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Problem 118

Number theory Difficulty 1.3 Multiple choice CEMC Fermat · Canada · 2013

Which number from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$ must be removed so that the mean (average) of the numbers remaining in the set is 6.1?

Pick one

Official solution

The original set contains 11 elements whose sum is 66.

When one number is removed, there will be 10 elements in the set.

For the average of these elements to be 6.1, their sum must be $10 \times 6.1 = 61$ .

Since the sum of the original 11 elements is 66 and the sum of the remaining 10 elements is 61, then the element that has been removed is $66-61=5$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.