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03 Jul 2018, 10:55
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61%
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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.
(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.
03 Jul 2018, 13:08
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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.
\(\frac{4799}{4800}=\frac{479900}{480000}\)
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
(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
General Discussion
29 Jul 2021, 18:34
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As mentioned by all popular replies :
The first statement gives us a linear equation and we can solve for x .
The Second Statement however gives us two values 100 or 600 ,
Note that if N=600 , the probability that exactly one of the two students would be siblings becomes 100% , Thus invalidating the statement . Which means we can eliminate 600 and pick 100.
Hence the Answer is (D)
The first statement gives us a linear equation and we can solve for x .
The Second Statement however gives us two values 100 or 600 ,
Note that if N=600 , the probability that exactly one of the two students would be siblings becomes 100% , Thus invalidating the statement . Which means we can eliminate 600 and pick 100.
Hence the Answer is (D)
