The scores of eight students on a quiz are $6,7,7,8,8,8,9$, and 10. Which score should be removed to leave seven scores with the same mode and range as the original eight scores, but with a higher average (mean)?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Since the range is unchanged after a score is removed, then the score that we remove cannot be the smallest or the largest (since each of these occurs only once). Thus, neither the 6 nor the 10 is removed. Since the mode is unchanged after a score is removed, then the score that we remove cannot be the most frequently occurring. Thus, the score removed is not an 8 .

Therefore, either a 7 or a 9 is removed.

Since we wish to increase the average, we remove the smaller of the two numbers, ie. the 7. (We could calculate that before any number is removed, the average is 7.875 , if the 7 is removed, the average is 8 , and if the 9 is removed, the average is 7.714 .)

Answer: (B)