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T is a set of y integers, where 0 < y < 7. If the average of

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T is a set of y integers, where 0 < y < 7. If the average of Set T is the positive integer x, which of the following could NOT be the median of Set T?

A. 0
B. x
C. –x
D. (1/3)y
E. (2/7)y
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Mar 2016, 05:55, edited 3 times in total.
Edited the question and added the OA
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New post 04 Apr 2009, 21:48
Zaur wrote:
T is a set of y integers, where 0 < y < 7. If the average of Set T is the positive integer x, which of the following could NOT be the median of Set T?

a) 0
b) x
c) –x
d) (1/3)y
e) (2/7)y

thanks in advance


Its E, which is neither an integer nor a multiple of 0.5. Since the set T's elements are integers, median should be either an integer or a multiple of 0.5.
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Re: T is a set of y integers, where 0 < y < 7. If the average of [#permalink]

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New post 04 Apr 2009, 23:13
Hi Gmat tiger,
You are right that the median should be either an integer or a multiple of 0.5 ( since the number of integers can be even)
But then, 1/3 is also not an integer and not a multiple of 0.5 !! Couldnt get this :(

GMAT TIGER wrote:
Zaur wrote:
T is a set of y integers, where 0 < y < 7. If the average of Set T is the positive integer x, which of the following could NOT be the median of Set T?

a) 0
b) x
c) –x
d) (1/3)y
e) (2/7)y

thanks in advance


Its E, which is neither an integer nor a multiple of 0.5. Since the set T's elements are integers, median should be either an integer or a multiple of 0.5.
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New post 05 Apr 2009, 05:39
Economist wrote:
Hi Gmat tiger,
You are right that the median should be either an integer or a multiple of 0.5 ( since the number of integers can be even)
But then, 1/3 is also not an integer and not a multiple of 0.5 !! Couldnt get this :(

GMAT TIGER wrote:
Zaur wrote:
T is a set of y integers, where 0 < y < 7. If the average of Set T is the positive integer x, which of the following could NOT be the median of Set T?

a) 0
b) x
c) –x
d) (1/3)y
e) (2/7)y

thanks in advance


Its E, which is neither an integer nor a multiple of 0.5. Since the set T's elements are integers, median should be either an integer or a multiple of 0.5.


y could be 2, 3, 4, 5, or 6. If y = either 3 or 6, y/3 is an integer.
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Re: T is a set of y integers, where 0 < y < 7. If the average of [#permalink]

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New post 24 Oct 2009, 20:19
E too

Y/3 is possible if Y = 3 or 6

2Y/7 does not meet the criteria - the remainder must be 0 or 0.5
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New post 30 Apr 2010, 11:40
Can someone break down all the choices as to why they can be median?
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New post 30 Apr 2010, 22:29
ksharma12 wrote:
Can someone break down all the choices as to why they can be median?


Rather than think about whether or not they can be the median, think about whether or not they could be an integer or a multiple of 0.5.

a) 0 integer
b) x could be an integer, all we know is that it's the average
c) –x same as b
d) (1/3)y could be an integer if y=3 or y=6
e) (2/7)y cannot be an integer or multiple of 0.5, as y is 1,2,3,4,5 or 6. Sufficient enough to answer the question
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New post 25 Sep 2010, 08:47
How C) -x could be the median?
Set consists of elements from 1 to 6, the average x is positive, the median is negative which is impossible due to the range from 1 to 6.
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Kronax wrote:
How C) -x could be the median?
Set consists of elements from 1 to 6, the average x is positive, the median is negative which is impossible due to the range from 1 to 6.


Phrase "T is a set of y integers, where 0 < y < 7" doesn't mean that T consist of elements from 1 to 6, it means that number of elements in T is from 1 to 6.

T is a set of y integers, where 0 < y < 7. If the average of Set T is the positive integer x, which of the following could NOT be the median of Set T?

A. \(0\) --> if \(T=\{0, 0, 3\}\) then \(mean=x=1\) and \(median=0\);

B. \(x\) --> if \(T=\{3\}\) then \(mean=x=3\) and \(median=x=3\);

C. \(-x\) --> if \(T=\{-1, -1, 5\}\) then \(mean=x=1\) and \(median=-x=-1\);

D. \(\frac{1}{3}y\) --> if \(T=\{1, 1, 1\}\) then \(mean=x=1\), \(# \ of \ elements=y=3\) and \(median=\frac{1}{3}y=1\);

E. \(\frac{2}{7}y\) --> now, as T is a set of integers then the median is either a middle term, so \(integer\) OR the average of two middle terms so \(\frac{integer}{2}\), but as \(y\) is an integer from 1 to 6 then \(\frac{2}{7}y\) is neither an \(integer\) nor \(\frac{integer}{2}\). So \(\frac{2}{7}y\) could not be the median.

Answer: E.

Hope it's clear.
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New post 25 Sep 2010, 22:23
Thank you Bunuel, now its clear!
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New post 17 Oct 2012, 02:04
It's not always the case that E holds true.
If T contains only one element, let's say 3. The mean is 3. The median OUGHT to be 3, never -3. So C is right.
Can anyone help me out?
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New post 17 Oct 2012, 04:02
Ousmane wrote:
It's not always the case that E holds true.
If T contains only one element, let's say 3. The mean is 3. The median OUGHT to be 3, never -3. So C is right.
Can anyone help me out?


The question is "which of the following could NOT be the median of Set T?"
It means we have to find the option for which the given number can NEVER be the median of Set T.

So, \(-3\) cannot be the median in your example, but there are many other cases when it can be.
Set T contains integers, so negative numbers are not excluded.

\(2/7y\) can never be an integer when \(0<y<7\), while the median MUST be an integer, doesn't matter what is \(y\) and what are the numbers in the set.
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New post 24 Nov 2015, 01:59
thanks Bunuel! great answer
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