In a basketball shooting competition, each competitor shoots ten balls which are numbered from 1 to 10. The number of points earned for each successful shot is equal to the number on the ball. If a competitor misses exactly two shots, which one of the following scores is not possible?
(A) 52
(B) 44
(C) 41
(D) 38
(E) 35
In a basketball shooting competition, each competitor shoots ten balls which are numbered from 1 to 10. The number of points earned for each successful shot is equal to the number on the ball. If a competitor misses exactly two shots, which one of the following scores is not possible?
(A) 52
(B) 44
(C) 41
(D) 38
(E) 35

## Solution

If all ten balls scored, a score of 55 is possible.

If ball 1 and 2 is missed the maximum possible score is 52. Similarly, if 9 and 10 are missed, the minimum score is 36 . Every score between 36 and 52 is also possible. Of the listed scores, 35 is the only score that is not possible.

ANSWER: (E)