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Intern  Joined: 30 Oct 2011
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If x and y are unknown positive integers, is the mean of the  [#permalink]

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11 00:00

Difficulty:   65% (hard)

Question Stats: 66% (02:32) correct 34% (02:43) wrong based on 372 sessions

### HideShow timer Statistics 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 !

Originally posted by mneeti on 13 Nov 2012, 13:23.
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]

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1
2
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

Hope it helps!
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Re: If x and y are unknown positive integers, is the mean of the  [#permalink]

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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

Hope it helps!

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]

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1
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]

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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]

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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]

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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]

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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
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Such questions wherein you need to think of all possible combinations tend to consume a lot of time and at the end of it, there is no guarantee that you have considered all possible number combinations.So is there a definite approach to such questions?
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Re: If x and y are unknown positive integers, is the mean of the  [#permalink]

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To find the mean of the sets we need to know the sum of x and y.
Statement 1. Mean of the set = (6 + 7 + 1 + 5 + 7)/6 = 26/6 = 4.33.
Since, x and y are positive integer, their possible values are (1,6), (2, 5), (3,4)
So, possible sets are {1, 1, 5, 6, 6, 7}. Median = (5+6)/2 = 5.5
{1, 2, 5, 5, 6, 7}. Median = 10/2 = 5
{1, 3, 4, 5, 6, 7}. Median = 9/2 = 4.5.
All possible values of median are greater than mean. Hence, Sufficient.
Statement 2. We need the sum of x and y to find the mean and not the difference of x and y. Hence, Insufficient. Re: If x and y are unknown positive integers, is the mean of the   [#permalink] 21 Dec 2018, 22:19
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