1989 AJHSME Problems/Problem 16

Problem

In how many ways can $47$ be written as the sum of two primes?

$\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 3 \qquad \text{(E)}\ \text{more than 3}$

Solution

For $47$ to be written as the sum of two integers, one must be odd and the other must be even. There is only one even prime, namely $2$ , so one of the numbers must be $2$ , making the other $45$ .

However, $45$ is not prime, so there are no ways to write $47$ as the sum of two primes $\rightarrow \boxed{\text{A}}$ .

1989 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 15	Followed by Problem 17
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1989 AJHSME Problems/Problem 16

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