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# A certain junior class has 600 students and a certain senior class has

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Math Expert
Joined: 02 Sep 2009
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A certain junior class has 600 students and a certain senior class has  [#permalink]

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03 Jul 2018, 10:55
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95% (hard)

Question Stats:

36% (02:29) correct 64% (01:54) wrong based on 53 sessions

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A certain junior class has 600 students and a certain senior class has 800 students. Among these students, there are N sibling pairs, consisting of a Junior and a Senior. What is the value of N?

(1) If a student is selected from each class at random, the probability that the students do not form a sibling pair is 4799/4800.

(2) If a student is selected from each class at random, the probability that exactly ONE of these students is a member of a sibling pair is 1/4.

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A certain junior class has 600 students and a certain senior class has  [#permalink]

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03 Jul 2018, 13:08
2
A certain junior class has 600 students and a certain senior class has 800 students. Among these students, there are N sibling pairs, consisting of a Junior and a Senior. What is the value of N?

(1) If a student is selected from each class at random, the probability that the students do not form a sibling pair is 4799/4800.
$$\frac{4799}{4800}=\frac{479900}{480000}$$
So prob they form =$$\frac{100}{600*800}=\frac{N}{800}*\frac{1}{600}$$...
So N=100
Suff

(2) If a student is selected from each class at random, the probability that exactly ONE of these students is a member of a sibling pair is 1/4.
$$\frac{N}{600}* \frac{(800-N)}{800}+\frac{N}{800}*\frac{(600-N)}{600}=\frac{1}{4}$$......
How?? - since we are looking exactly one and there are N pairs, we choose any of the N in class of 600, so we will have to choose students who are not part of this sibling pairs so 800-N out of other class of 800. But there can be other way where we choose any of N from 800 and all but this N from 600 so 600-N
$$N(800-N)+N(600-N)=\frac{(600*800)}{4}=120000$$..
$$N(800-N+600-N)=120000........N^2-700N+60000=0$$
$$(N-100)(N-600)=0$$
N can be 100 or 600
Insufficient

A

rajudantuluri, Added the reasoning. Hope it helps
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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A certain junior class has 600 students and a certain senior class has  [#permalink]

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04 Jul 2018, 14:09
chetan2u wrote:
A certain junior class has 600 students and a certain senior class has 800 students. Among these students, there are N sibling pairs, consisting of a Junior and a Senior. What is the value of N?

(1) If a student is selected from each class at random, the probability that the students do not form a sibling pair is 4799/4800.
$$\frac{4799}{4800}=\frac{479900}{480000}$$
So prob they form =$$\frac{100}{600*800}=\frac{N}{800}*\frac{1}{600}$$...
So N=100
Suff

(2) If a student is selected from each class at random, the probability that exactly ONE of these students is a member of a sibling pair is 1/4
N/600 * (800-N)/800+ N/800*(600-N)/600=1/4......
N(800-N)+N(600-N)=(600*800)/4=120000..
N(800-N+600-N)=120000........N^2-700N+60000=0
(N-100)(N-600)=0
N can be 100 or 600
Insufficient

A

Hi chetan2u,
Could you please elaborate the reasoning behind the equation you set up in statement 2. I fail to understand why we do 800-N/800 and 600-N/600.
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Posts: 6787
Re: A certain junior class has 600 students and a certain senior class has  [#permalink]

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04 Jul 2018, 23:56
added the reasoning in original post.
Hope it helps
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 15 Aug 2012
Posts: 42
Schools: AGSM '19
Re: A certain junior class has 600 students and a certain senior class has  [#permalink]

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05 Jul 2018, 08:46
chetan2u wrote:
added the reasoning in original post.
Hope it helps

Thank you chetan2u, that makes it very clear now
Re: A certain junior class has 600 students and a certain senior class has &nbs [#permalink] 05 Jul 2018, 08:46
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