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 (CREATIVE THINKING)

https://youtu.be/NW_rCdTO19w

~Education, the Study of Everything

Video Solution

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

Video Solution 2

https://youtu.be/abjnpBM1RYg

~savannahsolver

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 $83\cdot2=\boxed{\textbf{(E)}~166}$ .

2014 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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