1983 AHSME Problems/Problem 3

Problem 3

Three primes $p,q$ , and $r$ satisfy $p+q = r$ and $1 < p < q$ . Then $p$ equals

$\textbf{(A)}\ 2\qquad \textbf{(B)}\ 3\qquad \textbf{(C)}\ 7\qquad \textbf{(D)}\ 13\qquad \textbf{(E)}\ 17$

Solution

We are given that $p,q$ and $r$ are primes. In order to sum two another prime, either $p$ or $q$ has to be even, because the sum of an odd and an even is odd. The only odd prime is $2$ , and it is also the smallest prime, so therefore, the answer is $\fbox{\textbf{(A)}2}$ .

1983 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 4
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1983 AHSME Problems/Problem 3

Problem 3

Solution

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