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20 boys and 40 girls are in Group A, while at least 7 boys, together w

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20 boys and 40 girls are in Group A, while at least 7 boys, together w [#permalink] New post   27 Jun 2021, 07:55
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20 boys and 40 girls are in Group A, while at least 7 boys, together with some girls are in Group B. To choose one person from each of the group, the probability that both are boys is no greater than 1/15. Which of the following statements must be true?
Indicate all such statements.

A. The number of people in group B is greater than 34.

B. The number of girls in group B is greater than 32.

C. The number of girl in group B is less than 34.

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Re: 20 boys and 40 girls are in Group A, while at least 7 boys, together w [#permalink] New post   28 Jun 2021, 00:17
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For group A the probability of picking one boy is 20/60= 1/3
So, the probability of picking one boy from group B will at least 1/5 ( hence, 1/5 * 1/3 = 1/15)
group B has at least 7 boys. So group B must have at least 5*7= 35 person total
So, option A must be true.
option B is false for total 35 person, though it can be true if total person in increased. As it's partially true, we can't take it.
Same goes for option C

So, answer is "A"
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20 boys and 40 girls are in Group A, while at least 7 boys, together w [#permalink] New post   28 Jun 2021, 01:46
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Lets presume x number of girls (at least) in group B

Now, Probability of picking 1 boy from
Group A= 20/60=1/3
Group B= 7/(x+7)

So, Probabilitt of picking 2 boy from group A & B is
1/3×7/(x+7)=1/15
=> 7/(3x+21)=1/15
=> 3x+21=105
=> x=28

That means in group B the number of girls is 28 or higher.
So, the number of people in group B is (28+7)=35 or more.

Statement A:True.
Statement B:False; Girls# in B can be less than 32
Statement C:False; Girls# in B can be higher than 34

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Re: 20 boys and 40 girls are in Group A, while at least 7 boys, together w [#permalink] New post   28 Apr 2023, 20:06
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: 20 boys and 40 girls are in Group A, while at least 7 boys, together w [#permalink]
28 Apr 2023, 20:06
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