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Median

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by safina » Sun Feb 23, 2014 6:39 am
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) y/3
e) 2y/7
Ans - E

I chose the correct answer but I don't think I had the right reason. I chose E because that's the only non integer for all values of y but I don't know if that's how this needs to be answered.
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by Brent@GMATPrepNow » Sun Feb 23, 2014 7:38 am
safina 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) y/3
e) 2y/7
Ans - E

I chose the correct answer but I don't think I had the right reason. I chose E because that's the only non integer for all values of y but I don't know if that's how this needs to be answered.
If we have a set of y INTEGERS, there are two possible cases when it comes to the MEDIAN.
Case a: y is an ODD number, in which case the MEDIAN equals the one middle integer (when all of the integers are arranged in ascending order). In this case, the median must be an integer.

Case b: y is an EVEN number, in which case the MEDIAN equals the average of the two middle-most integers (when all of the integers are arranged in ascending order). To find the average of the two middle-most integers, we'll add them together and divide the SUM by 2. So, if their SUM is even, then we'll get an integer value for the median. If their SUM is odd, then the median will be something.5. For example, if the two middle-most integers are 3 and 6, the median will be 4.5.

CONCLUSION: In this scenario, the median of Set T will be EITHER an integer OR something.5.

When we check the answer choices, answer choice [spoiler]2y/7[/spoiler] can equal NEITHER an integer NOR something.5. We know this because y must be an integer AND 0 < y < 7. So, there's no way for [spoiler]2y/7[/spoiler] to ever evaluate to be an integer or something.5.

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Sun Feb 23, 2014 10:33 am
Hi safina,

Brent's properly explained/confirmed your thinking on this question. In the event that you didn't recognize the pattern behind this question, here's another way to find the correct answer: we need to prove which 4 answers are possible (and thus the 5th would not):

For the sake of ease, I'm going to set the variables:
Y = 3 so we'll have 3 integers in the set
X = 1 the average is the simplest positive integer

Could the median be.....
0? Yes, if the numbers were -1, 0, 2
1? Yes, if the numbers were 1, 1, 1
-X? Yes, if the numbers were -2, -1, 6
Y/3? Yes, if the numbers were 1, 1, 1

With the first four answers possible/eliminated, the correct answer must be what's left: E

GMAT assassins aren't born, they're made,
Rich
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