Track / Stage 3 / 48 of 260 #48 of 2000

Problem 48

AMC 10/12, early questions

Number theory Difficulty 3.2 Find the answer

In how many ways can $47$ be written as the sum of two primes?
$\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 3 \qquad \text{(E)}\ \text{more than 3}$

Your answer

Official 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 $\rightarrow \boxed{\text{A}}$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.