Difference between revisions of "2014 AMC 8 Problems/Problem 4"
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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> | ||
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+ | ==Video Solution== | ||
+ | https://youtu.be/6xNkyDgIhEE?t=580 | ||
==Solution== | ==Solution== | ||
− | 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>. | + | 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
Contents
Problem
The sum of two prime numbers is . What is the product of these two prime numbers?
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 . The other prime number is , and the product of these two numbers is .
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.