At a certain high school there 20 more female sophomores

for such kind of Problems , Grid method is of utmost useful.
i am unable to attach the grid, sorry for that.
By drawing grid for the above problem ,we can see that the number of female sophomores studying geometry can be different values.

Can anyone help further to approach this problem.

Any expert/ moderator ?

Bunuel : Can you suggest a fast way to approach this problem.

Given:
m = number of males, hence
m+20 = number of females
Question:
determine x%(m+20) (the number of females studying geometry).

1) 20 percent of all the sophomores are studying geometry -> tells you nothing about the females, spec -> not suff
2) 15 percent of the male sophomores are studying geometry -> again, have nothing on the females, spec-> not suff
1,2) means that 15% of the male and some of the female (an x percentage) make up to 20% of total
15%m+x%(m+20) = 20%(2m+20)
x%(m+20)=25%m+4; still indefinite -> not suff.

hope this helps.

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.

Thank you EMPOWERgmatRichC

I arrived to the correct answer through the grid method. Still, I found it a bit confusing. Anyone is kind enough to post the grid method?

Best,

Kindly check the attachment, and please excuse the handwriting. Hope it helps

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