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

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==Solution==
 
==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{166}</math>.
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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>.
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==Video Solution (CREATIVE THINKING)==
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https://youtu.be/NW_rCdTO19w
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 +
~Education, the Study of Everything
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 +
 
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==Video Solution ==
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https://youtu.be/6xNkyDgIhEE?t=580
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==Video Solution 2==
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https://youtu.be/abjnpBM1RYg
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~savannahsolver
  
 
==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}}

Latest revision as of 23:36, 11 December 2023

Problem

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

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

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

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

See Also

2014 AMC 8 (Problems • Answer Key • Resources)
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

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

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