Data Sufficiency

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

1. The avg score for men was less than 75
2. The group consisted of more men than women

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

1. The avg score for men was less than 75
2. The group consisted of more men than women

Statement 1: The average score for the men was less than 75.
Tells us only that the average score for the women was greater than 80.

Case 1: 1 man + 1 woman, sum = 2*80 = 160.
Let the man's score = 10.
Then the woman's score = 150.

Case 2: 10 men + 100 women, sum = 110*80 = 8800.
Let the men's average = 70, for a sum of 10*70 = 700.
Sum of the women's scores = 8100.
Women's average = 8100/100 = 81.

Since in the first case the average for the women is greater than 85, and in the second case the average for the women is less than 85, INSUFFICIENT.

The cases above illustrate that the average for the women depends on TWO variables:
1. The DISTANCE between the average for the men and the average for the whole group.
2. The RATIO of men to women -- in other words, how much WEIGHT is given to the men's average.

Statement 2: The group consisted of more men than women.
No way to determine the average for the women.

Statements 1 and 2 combined:
Here we have information about the two variables discussed above.
The DISTANCE between the average for the men and the average for the whole group is greater than 5.
Since there are more men than women, more WEIGHT is being given to the average for the men.
Thus, to compensate, the distance between the average for the women and the average for the whole group must also be greater than 5 -- in fact, it must be greater than the distance between the average for the men and the average for the whole group.
Thus, the average for the women must be greater than 85.
SUFFICIENT.

The correct answer is C.

To illustrate why the two statements combined are sufficient, let's examine two more cases.

If there were an equal number of men and women, and the men's average were exactly 75, then the women's average would be exactly 85.

Case 3: 1 man + 1 woman, sum = 2*80 = 160.
Let the man's score = 75.
Then the woman's score = 85.

But when the statements are combined, the relative number of men INCREASES, and their average score is LESS than 75.
Because MORE WEIGHT is being given to the men's lower scores, the average for the women must compensate by being GREATER than 85.

Case 4: 2 men + 1 woman, sum = 3*80 = 240.
Let's the men's average score = 70, for a sum of 2*70 = 140.
Then the woman's score = 100.

Case 4 illustrates that the average for the women must be GREATER than 85.