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Set T = {a, b, c, d, e} The distinct positive integers...

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by swerve » Sun Dec 03, 2017 12:51 pm
Set T = {a, b, c, d, e}

The distinct positive integers a, b, c, d, and e are listed in ascending order. Which of the following could not be the median of Set T?

A. (a + c)/2
B. (a + d)/2
C. (a + e)/2
D. (b + e)/2
E. (b + d)/2

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
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Set T = {a, b, c, d, e} The distinct positive integers...

by regor60 » Mon Dec 04, 2017 10:02 am
swerve wrote:Set T = {a, b, c, d, e}

The distinct positive integers a, b, c, d, and e are listed in ascending order. Which of the following could not be the median of Set T?

A. (a + c)/2
B. (a + d)/2
C. (a + e)/2
D. (b + e)/2
E. (b + d)/2

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
Possible answers B though E calculate the average of two numbers that span the median, C, so there is some chance that one of these averages could equal C. Knowing this then tells you the answer must be A


But let's prove this to ourselves:
Answer A, however, averages A and the median itself
Working through this: (A+C)/2 = A/2 + C/2 > does this equal C ? Let's assume it does and write: A/2 + C/2 = C, that would mean that:

A/2 = C/2. Can this be true ? No, because the problem wording indicates that A is less than C, therefore, A/2 can't equal C/2 and therefore Answer A can't be true A
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