2021 AMC 12B Problems/Problem 10
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Contents
Problem
Two distinct numbers are selected from the set so that the sum of the remaining
numbers is the product of these two numbers. What is the difference of these two numbers?
Solution
The sum of the first integers is given by
, so
.
Therefore,
Rearranging,
Looking at the possible divisors of ,
and
are within the constraints of
so we try those:
Therefore, the difference , choice E).
~ SoySoy4444
Video Solution by Punxsutawney Phil
https://YouTube.com/watch?v=yxt8-rUUosI&t=292s
Video Solution by OmegaLearn (Simon's Favorite Factoring Trick)
~ pi_is_3.14
See Also
2021 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
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 AMC 12 Problems and Solutions |
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