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A set of 15 different integers has median of 25 and a range

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Re: A set of 15 different integers has median of 25 and a range [#permalink]

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New post 11 Nov 2016, 01:08
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bhushangiri wrote:
A set of 15 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?

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


The constraints are median (which is easy to handle - just that the 8th integer will be 25) and range (which is 25). The important thing is that all integers are different. For the range to be constant and then have the greatest possible integer, the smallest integer should be as large as possible.

Since all integers are distinct, the smallest integer should be 7 less than 25 i.e. 18 (so 18, 19, 20, 21, 22, 23, 24, 25 are the first 8 integers)

For the range to be 25, the greatest integer should be 18+25 = 43

Answer (D)
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Kudos [?]: 17361 [1], given: 232

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Re: A set of 15 different integers has median of 25 and a range [#permalink]

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New post 16 Apr 2017, 15:15
I think the easiest way to approach this problem is process elimination
Let's look at answer D which is 43
25 is the 8th number in the sequence

43 - x = 25
x = 43 - 25
x = 18

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

Therefore, the answer is D

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Re: A set of 15 different integers has median of 25 and a range [#permalink]

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New post 13 May 2017, 14:49
bhushangiri wrote:
A set of 15 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?

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


Need to maximize the smallest integer. Given that all integers are different, the smallest integer will be 25 (the median) - 7 =18. 18+25=43.

18, 19, 20, 21, 22, 23, 24, 25, ......., 43

To maximize the smallest integer, the gap between each integer that is less than the median should be the smallest it can possibly be. In this case, the gap is 1 because each number must be an integer and each number must be different.

If the integers could be the same, then the lowest integer could be 25 and the highest could be 50.

Agree? Kudos. Have anything to add, please comment.

Kudos [?]: 26 [0], given: 122

Re: A set of 15 different integers has median of 25 and a range   [#permalink] 13 May 2017, 14:49

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