2014 AMC 8 Problems/Problem 4

Problem

The sum of two prime numbers is $85$. What is the product of these two prime numbers?

$\textbf{(A) }85\qquad\textbf{(B) }91\qquad\textbf{(C) }115\qquad\textbf{(D) }133\qquad \textbf{(E) }166$

Video Solution

https://youtu.be/6xNkyDgIhEE?t=580

Solution

Since the two prime numbers sum to an odd number, one of them must be even. The only even prime number is $2$. The other prime number is $85-2=83$, and the product of these two numbers is $83\cdot2=\boxed{\textbf{(E)}~166}$.

See Also

2014 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
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All AJHSME/AMC 8 Problems and Solutions

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