Difference between revisions of "2014 AMC 8 Problems/Problem 4"

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==Problem==
 
The sum of two prime numbers is <math>85</math>. What is the product of these two prime numbers?
 
The sum of two prime numbers is <math>85</math>. What is the product of these two prime numbers?
  
 
<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>
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==Video Solution==
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https://youtu.be/6xNkyDgIhEE?t=580
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==Solution==
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Since the two prime numbers sum to an odd number, one of them must be even. The only even prime number is <math>2</math>. The other prime number is <math>85-2=83</math>, and the product of these two numbers is <math>83\cdot2=\boxed{\textbf{(E)}~166}</math>.
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2014|num-b=3|num-a=5}}
 
{{AMC8 box|year=2014|num-b=3|num-a=5}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 22:26, 12 August 2020

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
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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