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The ratio of male to female applicants taking a school entra

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The ratio of male to female applicants taking a school entra

by Max@Math Revolution » Thu Dec 05, 2019 12:05 am
[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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by deloitte247 » Sat Dec 07, 2019 7:12 pm
Total applicants = Accepted + Rejected
Male to female acceptance ratio = 5:2 = 5/2
Total acceptance = male accepted + female accepted
Male accepted + female accepted = 140
Total accepted = 140
With male and female ratio;
$$Male\ accepted=\frac{5}{\left(5+2\right)}\cdot140=\frac{5}{7}\cdot140=100$$
$$Female\ accepted=\frac{2}{\left(5+2\right)}\cdot140=\frac{2}{7}\cdot140=40$$
Male to female rejection ratio = 1 : 1 =1/1
Given that the ratio of male to female applicants = 3:2 = 3/2; and the number of males and females that were rejected is unknown.
Let the total number of rejected applicants (both male and female) = x and x for both make and female
$$3:2=\left(100+x\right):\left(40+x\right)$$
$$\frac{3}{2}=\frac{\left(100+x\right)}{\left(40+x\right)}$$
$$3\left(40+x\right)=2\left(100+x\right)$$
$$120+3x=200+2x$$
$$x=80$$
Total number of rejected applicants = 2x = 2 * 80 = 160
Total applicants = Acceted + Rejected
= 140 + 160 = 300

Answer = option B
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by Max@Math Revolution » Sun Dec 08, 2019 5:15 pm
=>

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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