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CEMC Pascal

Algebra Difficulty 2.3 Junior Find the answer

Which number from the set {1,2,3,4,5,6,7,8,9,10,11}\{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?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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 10×6.1=6110 \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 must be removed is 66−61=566-61=5.

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