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# In a certain senior class, 72 percent of the male students

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Manager
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In a certain senior class, 72 percent of the male students [#permalink]

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21 May 2010, 11:26
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Question Stats:

51% (01:42) correct 49% (01:33) wrong based on 47 sessions

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In a certain senior class, 72 percent of the male students and 80 percent of the female students have applied to college. What fraction of the students in the 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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-a-certain-senior-class-72-percent-of-the-male-students-128279.html
[Reveal] Spoiler: OA
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Re: Gmat prep test question [#permalink]

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21 May 2010, 11:48
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You can figure it out by (2) alone because you can just take the two stats to arrive at the correct fraction*, regardless of knowing the total class amount. You would need (1) if it had asked "how many male students were in the class?"

*P(Male and Applied) / P(Applied) = P(Male)
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Re: Gmat prep test question [#permalink]

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21 May 2010, 11:51
Nice, thanks I cant believe I missed this one.
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Re: Gmat prep test question [#permalink]

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21 May 2010, 11:57
No problem, happens to the best of us
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Re: Gmat prep test question [#permalink]

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21 May 2010, 11:59
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marcusaurelius wrote:
In a certain senior class, 72 percent of the male students and 80 percent of the female students have applied to college. What fraction of the students in the 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.

oa is B

I chose c.

Yes I agree. You can figure out the answer using only 2)

What we need to find out ? --> fraction of male students

What we already know ? --> 72 percent male and 80 percent females have applied

2) 75 percent of class applied for college. Ok now look at the percent of males and females applied i.ie 72 and 80

the difference = 80 - 72 = 8

Now the final percentage = 75

This means that in this percentage there were more males in the class to shift the percentage towards them. Think of this: what if the percentage of males and females were same then the final percentage would have been 76.

Anyways back to our example

Thus the shift is 5/8 in favor of males to pull the percentage 3/8 towards males. Thus males percentage = 5/8 = 62.5%

Note: See if you learn this method you might not have to do the lengthy algebraic calculations. This can be done in 20 seconds with practice.
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Re: Gmat prep test question [#permalink]

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21 May 2010, 12:04
Great, thank you. When I was reading through the problem I think I assumed they were asking for the number of males rather than the percentage.
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Re: Gmat prep test question [#permalink]

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21 May 2010, 13:10
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marcusaurelius wrote:
Great, thank you. When I was reading through the problem I think I assumed they were asking for the number of males rather than the percentage.

I think you must have! Sorry if this repeats what others have said, but here's a solution that illustrates that pitfall, with a little additional commentary on Weighted Averages.

With just the info from the question stem, the overlapping sets chart looks like this. The question is “What is m/Total?” (or, “What is m/(m+f)?”)

------Have-----Haven’t----Total
M----0.72m-----0.28m-----m
F-----0.8f--------0.2f-------f
Total------------------------m+f

(1) Tells us that m+f = 840, but nothing about how the 840 splits between m and f.

(2) If 75% of students have applied to college, let’s put that expression in the chart:
---------Have--------Haven’t-------Total
M-------0.72m--------0.28m--------m
F--------0.8f-----------0.2f----------f
Total--0.75(m+f)---0.25(m+f)----m+f

We can pull two new equations out of the vertical Have and Haven’t columns:
0.72m + 0.8f = 0.75(m+f)
0.28m + 0.2f = 0.25(m+f)

Multiply everything by 100 to avoid dealing with decimals.
72m + 80f = 75(m+f)
28m + 20f = 25(m+f)

Move all m’s and f’s to one side:
-3m + 5f = 0
3m + -5f = 0

When we add the equations we get 0=0. Yikes! This is why you would conclude that (2) is insufficient!

All the math we’ve done so far is right, but there are two things we have overlooked:
a. We haven’t made full use of the fact that m and f are tightly related to one another, because there’s not a third gender (in this problem): m = total –f and f = total –m.
b. We were trying to solve for m and f. But our question is really about m/total. For combo problems (where you are solving for not one variable, but an expression with 2 or more), the “trick” is to solve for the combo as directly as you can.

So let’s back up to this:
---------Have--------Haven’t-------Total
M-------0.72m--------0.28m--------m
F--------0.8f-----------0.2f----------f
Total--0.75(m+f)---0.25(m+f)----m+f

Pull out that vertical sum from the “Have” column, and rewrite the f’s in terms of m.
0.72m +0.8f = 0.75(Total students)
0.72m + 0.8(Total students – m) = 0.75(Total students)
72m + 80(Total students) – 80m = 75(Total students)
5(Total students) = 8m
5/8 = m/Total students

5/8 of the students are male.

As others have noted, there is a “weighted average” insight we could have exploited. The “weighted average” formula here is:
(Fraction of the class that is male)*(male application rate) + (Fraction of the class that is female)*(female application rate = overall application rate.

Here’s another post I wrote on the subject:
weighted-average-problems-93260.html#p717555
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Re: Gmat prep test question [#permalink]

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21 May 2010, 14:32
Wow, awesome! thanks
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Re: Gmat prep test question [#permalink]

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24 May 2010, 10:00
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This ways is very conventional and fast. Put X like the total of all student in the class.SO the total of students aplly for college is 0.75 X. M is the total male student( inclduing not apply and aplly). thus the total girl wil be X- M, so the Male students apply is 0.72 M. the Female stduents that appliied will be 0.8(X-M)
----> 0.75X = 0.72 M +0.8(X-M)
----->solve this, it's going to be 0.05 X=0.08 M
------> M/X= 0.05/0.08 which means 5/8

Everything could be written to equation to be solved!!!!!!!!!!!!!!!!!!
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Re: In a certain senior class, 72 percent of the male students [#permalink]

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12 Oct 2013, 16:59
marcusaurelius wrote:
In a certain senior class, 72 percent of the male students and 80 percent of the female students have applied to college. What fraction of the students in the 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.

oa is B

I chose c.

Hi all, this problem shouldn't take more than 30 seconds.
We need to learn the concept of differentials and weighted average.

The weighted average is nothing but the average points weighted on each element. Therefore if we have the two data points in this case the percentage of males and percentage of females and there are given the total percentage we can find the ratio of the males/females easily.

Note that we only need the percentage or average. We don't really need to know the concrete values
Therefore, Statements like 1 will always be insufficient for this type of problems

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Re: In a certain senior class, 72 percent of the male students [#permalink]

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12 Oct 2013, 17:04
In a certain senior class, 72 percent of the male students and 80 percent of the female students have applied to college. What fraction of the students in the senior class is male?

Question: $$\frac{m}{m+f}=?$$ (so we are asked about #3)

(1) There are 840 students in the senior class --> $$m+f=840$$. Useless info. Not sufficient.

(2) 75 percent of the students in the senior class have applied to college. We know 2 from the stem and 1 from this statement, sufficient to get 3. Just to illustrate: $$0.72m+0.8f=0.75(m+f)$$ --> $$3m=5f$$ --> $$\frac{m}{f}=\frac{5}{3}$$ --> $$\frac{m}{m+f}=\frac{5}{8}$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-a-certain-senior-class-72-percent-of-the-male-students-128279.html
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Re: In a certain senior class, 72 percent of the male students   [#permalink] 12 Oct 2013, 17:04
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