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If x and y are unknown positive integers, is the mean of the

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If x and y are unknown positive integers, is the mean of the [#permalink] New post 13 Nov 2012, 12:23
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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
[Reveal] Spoiler:
A
, I am unable to understand why statement 2 is not sufficient. Please help, thanks !
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Nov 2012, 13:30, 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] New post 14 Nov 2012, 00:03
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] New post 14 Nov 2012, 00:09
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] New post 14 Nov 2012, 00:23
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] New post 14 Nov 2012, 00:24
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.

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Re: If x and y are unknown positive integers, is the mean of the [#permalink] New post 14 Nov 2012, 00:56
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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Re: If x and y are unknown positive integers, is the mean of the [#permalink] New post 14 Nov 2012, 01:14
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 [#permalink] New post 08 May 2014, 06:25
when we see a summation (x+y) we must understand that this implies a restriction (x & y = positive integer) on x and y. (x,y) can be (1,6), (2,5), (3, 4), (4,3), (5,2) and (6,1). if we consider all these cases we get only one type of answer for this question.

When we see a negative summation between two number the range is not fixed. Eg x-y can be 500000-499997 or x-y can be 7-4
hence choice is not sufficient
Re: If x and y are unknown positive integers, is the mean of the   [#permalink] 08 May 2014, 06:25
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