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a median of 25 and a range of 25

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by sanju09 » Wed Mar 23, 2011 2:07 am
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



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by AIM GMAT » Wed Mar 23, 2011 2:17 am
IMO D . 43

25 = median = 8th term

greatest possible interger so we need the max number .

7 terms before 25 and 7 terms after 25

so 25-7 = 18 will be the least term on the set .

The range is 25 , max - least = 25
=> least + range = max
=> 18+25 = 43
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by Anurag@Gurome » Wed Mar 23, 2011 3:12 am
sanju09 wrote: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
Median of a set of 15 different integers will be the 8th integer of the series when arranged according to their values.

Now, Largest - Smallest = Range => Largest = (Smallest + Range)
As the range is fixed, we can maximize largest number by maximizing the smallest number.

Maximum possible value of the smallest integer in the set is (25 - 7) = 18, as all the terms are different and 25 is the 8th term.

Hence, greatest possible integer in the set = (18 + Range) = (18 + 25) = 43

The correct answer is D.
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