necessary because the result is exactly $n$ dollars where $n$ is a positive integer. The smallest value of $n$ is

$\text{(A)} \ 1 \qquad \text{(B)} \ 13 \qquad \text{(C)} \ 25 \qquad \text{(D)} \ 26 \qquad \text{(E)} \ 100$

Solution

Since when the sales tax is calculated, it as to be an integer, that means that $\frac{1}{25}n$ has to be an integer. The smallest positive non zero number that this can is occur is $\fbox{\text{(C)25}}$

1980 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Problem 16
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1980 AHSME Problems/Problem 15

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