Which of the following cannot be the median of five positive integers a, b, c, d, and e?

(A) a

(B) d + e

(C) b + c + d

(D) (b + c + d) / 3

(E) (a + b + c + d + e) / 5


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Note that you are not given that the numbers are arranged in ascending order. They could be any way when arranged in ascending order. Keeping this in mind, try to find easy ways of getting the median.

(A) a
a could be the middle number

(B) d + e
Middle number could be other than d and e and d and e could be the numbers smaller than the middle numbers e.g.
1 , 1, 2, 2, 2
- Median is 2 which is 1 + 1

(D) (b + c + d) / 3
Avg of 3 numbers can certainly be the median - say all numbers are equal: 2, 2, 2, 2, 2 - median is 2 - avg of any 3 numbers

(E) (a + b + c + d + e) / 5
Avg of all 5 numbers can certainly be the median - say all numbers are equal: 2, 2, 2, 2, 2 - median is 2 - avg of all 5 numbers

(C) b + c + d
Now, you don't need to worry about (C) and you can just mark it but note why it cannot be the median.
Out of 5 positive numbers, median will be the middle number. b , c or d cannot be the middle number. So either a or e will be the median. Two numbers will be smaller than (or equal to) the median and two numbers will be greater (or equal to). So even if you pick both numbers which are smaller than the median, you will still need to pick one which is equal or greater. So sum of 3 numbers will certainly be greater than the median.

Answer (C)
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