Ratio problem

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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Wed May 26, 2010 11:44 pm

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

1)There are 840 students in senior class

2)75 % of students in senior class have applied to college

OA B

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Source: Beat The GMAT — Data Sufficiency | Wed May 26, 2010 11:44 pm

gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Wed May 26, 2010 11:57 pm

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

1)There are 840 students in senior class

2)75 % of students in senior class have applied to college

OA B

Let T be the total number of students in senior class.

Let M be Number of Male students

F be the female students

T = M+F

St 2 says :

0.72 M + 0.8 F = 0.75 T

0.72 M + 0.8( T-M)

0.72M + 0.8 T -0.8M = 0.75 T

0.08 M = 0.05 T

M/T = 5/8

Sufficient !!

St 1 T= 840 It does not speak about M /F . Insufficient !!

Pick B.

R&D on GMAT algorithm:

https://www.beatthegmat.com/r-d-on-gmat- ... tml#305739

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Thu May 27, 2010 5:26 am

This is a weighted avg question. In weighted averages, the overall is always between the averages of the two groups (male / female). How close the weighted average is to each group is determined by the ratio of one group size to the other. For instance if there are twice as many males as females, the weighted average will be twice as close to the males' datapoint as to the females'

We already know the datapoints for males (72%) and females (80%). To find the fraction of students who are male, we need the ratio of male to female (or male to total). Good rephrases would include "What is m/(m+f)?" "What is m/f?" and "what is the weighted average?"

(1) gives us no way to determine the ratio of male to female

(2) The weighted average (75%) is closer to the males' datapoint (72%) than to the females' (80%). Based on what I wrote in the first paragraph, the weighted average's proximity to each datapoint is determined by the ratio of group sizes, so this statement gives us the means to find the ratio of males/females. It's sufficient.

If you wanted to do the math from (2) you would write "72% of all males and 80% of all females is the same as 75% of all students" --> .72m+.80f=.75(m+f). This can be solved for the ratio m/f.

The answer is B. If the above doesn't make sense, a step by step video may help: This is GMATPrep question 1107

-Patrick

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aloneontheedge: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Thu Jan 28, 2010 2:07 am; Thanked: 9 times

by aloneontheedge » Thu Aug 19, 2010 10:55 am

Patrick_GMATFix wrote:This is a weighted avg question. In weighted averages, the overall is always between the averages of the two groups (male / female). How close the weighted average is to each group is determined by the ratio of one group size to the other. For instance if there are twice as many males as females, the weighted average will be twice as close to the males' datapoint as to the females'

We already know the datapoints for males (72%) and females (80%). To find the fraction of students who are male, we need the ratio of male to female (or male to total). Good rephrases would include "What is m/(m+f)?" "What is m/f?" and "what is the weighted average?"

(1) gives us no way to determine the ratio of male to female

(2) The weighted average (75%) is closer to the males' datapoint (72%) than to the females' (80%). Based on what I wrote in the first paragraph, the weighted average's proximity to each datapoint is determined by the ratio of group sizes, so this statement gives us the means to find the ratio of males/females. It's sufficient.

If you wanted to do the math from (2) you would write "72% of all males and 80% of all females is the same as 75% of all students" --> .72m+.80f=.75(m+f). This can be solved for the ratio m/f.

The answer is B. If the above doesn't make sense, a step by step video may help: This is GMATPrep question 1107

-Patrick

Patrick,
I am not getting this.
Question stem says,72% male and 80% female apply.
Stmnt 1: There are 840 students in senior class
why cant i use 0.72m + 0.8f = 840?

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wdgolden: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Tue Aug 17, 2010 10:55 am; Thanked: 2 times

by wdgolden » Thu Aug 19, 2010 9:38 pm

why cant i use 0.72m + 0.8f = 840?

That statement is equivalent to saying 72% of the males plus 80% of the females equals 100% of the males and 100 % of the females.

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Thouraya: Master | Next Rank: 500 Posts; Posts: 112; Joined: Wed Jan 20, 2010 5:46 am; Thanked: 1 times

by Thouraya » Sun May 29, 2011 4:29 am

Experts, shouldn't the questions be: What fraction of the students in the senior class WHO APPLIED TO COLLEGE are male? (for B to be correct, otherwise, we can't determine the ratio of all males). Thanks

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