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21 Jan 2016, 02:09
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B
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If Set A consists of 10 numbers, each number reciprocal of a prime number. Is the median of the Set A > 1/5?
(1) There are at least 5 different numbers in the Set.
(2) No number is used more than 2 times in the set.
(1) There are at least 5 different numbers in the Set.
(2) No number is used more than 2 times in the set.
Updated on: 21 Jan 2016, 10:07
Originally posted by godblessme on 21 Jan 2016, 04:25.
Last edited by godblessme on 21 Jan 2016, 10:07, edited 1 time in total.
Last edited by godblessme on 21 Jan 2016, 10:07, edited 1 time in total.
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chetan2u
IMO B
Statement 1
There are atleast 5 different numbers means 5 numbers could be same lets consider 2 possible cases:
(1/2,1/2,1/2,1/2,1/2,1/3,1/5,1/7,1/11,1/13) in this case Md>1/5
(1/2,1/3,1/5,1/5,1/5,1/5,1/5,1/7,1/11,1/13) in this case Md=1/5 so, no definite answer is obtained
Statement 2
let us consider different cases:
let us suppose 5 greatest numbers are repeated twice (1/2,1/2,1/3,1/3,1/5,1/5,1/7,1/7,1/11,1/11) in this case Md=1/5
let us suppose no number is repeated(1/2,1/3,1/5,1/7,1/11,1/13,1/17,1/19,1/23,1/29) in this case Md is atmost equal to 1/5 but never greater, so, the answer is NO, thus a definite answer is obtained, hence Sufficient
Answer is B
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General Discussion
Editing the solution:
Median > 1/5?
St1: There are atleast 5 different numbers in the Set.
Considering that there are exactly 5 different numbers and picking the greatest 5 reciprocals we will have set A = {1/2, 1/2, 1/3, 1/3, 1/5, 1/5, 1/7, 1/7, 1/11, 1/11} --> Median = 1/5.
But, if A = {1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/3, 1/5, 1/7, 1/11} --> Median of set A > 1/5
St1 is not sufficient
St2: No number is used more than 2 times in the set
Consider the case where we get the max value of median, A = {1/2, 1/2, 1/3, 1/3, 1/5, 1/5, 1/7, 1/7, 1/11, 1/11} --> Median = 1/5
If A = {1/2, 1/2, 1/3, 1/3, 1/5, 1/7, 1/7, 1/11, 1/11, 1/13} --> Median < 1/5
Thus median value cannot exceed 1/5
St2 is sufficient
Answer: B
Median > 1/5?
St1: There are atleast 5 different numbers in the Set.
Considering that there are exactly 5 different numbers and picking the greatest 5 reciprocals we will have set A = {1/2, 1/2, 1/3, 1/3, 1/5, 1/5, 1/7, 1/7, 1/11, 1/11} --> Median = 1/5.
But, if A = {1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/3, 1/5, 1/7, 1/11} --> Median of set A > 1/5
St1 is not sufficient
St2: No number is used more than 2 times in the set
Consider the case where we get the max value of median, A = {1/2, 1/2, 1/3, 1/3, 1/5, 1/5, 1/7, 1/7, 1/11, 1/11} --> Median = 1/5
If A = {1/2, 1/2, 1/3, 1/3, 1/5, 1/7, 1/7, 1/11, 1/11, 1/13} --> Median < 1/5
Thus median value cannot exceed 1/5
St2 is sufficient
Answer: B
1/5 + 1/5 )/2 = 1/5 .... 
