abhasjha wrote:At a certain high school, there are 20 more female sophomores than male sophomores.How many of the female sophomores are studying geometry?

(1) 20 percent of all the sophomores are studying geometry
(2)15 percent of the male sophomores are studying geometry

The question stem requires that there be 20 more female sophomores than male sophomores.
The following cases satisfy both statements.

Case 1: Male sophomores = 100, Female sophomores = 120
Statement 1: Total sophomores studying geometry = .2(220) = 44.
Statement 2: Male sophomores studying geometry = .15(100) = 15.
In this case, female sophomores studying geometry = 44-15 = 29.

Case 2: Male sophomores = 200, Female sophomores = 220
Statement 1: Total sophomores studying geometry = .2(420) = 84.
Statement 2: Male sophomores studying geometry = .15(200) = 30.
In this case, female sophomores studying geometry = 84-30 = 54.

Thus, when the statements are combined, the number of female sophomores studying geometry can be different values.
INSUFFICIENT.

The correct answer is E.

I believe this question could be answered fast if you look the big picture. Question stem is looking for the number of certain group of sophmores. However, from the question stem and from both statements we have only relations between groups. This is in 99% clear sign that there could be a lot of combinations for the solution and therefore the correct answer is E.