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