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

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A set of 15 different integers has median of 25 and a range [#permalink]  12 Aug 2008, 03:50
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Aug 2014, 00:15, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: A set of 15 different integers has median of 25 and a range [#permalink]  12 Aug 2008, 04:16
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bhushangiri wrote:
A set of 15 different integers has median 25 and range 25. What could be the greatest possible integer in this set ?

OA is 43.

How 43 ? I am getting 50.

50 can not be the highest number.

for the range to be 25, (50 - least number) = 25, i.e least number is 25
But it's given that 25 is median and since each number is different, there must be 7 smaller numbers than 25
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Re: set of 15 integers [#permalink]  12 Jun 2009, 12:01
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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?

Given 15 different integers, lets say

n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, n11, n12, n13, n14, n15

Also given median is 25 i.e. n8 = 25

n1, n2, n3, n4, n5, n6, n7, 25, n9, n10, n11, n12, n13, n14, n15

As each integer is different we need to find the maximum values for all those numbers before the median.

the maximum value n7 can have is one less then the median i.e. 24, similarly n6 will be one less than 24 i.e. 23 ... using this process the values for all number before the median would be..

18, 19, 20, 21, 22, 23, 24, 25, n9, n10, n11, n12, n13, n14, n15

Also given the range is 25 i.e. n15 - n1 (18) = 25
The maximum value n15 can have is 25 + n1 (18) = 43
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Re: set of 15 integers [#permalink]  17 May 2011, 23:11
8 different numbers from 1st to 8th number gives lowest number = 25-8= 18
hence max number = 18+25 = 43.
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Re: A set of 15 different integers has median of 25 and a range [#permalink]  02 Sep 2013, 13:05
bhushangiri wrote:
A set of 15 different integers has median 25 and range 25. What could be the greatest possible integer in this set ?

OA is 43.

How 43 ? I am getting 50.

Try to right down 25 in the middle as a median and 7 numbers to the left and 7 nubers to the right.
You will see clearly that the minimum possible least number is 18 to the left of 25.
Hence 18+25 -->43

18 19 20 21 22 23 24 25 ....... --> the least possible
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Re: A set of 15 different integers has median of 25 and a range [#permalink]  02 Sep 2013, 13:26
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bhushangiri wrote:
A set of 15 different integers has median 25 and range 25. What could be the greatest possible integer in this set ?

OA is 43.

How 43 ? I am getting 50.

Similar question to practice:
Quote:
A set of 25 different integers has a median of 50 and a range of 50. What is the greatest possible integer that could be in this set?

(A) 62
(B) 68
(C) 75
(D) 88
(E) 100

Discussed here: a-set-of-25-different-integers-has-a-median-of-50-and-a-129345.html

Variation of this question: a-set-of-25-integers-has-a-median-of-50-and-a-range-of-128463.html
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Re: set of 15 integers [#permalink]  09 Aug 2014, 02:58
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Re: set of 15 integers   [#permalink] 09 Aug 2014, 02:58
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