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If x and y are unknown positive integers, is the mean of the [#permalink]
 13 Nov 2012, 13:23
Question Stats:
52% (03:14) correct
47% (01:51) wrong based on 1 sessions
If x and y are unknown positive integers, is the mean of the set {6, 7, 1, 5, x, y} greater than the median of the set? (1) x + y = 7 (2) x - y = 3 OA is , I am unable to understand why statement 2 is not sufficient. Please help, thanks !
Last edited by Bunuel on 13 Nov 2012, 14:30, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x and y are unknown positive integers, is the mean of the [#permalink]
14 Nov 2012, 01:03
If x and y are unknown positive integers, is the mean of the set {6, 7, 1, 5, x, y} greater than the median of the set? (1) x + y = 7 (2) x - y = 3 STAT1 since x+y = 7 so the mean of the set is fixed mean = (1 + 5 + 6 + 7 + 7 ) / 6 = 26/6 = 4.33 Since, x and y are both positive integers so only possible values for the pair x,y is (1,6), (2,5) and (3,4). Respective sets will become { 1,1,5,6,6,7 } -> median = (5+6)/2 = 5.5 { 1,2,5,5,6,7 } -> median = (5+5)/2 = 5 { 1,3,4,5,6,7 } -> median = (4+5)/2 = 4.5 In all the cases median is greater than the mean. So, A is SUFFICIENT STAT2 x-y = 3 case1 x=10, y=7 mean = (1+5+6+7+7+10)/6 = 6 set is {1,5,6,7,7,10} -> median = (6+7)/2 = 6.5 median > mean case2 x=26, y=23 mean = (1+5+6+7+23+26)/6 = 11.3 set is { 1,5,6,7,23,26 } -> median = (6+7)/2 = 6.5 median < mean So, NOT SUFFICIENT Hence, Answer is A. Hope it helps!
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Re: If x and y are unknown positive integers, is the mean of the [#permalink]
14 Nov 2012, 01:09
nktdotgupta wrote: If x and y are unknown positive integers, is the mean of the set {6, 7, 1, 5, x, y} greater than the median of the set?
(1) x + y = 7
(2) x - y = 3
STAT1
since x+y = 7 so the mean of the set is fixed
mean = (1 + 5 + 6 + 7 + 7 ) / 6 = 26/6 = 4.33
Since, x and y are both positive integers so only possible values for the pair x,y is (1,6), (2,5) and (3,4). Respective sets will become
{ 1,1,5,6,6,7 } -> median = (5+6)/2 = 5.5
{ 1,2,5,5,6,7 } -> median = (5+5)/2 = 5
{ 1,3,4,5,6,7 } -> median = (4+5)/2 = 4.5
In all the cases median is greater than the mean.
So, A is SUFFICIENT
STAT2
x-y = 3
case1 x=10, y=7
mean = (1+5+6+7+7+10)/6 = 6
set is {1,5,6,7,7,10} -> median = (6+7)/2 = 6.5
median > mean
case2 x=26, y=23
mean = (1+5+6+7+23+26)/6 = 11.3
set is { 1,5,6,7,23,26 } -> median = (6+7)/2 = 6.5
median < mean
So, NOT SUFFICIENT
Hence, Answer is A.
Hope it helps! Thanks for your solution. In case, X and Y were 'unknown integers' instead of 'unknown positive integers', answer would be E. I am right?
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Re: If x and y are unknown positive integers, is the mean of the [#permalink]
14 Nov 2012, 01:23
It will take too long time to compute this by using numbers. Is there any shorter way (Bunuel !!!)??
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Re: If x and y are unknown positive integers, is the mean of the [#permalink]
14 Nov 2012, 01:24
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Re: If x and y are unknown positive integers, is the mean of the [#permalink]
14 Nov 2012, 01:56
nktdotgupta wrote: No, In that case answer will be C as you can find out the exact values of x and y using (1) and (2) so you can tell the mean and median for sure. Hi Ankit, I tried solving the problem with X and Y as unknown integers but I still think the answer would be A and not C. Can you please help on this. Thanks !
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BSchool Thread Master
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Re: If x and y are unknown positive integers, is the mean of the [#permalink]
14 Nov 2012, 02:14
mneeti wrote: nktdotgupta wrote: No, In that case answer will be C as you can find out the exact values of x and y using (1) and (2) so you can tell the mean and median for sure. Hi Ankit, I tried solving the problem with X and Y as unknown integers but I still think the answer would be A and not C. Can you please help on this. Thanks ! Hi, yes the answer will still be A. I was thinking that taking negative numbers might change the answer but it doesn't look like. Yes but if x and y can be non integers also then the answer will not be A as in that case both x and y can be equal to 3.5 and the median will be 4.25 in that case.
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Re: If x and y are unknown positive integers, is the mean of the
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14 Nov 2012, 02:14
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