2015 AMC 8
Complete problem set with solutions and individual problem pages
Problem 13 Medium
How many subsets of two elements can be removed from the set so that the mean (average) of the remaining numbers is ?
- A.
- B.
- C.
- D.
- E.
Answer:D
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 .
Think Academy Powered by ChatGPT