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

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

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.

@@ Line 1: / Line 1: @@
-''hello''
+==Problem==
+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>
+==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{\textbf{(E)}~166}</math>.
+==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==
+{{AMC8 box|year=2014|num-b=3|num-a=5}}
+{{MAA Notice}}

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