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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8454
GMAT 1: 760 Q51 V42
GPA: 3.82
The ratio of male to female applicants taking a school entrance exam w  [#permalink]

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05 Dec 2019, 01:28
1
00:00

Difficulty:

65% (hard)

Question Stats:

64% (03:12) correct 36% (02:42) wrong based on 44 sessions

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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 09 Aug 2017 Posts: 679 Re: The ratio of male to female applicants taking a school entrance exam w [#permalink] ### Show Tags 05 Dec 2019, 09:41 1 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. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8454 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The ratio of male to female applicants taking a school entrance exam w [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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The ratio of male to female applicants taking a school entrance exam w  [#permalink]

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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
The ratio of male to female applicants taking a school entrance exam w   [#permalink] 17 Jan 2020, 23:03
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