Difference between revisions of "2015 AMC 8 Problems/Problem 13"
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<math>\textbf{(A)}\text{ 1}\qquad\textbf{(B)}\text{ 2}\qquad\textbf{(C)}\text{ 3}\qquad\textbf{(D)}\text{ 5}\qquad\textbf{(E)}\text{ 6}</math> | <math>\textbf{(A)}\text{ 1}\qquad\textbf{(B)}\text{ 2}\qquad\textbf{(C)}\text{ 3}\qquad\textbf{(D)}\text{ 5}\qquad\textbf{(E)}\text{ 6}</math> | ||
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==Solutions== | ==Solutions== | ||
Revision as of 01:19, 21 January 2023
Contents
Problem
How many subsets of two elements can be removed from the set 
so that the mean (average) of the remaining numbers is 6?
h
Solutions
Solution 1
Since there will be 
elements after removal, and their mean is 
, we know their sum is 
. We also know that the sum of the set pre-removal is 
. Thus, the sum of the 
elements removed is 
. There are only 
subsets of elements that sum to 
: 
.
Solution 2
We can simply remove 
subsets of numbers, while leaving only behind. The average of this one-number set is still , so the answer is .
-tryanotherangle
Video Solution
~savannahsolver
Video Solution by OmegaLearn
https://youtu.be/51K3uCzntWs?t=68
~ pi_is_3.14
See Also
| 2015 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 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. 
