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# The probability of picking a boy in a class is 1/3. If two boys are re

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Math Expert
Joined: 02 Aug 2009
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The probability of picking a boy in a class is 1/3. If two boys are re [#permalink]

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25 Jan 2018, 21:12
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62% (00:46) correct 38% (01:13) wrong based on 63 sessions

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The probability of picking a boy in a class is $$\frac{1}{3}$$. If two boys are removed from the class, the probability of picking a boy in the class goes down to $$\frac{5}{16}$$. What is the number of boys in the class?

(A) 20
(B) 22
(C) 32
(D) 34
(E) Data insufficient

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Joined: 29 Jun 2017
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Re: The probability of picking a boy in a class is 1/3. If two boys are re [#permalink]

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25 Jan 2018, 21:53
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chetan2u wrote:
The probability of picking a boy in a class is $$\frac{1}{3}$$. If two boys are removed from the class, the probability of picking a boy in the class goes down to $$\frac{5}{16}$$. What is the number of boys in the class?

(A) 20
(B) 22
(C) 32
(D) 34
(E) Data insufficient

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let x be boys so total class 3x
now x-2 are boys so total are 3x-2
(x-2)/ (3x-2) = 5/16
16x-32 = 15x -10
16x-15x = 32-10
x=22

IMO B ??
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Intern
Joined: 29 Jul 2017
Posts: 12
GMAT 1: 650 Q50 V27
Re: The probability of picking a boy in a class is 1/3. If two boys are re [#permalink]

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26 Jan 2018, 04:27
Let the total number of students in the class be 'T' and,
the number of boys among them be 'B'.
Therefore, probability of picking a boy = B/T = 1/3 ...(1)
If two boys are removed from the class, the probability of picking a boy = (B-2)/(T-2) = 5/16 ...(2)
Solving the two equations we get B = 22

Ans B
Intern
Joined: 22 Aug 2017
Posts: 11
The probability of picking a boy in a class is 1/3. If two boys are re [#permalink]

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26 Jan 2018, 07:10
1:3:4
(1+3= a total of 4)

5:16:21
(5+16= a total of 21)

With ratios, you can add the parts to get a whole (part:part:whole)

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Posts: 2442
Re: The probability of picking a boy in a class is 1/3. If two boys are re [#permalink]

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29 Jan 2018, 11:00
chetan2u wrote:
The probability of picking a boy in a class is $$\frac{1}{3}$$. If two boys are removed from the class, the probability of picking a boy in the class goes down to $$\frac{5}{16}$$. What is the number of boys in the class?

(A) 20
(B) 22
(C) 32
(D) 34
(E) Data insufficient

The ratio of boys to total students is x : 3x, thus:

(x - 2)/(3x - 2) = 5/16

16(x - 2) = 5(3x - 2)

16x - 32 = 15x - 10

x = 22

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Director
Joined: 07 Dec 2014
Posts: 998
The probability of picking a boy in a class is 1/3. If two boys are re [#permalink]

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29 Jan 2018, 12:16
chetan2u wrote:
The probability of picking a boy in a class is $$\frac{1}{3}$$. If two boys are removed from the class, the probability of picking a boy in the class goes down to $$\frac{5}{16}$$. What is the number of boys in the class?

(A) 20
(B) 22
(C) 32
(D) 34
(E) Data insufficient

let b=boys in class
let 2b=girls in class
(b-2)/2b=5/11
b=22
B
The probability of picking a boy in a class is 1/3. If two boys are re   [#permalink] 29 Jan 2018, 12:16
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