djkvakin wrote:In a certain senior class, 72% of the male students and 80% of female students have applied to college. What fraction of the students in the senior class are male?
(1) There are 840 students in the senior class
(2) 75% of the students in the senior class have applied to college.

The official answer is B

Please explain why.

stmt1 : doesn't give much info about % of male or female (insufficient)
stmt2 : 75% is total of those who've applied for college but we don't know what is % of male or female within these 75% (insufficient)

using both and from information given in the question 72% of male and 80% of female have applied to college but we don't know what is their individual %. we should know at least one % to determine

Note 72% and 80% here will be subset of total male and female from total 75% but we don't know their individual % in this 75% lot

so E

The correct answer is definitely choice B, and this is yet another weighted average problem.

From the stem, 72% of the males, and 80% of the females applied to college. The second statement tells us that, overall, 75% of them applied to college.

Question. What if, overall, 76% applied to college? Because 76 is 4 units away from 72, and also 4 units away from 80, wouldn't it then be clear that half are males and half are females?

In the question, we have:

72...75.....80
(M)...........(F)

Because the overall average is only 3 units away from 72 (the males), but 5 units away from 80 (the females), there are clearly more males. In fact, the males to female proportion is exactly 5:3. Therefore, the male to total ratio is 5:8, and the second statement is sufficient by itself. (Because the overall average is closer to the male average, there must be more males "weighting" the average).

You can take this as a general takeaway. Let's call the grand average MEAN. If X is x units away from MEAN, and Y is y units away from MEAN, then the proportion X/Y is just y/x.

And because this is DS, you don't even need to compute the 5:8 ratio; instead, you just need to realize that you COULD compute the appropriate ratio.

amazing explanation testluv! thank you.

The quality of posts of instructors are always enlighting so I was going through the posts of Testluv and found this.

I think the explanations above are good but is it necessary ?

If Males = x and Females = y
from 2) we get

0.72x + 0.8 y = 0.75(x+y)
0.05y = 0.03 x
x/y = 5/3

Sufficient.

1) helps us to get the exact nos. but not necessary as Q asks only the fractions.

kstv wrote:The quality of posts of instructors are always enlighting so I was going through the posts of Testluv and found this.

I think the explanations above are good but is it necessary ?

If Males = x and Females = y
from 2) we get

0.72x + 0.8 y = 0.75(x+y)
0.05y = 0.03 x
x/y = 5/3

Sufficient.

1) helps us to get the exact nos. but not necessary as Q asks only the fractions.

Certainly, we can also solve the problem algebraically as you did. But if you understand the balanced average concept well, you can also answer this particular question very quickly without doing any scratchwork at all. And, we can apply this concept to a lot of average and weighted average problems (in particular within data sufficiency).

So, really it is not about whether an approach is "necessary"--whether you have to do it a certain way.

Instead, you want to be open to multiple approaches since most GMAT problems can be approached in multiple ways.

kstv wrote:The quality of posts of instructors are always enlighting so I was going through the posts of Testluv and found this.

I think the explanations above are good but is it necessary ?

If Males = x and Females = y
from 2) we get

0.72x + 0.8 y = 0.75(x+y)
0.05y = 0.03 x
x/y = 5/3

Sufficient.

1) helps us to get the exact nos. but not necessary as Q asks only the fractions.

Sorry, but x/y is not what the question was asking, isn't it?

"What fraction of the students in the senior class are male?", meaning x/(x+y). Am I right?

Thanks!