Data Sufficiency

BTGmoderatorDC wrote:At a certain company, a test was given to a group of men and women seeking for promotions. If the average (arithmetic mean) score for the group was 80, was the average score for the women more than 85?

(1) The average score for the men was less than 75.
(2) The group consisted of more men than women.

OA C

Source: Official Guide

Say

> the average score of men = x;
> the average score of women = y;
> the number of men = m;
> the number of women = w

Thus, total score of the group = mx + wy
Average score of the group = (mx + wy)/(m + w) = 80

We have to determine whether y > 85

Let's take each statement one by one.

(1) The average score for the men was less than 75.

=> x < 75. No information about the average score of men and/or the number of men/women. Insufficient.

(2) The group consisted of more men than women.

=> m > w. No information about the average scores. Insufficient.

(1) and (2) together

Since there are more men than women with their average score less than by more than 5 [> (80 - 75)] from the group's average score (80), to maintain the average score of the group = 80, the fewer women than men must have their average score greater than 80 by at least 5 points. This implies that the average score of women is greater than 85. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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