Data Sufficiency

sam2304 wrote:What fraction of this year's graduation students at a certain college are males?
(1) Of this year's graduation students, 35% of male and 20% of female transferred from another college.
(2) Of this year's graduation students, 25% transferred from another college.

OA: C

I have few doubts about this question.

The solution goes this way
Both statements themselves are INSUFF.
With 1 and 2
0.35M + 0.2F = 0.25(M+F)
0.10M = 0.05F
So now we get the ratio of males/overall of those who got transferred

My doubt is "the question asks for what fraction of graduates are males ?" and what we got is related to only those who have transferred from another college i.e only 25%.
Why can't the other 75% have a different ratio ?

Say out of 100 students 25 are transferred from another college and we have their male/female split up but what about the rest of 75 students, what if there are only 10 males and 65 females ?

How can the ratio for the other be same to those who have got transferred ?

How can the above solution help in answering the question ?
Am i missing something here ?

Any advice would be very helpful

Hey sam2304,

You're on the right track with this one - you just forgot what your variables stand for.

You let M = all male graduates
and you let F = all female graduates

The target question asks, "What fraction of this year's graduation students at a certain college are male?" In other words, we want the value of M/(M+F)

Statement 1:
You wrote: Total number of graduates who transferred = 0.35M + 0.2F
Since this info is not enough to find the value of M/(M+F), statement 1 is INSUFFICIENT

Statement 2:
You wrote: Total number of graduates who transferred = 0.25(M+F)
Since this info is not enough to find the value of M/(M+F), statement 2 is INSUFFICIENT

Statements 1 & 2:
Since you have 2 algebraic expressions for "Total number of graduates who transferred", you combined them to get: 0.35M + 0.2F = 0.25(M+F)
After some manipulation, you got: 0.10M = 0.05F (Perfect)

At this point, I suggest multiplying both sides by 20 to get 2M = F
From here, we can find the value of M/(M+F)
Since 2M = F, we can replace F with 2M to get: M/(M+F) = M/(M+2M)= M/3M = 1/3

Since we can now find the value of M/(M+F), statements 1&2 combined are SUFFICIENT

So, the OA = C

Cheers,
Brent