Statistics

[koby_gen]

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

[4GMAT_Mumbai]

Hi,

The median is (b+c)/2.

Let us consider each of the options.

A. The median could be (a+c)/2 if a = b.

B. It is (b+c)/2

C. It could be (a+d)/2 if a=b and c=d

d. It could be (b+d)/2 if c=d

E. It cannot be (c+d)/2 as b can never be equal to d.

Is it E?

Thanks. Hope it helps.

[MAAJ]

IMO [spoiler](E)[/spoiler]

The median is the middle number. In this case, because we got 4 numbers, there isn't an exact middle number so we must take the two middle numbers and divide by 2.
(A) (a+c)/2 -> a could be equal to b, so this could equal (b+c)/2
(B) (b+c)/2 -> this is the median
(C) (a+d)/2 -> a could be equal to b and d could be equal to c, so this could equal (b+c)/2
(D) (b+d)/2 -> d could be equal to c, so this could equal (b+c)/2
(E) (c+d)/2 -> this can't be equal to (b+c)/2

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