A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in this set?

A) 32
B) 37
C) 40
D) 43
E) 50

Ans is D i.e.43

Assume first value A and Last value x

Range is 25=x-A Also Median =25

Set of different integers
Only one value satisfy this 43-18

18,19,20,21,22,23,24,25

Harish,

sometimes, when the algebraic solution is not obvious, it can be advantageous to roll up your sleeves and attack the problem with "brute force." In this case, the median is 25, so the 8th number in ascending order must be 25. Moreover, the range is 25, so the difference between the smallest and largest numbers must be 25.

Because this is a "could" problem that asks for the "greatest possible integer," let's attack the largest integers first.

E) 50: If 50 is greatest number than 25 must be smallest (as the range is 25). This, obviously, cannot yield a median of 25.

D) 43: If 43 is greatest number than 18 must be smallest (as the range is 25). Now, just list numbers to check whether 25 can be the 8th number in ascending order. 18, 19, 20, 21, 22, 23, 24, 25... As 25 is the 8th number, the correct answer is D.

-dan