Hi All,

By TESTing VALUES, you can prove the answer to this question changes.

We're told that there are 20 MORE female sophomores than male sophomores. We're asked how MANY female sophomores study geometry.

From the prompt, we can create the equation...

F = M + 20

Fact 1: 20% of all sophomores study geometry.

This provides a minor restriction - since 20% of ALL sophomores study geometry, the total number of sophomores has to be a MULTIPLE of 5. For example 20% of 8 is 1.6 and you can't have "0.6" students, so there CAN'T be 8 total students.

IF....

M = 5

F = 25

We know that 20%(30) = 6 students study geometry, BUT we don't know how many of those 6 are female.

Fact 1 is INSUFFICIENT

Fact 2: 15% of the male sophomores study geometry.

This gives us NO information on the number of females studying geometry.

Fact 2 is INSUFFICIENT

Combined, we know...

F = 20 + M

F + M is a multiple of 5

20%(F+M) study geometry

15%(M) study geometry

By extension, the number of males MUST be a multiple of 20, since 15% of the males study geometry and multiples of 20 are the ONLY values that give us an INTEGER number of males.

eg. 15%(20) = 3 students

eg. 15%(21) = 3.15 students which is NOT possible

While this might appear to be a lot of information, it's still not enough to get us a consistent answer. Here's proof:

M = 20

F = 40

(F+M) = 60

15%(20) = 3 males study geometry

20%(60) = 12 students study geometry

12 - 3 = 9 females study geometry

As we increase the total number of students, the total number of females and males who study geometry WILL increase...

M = 40

F = 60

(F+M) = 100

15(40) = 6 males study geometry

20%(100) = 20 students study geometry

20 - 6 = 14 females study geometry

Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,

Rich

This is great explanation indeed. Can really well relate to it.