In a certain senior class, 72 percent of the male students : GMAT Data Sufficiency (DS)
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# In a certain senior class, 72 percent of the male students

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

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15 Aug 2009, 19:13
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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 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
[Reveal] Spoiler: OA

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Re: What fraction of the students in the senior class are male? [#permalink]

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15 Aug 2009, 20:21
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B

First of all, we have a red flag in the problem: it is a %-problem and it does not tell us about any absolute value, only about % and fraction. So, if we have one DS-statement only with one absolute value, the statement is useless for solving the problem.

1) Yeah, it stands here to catch us.

2) How to determine sufficiency of the statement for a few seconds? Just try slightly to increase or decrease 75% in your mind, do you need to change a fraction? Of course, as you need to have more/less male/female ratio to decrease/increase 75%.
If it is difficult, the traditional solution:

75% = (72%*male + 80%*female)/(male + female) = (72% male/female+ 80%) / (male/female + 1) - we can find male/female fraction.

Now, male/(male + female) = 1 / (1 + female/male) - using information from the statement above, we can find the fraction of the students who are male.
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Re: What fraction of the students in the senior class are male? [#permalink]

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14 Oct 2009, 22:03
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If X is the FRACTION of the male students in the senior class, then 1-X is the fraction of female in class.

1) is not sufficient to solve the problem
2) from the provided information, we have:

0.72*X + 0.80*(1-X) = 0.75 <=> X = 5/8
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Re: What fraction of the students in the senior class are male? [#permalink]

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15 Oct 2009, 06:11
B

X are the students in the senior class. M and F are men and women respectively.

We have M+F=X.

And 0,72*M+0,82*F apply to college.

(1) M+F=840 n.s.

(2) (a) M+F=X

(b) 0,72*M+0,82*F=0,75*X
(b) => (a) and solve for M/X.
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Re: What fraction of the students in the senior class are male? [#permalink]

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12 Mar 2011, 22:55
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I got this problem wrong as usual...I HATE DS!

Anyway I checked the answer and it dawned on me that B is sufficient. However, I still cant seem to get 5/8, what am I doing wrong?
X = m + f where X is total number of students in college.
So from B) 75% of all students applied to college. Therefore we have 75% (X)
Now we know 72% male students applied to college, therefore the male number will be 72% of 75% of X
The fraction should be:
( 72% of 75% of X) / X
This gives me around 54/100 males attending college.
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Re: What fraction of the students in the senior class are male? [#permalink]

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13 Mar 2011, 01:56
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thesfactor wrote:
I got this problem wrong as usual...I HATE DS!

Anyway I checked the answer and it dawned on me that B is sufficient. However, I still cant seem to get 5/8, what am I doing wrong?
X = m + f where X is total number of students in college.
So from B) 75% of all students applied to college. Therefore we have 75% (X)
Now we know 72% male students applied to college, therefore the male number will be 72% of 75% of X
The fraction should be:
( 72% of 75% of X) / X
This gives me around 54/100 males attending college.

Check this:
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 are male?

This is weighted average question.

Q: $$\frac{m}{m+f}=?$$

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

(2) 75 percent of the students in the senior class have applied to college --> $$0.72m+0.8f=0.75(m+f)$$ --> $$3m=5f$$ --> $$\frac{m}{f}=\frac{5}{3}$$ --> $$\frac{m}{m+f}=\frac{5}{8}$$. Sufficient.

Also discussed here: percentage-students-101231.html

Hope it helps.
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Re: What fraction of the students in the senior class are male? [#permalink]

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13 Mar 2011, 08:50
m+f=T

1. is insufficient
2. .72m+.80f=.75(T) suf.
.72M+ .8(T-M)=0.75T SUF.

B Ans.
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Re: What fraction of the students in the senior class are male? [#permalink]

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13 Mar 2011, 16:32
1. Not sufficient.

no information about the number of males / females in the class

2. Sufficient

with the given info , the fraction can be easily found. Male = 5/8(total students)

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Re: What fraction of the students in the senior class are male? [#permalink]

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31 May 2013, 14:38
walker wrote:
B

First of all, we have a red flag in the problem: it is a %-problem and it does not tell us about any absolute value, only about % and fraction. So, if we have one DS-statement only with one absolute value, the statement is useless for solving the problem.

1) Yeah, it stands here to catch us.

