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The ratio of male to female applicants taking a school entrance exam w

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New post 05 Dec 2019, 01:28
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A
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Question Stats:

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[GMAT math practice question]

The ratio of male to female applicants taking a school entrance exam was \(3:2\), the ratio of male to female acceptances to the school is \(5:2\), the ratio of male to female rejections to the school is \(1:1\), and the number of acceptances is \(140\). What is the total number of applicants?

A. \(280\)

B. \(300\)

C. \(320\)

D. \(340\)

E. \(360\)

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New post 05 Dec 2019, 09:41
Accepted + Rejected = Total Applicants

Acceptance ratio for male to female M/F = 5/2
Total accepted M+F = 140
From this M = 100, F=40

Rejection ratio for male and females= 1/1
Now suppose x males and x females were rejected
(100+x)/(40+x)= 3/2 ( 3/2 is ratio of male to female applicants.)
Calculate x= 80

So total applicants 100+2x+40= 300. Answer is B.
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New post 08 Dec 2019, 18:39
=>

We can assume the numbers of male and female acceptances are \(5p\) and \(2p\), respectively, and the number of each of male and female rejections is \(r\).

We have \((5p + r) : (2p + r) = 3:2\) or \(10p + 2r = 6p + 3r\) (by cross multiplying).

Then we have \(r = 4p.\)

Since \(7p = 140\), we have \(p = 20\) and \(r = 4(20) = 80.\)

Therefore, total number of applicants is \(7p + 2r = 7(20) + 2(80) = 140 + 160 = 300.\)

Therefore, B is the answer.
Answer: B
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New post 17 Jan 2020, 23:03
Let the total # of applicants be 5x (Male: 3x; Female: 2x).
Number of male applicants accepted = {140/(5+2)}*5 = 100
Number of female applicants accepted = {140/(5+2)}*2 = 40

Number of male applicants rejected = 3x - 100............(i)
Number of female applicants rejected = 2x - 40...........(ii)
Since the ratio of male and female rejections are in the ratio 1:1, (i) and (ii) are equal. Therefore:
3x -100 = 2x - 40....> x = 60
5x =300.
ANS: b
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The ratio of male to female applicants taking a school entrance exam w   [#permalink] 17 Jan 2020, 23:03
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