Sets /Table Method

[sukhman]

Is the ratio of mean income of women without a college education to the mean income of men without a college education greater than 2 to 1 ?
1) Mean income of all women $ 6800 vs all men $ 11,800
2) Mean income of college educated women $ 10,400 vs college educated men $ 17,200

[MartyMurray]

Statement 1:

This provides no information on the mean incomes of those women and men without college educations.

Insufficient.

Statement 2:

This provides information only on the mean incomes of women and men who are college educated.

Insufficient.

Statements Combined:

Since the mean income of college educated women is higher than that of all women, the mean income of women without a college education must be lower than the mean income of all women.

Similarly, since the mean income of college educated men is higher than that of all men, the mean income of men without a college education must be lower than the mean income of all men.

So the maximum possible income of women without a college education is just below $6800 and the maximum of men without a college education is just below $11,800. So it is possible for the answer to the question to be "No."

At the same time, the proportions of college educated and not college educated people of each gender makes a difference.

For instance, if 1/3 of men are not college educated men and 2/3 are college educated, then in order to create a weighted average of 11,800, we need the not college educated men to have a mean income of 1000, which is less than 1/2 of the theoretical maximum mean income of not college educated women, which is just below 6800.

So the answer to the question could be "Yes."

So combined the statements support two different answers to the question.

Insufficient.

The correct answer is E.