A, B, C, D, E, and F are six consecutive positive odd integers in incr

Question

A, B, C, D, E, and F are six consecutive positive odd integers in increasing order. What is the value of the median of these six integers?

(1) The sum of the two smallest integers is greater than the largest integer by 13
(2) The average (arithmetic mean) of these integers is 26

gmatophobia · Answer

Let the value of C = x

A = x - 4

B = x - 2

C = x

D = x + 2

E = x + 4

F = x + 6

The median of the set =  \frac{C + D }{ 2} = \frac{2x + 2 }{ 2} = x + 1

Hence if we know the value of x (i.e. C) we can find the median of the set.

Statement 1

(1) The sum of the two smallest integers is greater than the largest integer by 13

x - 4 + x - 2 - (x + 6) = 13

2x - x - 6 - 6 = 13

x = 25

Sufficient

We can eliminate B, C, and E

Statement 2

(2) The average (arithmetic mean) of these integers is 26

This is a uniformly spaced set. Hence the mean = median.

The information is sufficient.

Option D

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