sanju09 wrote:A university has 2,000 faculty members all of whom have a masters degree, and some of whom also have a doctorate. 35 percent of the faculty members are female. What fraction of the faculty members are female doctorate holders?

1. 20 percent of the male faculty members have a doctorate.
2. A total of 1140 faculty members have only a masters degree.

[spoiler]Source: majortests.com[/spoiler]

Here's how one should go about solving this DS question

What do we know: total = 2000, all have Masters, 35% female
--> we know the number of male faculty and the number of female faculty... nothing else

Statement 1

1. 20 percent of the male faculty members have a doctorate.

ok, they only talk about male..gives us nothing about female doctorates... eliminated.. choices A and D are out!

Statement 2

2. A total of 1140 faculty members have only a masters degree.

ok, this is a bit better... but again, nothing specific to female doctorates... eliminated.. choice B is out.. left with C and E

Statements 1 & 2 combined

1. 20 percent of the male faculty members have a doctorate.
2. A total of 1140 faculty members have only a masters degree.

ok, (1) gives total no. of non-doctorates... from which we can find out total no. of doctorates
cool, (2) can give info about female doctorates... well, not directly.. but it gives us % of males who are doctorates...
from this, we can find total no. of male doctorates and then subract this from the total no. of doctorates to get the number of female doctorates... this is enough to get the answer... both combined are sufficient to answer the question --> [spoiler]answer is (C)[/spoiler]