1996 AMC 8 Problem 12

Attempt Problem 12 of the 1996 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1996 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

12.

What number should be removed from the list
1,2,3,4,5,6,7,8,9,10,111, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
so that the average of the remaining numbers is 6.1?6.1?
44
55
66
77
88
Answer: B
Concepts:meanwork backwards
Small hint:
The eleven numbers add up to 6666
Big hint:
Ten numbers averaging 6.16.1 must total 61;61; find what was removed
Solution:
The sum of 11 through 1111 is 66.66. For ten numbers to average 6.1,6.1, their sum must be 10⋅6.1=61.10 \cdot 6.1 = 61.
So the removed number is 66−61=5.66 - 61 = 5.
Thus, the correct answer is B .
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