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1999 CEMC Gauss (Grade 7) Problems/Problem 14

Problem

Which of the following is an odd integer, contains the digit $5$, is divisible by $3$, and lies between $12^2$ and $13^2$?

$\text{(A)}\ 105 \qquad \text{(B)}\ 147 \qquad \text{(C)}\ 156 \qquad \text{(D)}\ 165 \qquad \text{(E)}\ 175$

Solution

$156$ is even, so it cannot be the answer.

$147$ does not contain the digit $5$, so it can be eliminated. This means the answer must be A, D, or E.

We have $12^2 = 144$ and $13^2 = 169$. The only remaining answer that is between those two numbers is $\boxed {\textbf {(D)} 165}$.

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