BTGmoderatorDC wrote:The 10 students in a history class recently took an examination. What was the maximum score on the examination?

(1) The mean of the scores was 75.
(2) The standard deviation of the scores was 5.

Given: 10 students in a history class recently took an examination

We have to find out the maximum score on the examination.

Let's take each statement one by one.

(1) The mean of the scores was 75.

Certainly not sufficient as there cannot be a unique value for the maximum score. If each of the 10 students scores 75, then the maximum score is 75; however, if one of them scores 70, each of the 10 students scores 75 and one of them scores 80, the mean is 75 and the maximum score is 80. There can be many answers. Insufficient.

(2) The standard deviation of the scores was 5.

Certainly not sufficient as merely with this information, we cannot get the value of the maximum score.

(1) and (2) together

Though computation of Standard Deviation is not within the scope of the GMAT, its interpretation and analysis are.

We have three data points

1. Number of students = 10
2. Mean score = 75
3. SD = 5

Case 1: Say the scores of 10 students are: X, 75, 75, 75, 75, 75, 75, 75, 75, and Y. The values of X and Y are such that the SD of the scores = 5. The maximum score would be Y; Y can be computed, we need not calculate it.

Case 2: Say the scores of 10 students are: P, X, 75, 75, 75, 75, 75, 75, Y, and Q. The values of X, P, Q, and Y are such that the SD of the scores = 5. The maximum score would be Q.

Y ≠ Q (Not necessarily). No unique answer.

The correct answer: E

Hope this helps!

-Jay
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