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# In a class with 12 children, q of the children are girls. Two children

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Math Expert
Joined: 02 Sep 2009
Posts: 58316
In a class with 12 children, q of the children are girls. Two children  [#permalink]

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28 Jan 2018, 23:40
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Difficulty:

75% (hard)

Question Stats:

44% (01:57) correct 56% (02:10) wrong based on 71 sessions

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In a class with 12 children, q of the children are girls. Two children will be randomly chosen simultaneously. What is the value of q?

(1) The probability that two girls will be chosen together is 1/11.
(2) The probability that one boy will be chosen and one girl will be chosen is 16/33.

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Re: In a class with 12 children, q of the children are girls. Two children  [#permalink]

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28 Jan 2018, 23:53
Bunuel wrote:
In a class with 12 children, q of the children are girls. Two children will be randomly chosen simultaneously. What is the value of q?

(1) The probability that two girls will be chosen together is 1/11.
(2) The probability that one boy will be chosen and one girl will be chosen is 16/33.

Out of 12 children, girls = q, Boys = (12-q).

(1) Probability of choosing two girls = q/12 * (q-1)/11 = 1/11 (Given)
Solving the above we get q*(q-1) = 12 or q=4. Thus there are 4 girls. Sufficient.

(2) Probability of choosing one boy and one girl = Probability of EITHER choosing first child as boy & second child as girl OR choosing first child as girl & second child as boy
= (12-q)/12 * q/11 + q/12 * (12-q)/11 = 16/33 (Given)
Solving the above we get: 2*q*(12-q) = 64 or q(12-q) = 32.
Here we could have either q=8 and 12-q = 4 Or we could have q=4 and 12-q = 8.
So the number of girls could be either 4 or 8, not a unique value. Not Sufficient.

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In a class with 12 children, q of the children are girls. Two children  [#permalink]

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29 Jan 2018, 07:12
Bunuel wrote:
In a class with 12 children, q of the children are girls. Two children will be randomly chosen simultaneously. What is the value of q?

(1) The probability that two girls will be chosen together is 1/11.
(2) The probability that one boy will be chosen and one girl will be chosen is 16/33.

ATTENTION!!! : Since this is a Data Sufficiency question therefore it's important for us to understand that we need not get into the entire calculation to find the value of q. Instead all we need to know is whether the information given is sufficient to answer the question or not.

Question : Number of girls, q = ?

Statement 1: The probability that two girls will be chosen together is 1/11.

i.e. qC2 / 12C2 = 1/11 . Unique solution to follow as q is positive, hence
SUFFICIENT

Statement 2:The probability that one boy will be chosen and one girl will be chosen is 16/33.

i.e. qC1 * (12-q)C1 / 12C2 = 16/33 . But here the value of q and (12-q) will be interchangeable and might be different if q≠6 so we need to calculate the exact value of q,

i.e. q = 8 or 4 hence
NOT SUFFICIENT

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In a class with 12 children, q of the children are girls. Two children   [#permalink] 29 Jan 2018, 07:12
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