2) How to determine sufficiency of the statement for a few seconds? Just try slightly to increase or decrease 75% in your mind, do you need to change a fraction? Of course, as you need to have more/less male/female ratio to decrease/increase 75%.
If it is difficult, the traditional solution:

75% = (72%*male + 80%*female)/(male + female) = (72% male/female+ 80%) / (male/female + 1) - we can fine male/female fraction.

Now, male/(male + female) = 1 / (1 + female/male) - using information from the statement above, we can find the fraction of the students who are male.

I was confused by your "quick" solution to determine sufficiency. Can you elaborate for me please?
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Re: What fraction of the students in the senior class are male? [#permalink]

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01 Jun 2013, 00:24
tmipanthers wrote:
walker wrote:
B

First of all, we have a red flag in the problem: it is a %-problem and it does not tell us about any absolute value, only about % and fraction. So, if we have one DS-statement only with one absolute value, the statement is useless for solving the problem.

1) Yeah, it stands here to catch us.

2) How to determine sufficiency of the statement for a few seconds? Just try slightly to increase or decrease 75% in your mind, do you need to change a fraction? Of course, as you need to have more/less male/female ratio to decrease/increase 75%.
If it is difficult, the traditional solution:

75% = (72%*male + 80%*female)/(male + female) = (72% male/female+ 80%) / (male/female + 1) - we can fine male/female fraction.

Now, male/(male + female) = 1 / (1 + female/male) - using information from the statement above, we can find the fraction of the students who are male.

I was confused by your "quick" solution to determine sufficiency. Can you elaborate for me please?

Look closely at the alligation rule here, http://www.youtube.com/watch?v=SDA9buSrdlY
So, if we know the avg of population 1 and avg of population 2 and also we know the combined avg of population 1 and 2
we can tell the proportion of population 1 and population 2 in combined population.

Male 72% and 80% female. Total 75% of class (class made of Male and Female. Hence total population)
B gives the combined avg. Enough. No need to solve even.
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Re: In a certain senior class, 72 percent of the male students [#permalink]

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13 Oct 2013, 05:17
tejal777 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 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

This is a classic weighted average problem. Once you start to even think about drawing a matrix for an OS problem, check the statements out. You are given 2 data points and are asked for the ratio. If you have the weighted average you can know the ratio. The weighted average would just be in this case the TOTAL % that applied to college. Remember that for these questions we DON'T need the concrete value (Statement 1). All we need is the weighted average. Questions such as this one are pretty common, try to get used to spotting them right away.

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

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09 Nov 2013, 18:41
I did not know the ratio -> weighted average trick until doing this problem, but I think I figured it out.

m/f=a/b where a and b are given
x = m/(m+f)
1/x = 1 + f/m
1/x = 1 + b/a
1/x = (a + b)/a
x = a/(a+b)

Trick: m/(m+f) = a/(a+b) when m/f = a/b.
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Re: In a certain senior class, 72 percent of the male students [#permalink]

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24 Jan 2015, 18:40
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Re: In a certain senior class, 72 percent of the male students [#permalink]

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28 Jan 2015, 04:15
Table notation

------Applied------Not applied-------Total

Male--0.72x---------------------------x

Fem--0.8y-----------------------------y

Total--0.72x+0.8y--------------------x+y

Question: what is the x/x+y?

St.1. x+y=840. No informatiin about x. INSUFF

St.2. 0.72x+0.8y=0.75(x+y)--->we get x/y=5/3 or x/x+y=5/8. SUFF

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

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16 Feb 2016, 06:33
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Re: In a certain senior class, 72 percent of the male students [#permalink]

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16 Feb 2016, 17:59
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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 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

This question has a logic, which is frequently given on GMAT Math exam lately. The logic is there are 4 variables, and a question includes percentage and the number of percentage should be 3, which makes the con sufficient.
That is, this is a frequently given question, which is "2 by 2" question like the table below. There are 4 variables.
Attachment:

GCDS tejal777 In a certain senior class 72 percent (20160217).jpg [ 35.6 KiB | Viewed 1670 times ]

The question asks percentage and the number of percentage should be 3. In the original condition, the number of percentage is 2(72%, 80%) and 75% in 2), which makes the number of percentage 3 in total. Thus, it is sufficient and the answer is B.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

 from con 1) and con 2), if one of the conditions is given by numbers and the other is given by ratio (percent,fraction), then the condition with ratio (percent,fraction) value has higher chance of being the answer.
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Re: In a certain senior class, 72 percent of the male students   [#permalink] 16 Feb 2016, 17:59
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