Art of Problem Solving

2014 AMC 8 Problems/Problem 4: Difference between revisions

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<math>\textbf{(A) }85\qquad\textbf{(B) }91\qquad\textbf{(C) }115\qquad\textbf{(D) }133\qquad \textbf{(E) }166</math>
<math>\textbf{(A) }85\qquad\textbf{(B) }91\qquad\textbf{(C) }115\qquad\textbf{(D) }133\qquad \textbf{(E) }166</math>


==Video Solution by OmegaLearn==
==Video Solution (CREATIVE THINKING)==
https://youtu.be/NW_rCdTO19w
 
~Education, the Study of Everything
 
 
==Video Solution ==
https://youtu.be/6xNkyDgIhEE?t=580
https://youtu.be/6xNkyDgIhEE?t=580
~ pi_is_3.14


==Video Solution 2==
==Video Solution 2==

Revision as of 10:16, 2 July 2023

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

See Also

2014 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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