saswata4s wrote:

In a certain group of women, 70 percent of the women were employed and 25 percent did not have a graduate degree. Which of the following statements cannot be true?

I. No woman in the group who had a graduate degree was unemployed

II. Less than half of the women in the group were employed and had a graduate degree

III. The number of unemployed women with a graduate degree was 50 percent greater than the number of employed women without a graduate degree

A) I only

B) II only

C) III only

D) I and III only

E) II and III only

Ans - A,

Assuming that only Employed/Unemployed and Degree/No degree classes exist.

70% Unemployed so 30% employed and 75% college degree so 25% no college degree.

1. No woman in the group who had a graduate degree was unemployed

70% unemployed and 75% college degree. We need to exhaust either of the two to prove statement 1 correct. It is not possible to do so at both are more than 50%. So Cannot be true.

2. Less than half of the women in the group were employed and had a graduate degree

Let all the 30% Unemployed have a college degree. So the remaining % of persons with a college degree is 45. Statement 1 can be true.

3. The number of unemployed women with a graduate degree was 50 percent greater than the number of employed women without a graduate degree.

Just try to fit in the above scenario.

Let 10% be employed with no college degree. So 50% higher means 15% are unemployed with a graduate degree.

So remaining,

60% - employed

60% - college degree

15% - unemployed

15% - no college degree

So rest 60% employed and college degree and 15% unemployed and no college degree. So statement 3 can be proved.

Thus Statement A only cannot be proved.

IMO: A