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# If Set A consists of 10 numbers, each number reciprocal of a prime num

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If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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21 Jan 2016, 02:09
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Question Stats:

29% (02:13) correct 71% (02:09) wrong based on 83 sessions

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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) 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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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Updated on: 21 Jan 2016, 08:30
2
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

Originally posted by Vyshak on 21 Jan 2016, 03:27.
Last edited by Vyshak on 21 Jan 2016, 08:30, edited 1 time in total.
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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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Updated on: 21 Jan 2016, 10:07
4
chetan2u wrote:
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 atleast 5 different numbers in the Set.
2) No number is used more than 2 times in the set.

OA and solution after two days..

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

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.
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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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21 Jan 2016, 06:17
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Hi @godblessme, I agree that St1 is not sufficient and I made a mistake above. But, St2 is sufficient as it provides a definitive answer that median is less than or equal to 1/5 and not greater than 1/5.

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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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21 Jan 2016, 10:04
Vyshak wrote:
Hi godblessme, I agree that St1 is not sufficient and I made a mistake above. But, St2 is sufficient as it provides a definitive answer that median is less than or equal to 1/5 and not greater than 1/5.

Hi Vyshak

Thanks for pointing out my mistake, i misread the question as is Md<1/5 whereas it was is Md>1/5, yes you are right statement 2 alone is sufficient to obtain a definitive answer thank you and please consider a kudos for my post m trying hard to unlock tests
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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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21 Jan 2016, 10:14
Hello ,

Answer should be as per vyshak!! My friend godbless me the question stem is IS Median>1/5 which will never be the case as per your solution it can be either< or = !! Hope it helps
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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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21 Jan 2016, 10:19
rocky1988 wrote:
Hello ,

Answer should be as per vyshak!! My friend godbless me the question stem is IS Median>1/5 which will never be the case as per your solution it can be either< or = !! Hope it helps

Yup my fren Rocky got it and so i have already deleted my post and even modified my solution Please consider a kudos for your fren
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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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21 Jan 2016, 18:48
Guys : option 2 is sufficient : Max it can hit 1/5 1/5 + 1/5 )/2 = 1/5 ....
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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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21 Jan 2016, 19:16
D. Both are insufficient.
(1)
1/5,1/7,1/11,1/13,1/17

(2)
Irrelevant if the first prime number is 1/5 or greater.
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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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22 Jan 2016, 11:05
I feel like it's B, no?

Is the median of the Set A > 1/5?

1) There are at least 5 different numbers in the Set.

Could be:

1/13, 1/11, 1/7, 1/5, 1/5, 1/3, 1/3, 1/2, 1/2, 1/2 YES
1/13, 1/13, 1/11, 1/11, 1/7, 1/5, 1/5, 1/3, 1/3, 1/2, NO

2) No number is used more than 2 times in the set.

1/11, 1/11, 1/7, 1/7, 1/5, 1/5, 1/3, 1/3, 1/2, 1/2 median=1/5. This is the BIGGEST fraction the median could be. Choosing any other number would make the median smaller, so the median cannot be larger than 1/5.
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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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22 Jan 2016, 22:59
chetan2u wrote:
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 atleast 5 different numbers in the Set.
2) No number is used more than 2 times in the set.

Hi,

Lets see first the info provided by the Q

1) Set has 10 numbers.
2) each is a reciprocal of a prime number. so each is a fraction of form : 1/2,1/3,1/5...
3) Median for this set will depend on 5th and 6th numbers in the ascending/descending order.

lets see the statements..

1) There are atleast 5 different numbers in the Set.
the numbers could be 1/2,1/2,1/2,1/2,1/3,1/3,1/5,1/7,1/7,1/11... median = 1/3.. >1/5 YES
the numbers could be 1/2,1/3,1/5,1/7,1/7,1/7,1/7,1/7,1/7,1/11... median = 1/7.. >1/5 NO..
we get two different answers .. insuff

2) No number is used more than 2 times in the set.
We now know that each number can be written only twice..
since we are looking for 'larger', so lets test for the best possible case for largest number possible..
best case will be when biggest number are used twice..
It will be reciprocal of smallest number 2,3,5,7,11..
so largest possible numbers in the set is$$\frac{1}{2},\frac{1}{2},\frac{1}{3},\frac{1}{3},\frac{1}{5},\frac{1}{5},\frac{1}{7},\frac{1}{7},\frac{1}{11},\frac{1}{11}$$..
median =1/5..
so largest possible median = 1/5, which is not > 1/5..
Sufficient..
ans B
_________________

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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num  [#permalink]

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Re: If Set A consists of 10 numbers, each number reciprocal of a prime num   [#permalink] 10 Sep 2018, 21:04
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