Data Sufficiency

In a certain senior class, 72 percent of the male students and 80 percent of the female students have allplied to collega. What fraction of the student in the senior class are male?

(1) There are 840 students in the senior class.
(2) 75 percent of the students in the senior class have applied to college.

Please explain your answer choice

erdnah wrote:In a certain senior class, 72 percent of the male students and 80 percent of the female students have allplied to collega. What fraction of the student in the senior class are male?

(1) There are 840 students in the senior class.
(2) 75 percent of the students in the senior class have applied to college.

Please explain your answer choice

IMO Ans is C

Suppose there are X male students and Y female students

Stmt 1 => X+Y = 840 no further info so NOT SUFF

Stmt 2 => 75*840/100 students have applied to college NOT SUFF

Both together
72*X/100 + 80*Y/100 = 75*840/100

Above eq with stmt 1 can be solved for X and fraction of male students can be calculated... SO C

What's the OA?

OA is B.

I think I found the way (with you're help):
0.72m + 0.8f = y (All appliciants)
m + f = x (All students)

Since we're looking for m/x:
(0.72m + 0.8f) / x = 0.75 / 1

We can plug in f = x - m:
(0.72m + 0.8(x - m)) / x = 0.75
0.72m + 0.8x - 0.8m = 0.75x
-0.08m = -0.05x
1.6m = x
= 62,5% male

Is this correct? Is there an easier way? I can't get rid off that feeling...

Oh yeah, that's correct.. stmt 2 itself is suff

That tells me I need to be more vigilant... :roll:

That's the method I used...

How about looking at it like this :

1> Insufficient.. not going into details..

2> Since we only need to find out the fraction of male students, and are not concerned with the actual number:

Lets say total number of students = 100
75% have applied = 75 students

Let number of male students = x
No. of female students = 100-x

Based on the fact that 72% male, and 80% female students applied, we now have Total number of applicants =
(72*x/100) + 80*(100-x)/100
Equating =>
(72*x/100) + 80*(100-x)/100 = 75
solving : x = 500/8

Therefore fraction of Male applicants =
x/100 = 500/(8*100) = 5/8

Hence 2 alone is enough