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Which of the following CANNOT be the median of the four positive integers a, b, c, and d, where a < b < c < d ? (A) (a+c)/2 (B) (b+c)/2 (C) (a+d)/2 (D) (b+d)/2 (E) (c+d)/2

As written, there's something wrong with the question. Are some of the inequality signs supposed to be 'greater than or equal to' signs?

Here we know the median is the average of the two 'middle numbers', so the median is (b+c)/2. If a < b, then (a+c)/2 is less than (b+c)/2, so (a+c)/2 cannot be the median. Similarly, if c < d, then (b+c)/2 is less than (b+d)/2, so (b+d)/2 cannot be the median. Finally (c+d)/2 is certainly greater than the median as well. So as written there are three correct answers, A, D and E.
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Which of the following CANNOT be the median of the four positive integers a, b, c, and d, where a < b < c < d ? (A) (a+c)/2 (B) (b+c)/2 (C) (a+d)/2 (D) (b+d)/2 (E) (c+d)/2

As written, there's something wrong with the question. Are some of the inequality signs supposed to be 'greater than or equal to' signs?

Here we know the median is the average of the two 'middle numbers', so the median is (b+c)/2. If a < b, then (a+c)/2 is less than (b+c)/2, so (a+c)/2 cannot be the median. Similarly, if c < d, then (b+c)/2 is less than (b+d)/2, so (b+d)/2 cannot be the median. Finally (c+d)/2 is certainly greater than the median as well. So as written there are three correct answers, A, D and E.

Thanks for confirming, Ian. I thought there was something wrong with the question, too.

as given positive integers a, b, c, and d, where a < b < c < d ?

since all are positive integers arranged in increasing order. mean of these will be a no greater then b and less then c. (A) (a+c)/2

This can be the median if resulting no is >b which is possible here as this is less than c already

(B) (b+c)/2

This is also possible coz resulting no must be > b and <c here. (C) (a+d)/2 This can be the median if resulting no is >b and <c which is possible here (D) (b+d)/2 This is also possible here as resulting no is >b and may be <c which is possible here

(E) (c+d)/2

This can never be median coz this no is always greater then c which violates the 2 condition defined here for median

as given positive integers a, b, c, and d, where a < b < c < d ?

since all are positive integers arranged in increasing order. mean of these will be a no greater then b and less then c. (A) (a+c)/2

This can be the median if resulting no is >b which is possible here as this is less than c already

If a < b < c < d, then (a + c)/2 cannot possibly be the median of a, b, c and d. The median of those four numbers is the average of the two middle numbers, so is equal to (b+c)/2. If a < b, then (a+c)/2 is strictly less than (b+c)/2; they cannot be equal.

I googled this question, and the OA is E, but the original question is different from the one in the post above. The actual question says that a < b < c < d, in which case (c+d)/2 must be greater than the median, while all the other choices could be equal to the median.
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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

1<2<6<7 here a+c/2 creates a no (1+6)/2 =3.5 which is greater then b so condition is true.

IanStewart wrote:

sandeeepsharma wrote:

Hi OA is E

as given positive integers a, b, c, and d, where a < b < c < d ?

since all are positive integers arranged in increasing order. mean of these will be a no greater then b and less then c. (A) (a+c)/2

This can be the median if resulting no is >b which is possible here as this is less than c already

Quote:

If a < b < c < d, then (a + c)/2 cannot possibly be the median of a, b, c and d. The median of those four numbers is the average of the two middle numbers, so is equal to (b+c)/2. If a < b, then (a+c)/2 is strictly less than (b+c)/2; they cannot be equal.

I googled this question, and the OA is E, but the original question is different from the one in the post above. The actual question says that a < b < c < d, in which case (c+d)/2 must be greater than the median, while all the other choices could be equal to the median.

Re: Which of the following CANNOT be the median of the four [#permalink]

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23 Apr 2014, 04:22

Interesting, I just got this question on a Jeff Sackman problem set that I paid $20 for.

I was looking at his explanation and thought that it HAD to be wrong, for the same reasoning as per above. His question was written exactly as above. I have sent an email but not sure if he will reply.

We will see....

gmatclubot

Re: Which of the following CANNOT be the median of the four
[#permalink]
23 Apr 2014, 04:22