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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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19 Jan 2018, 21:44
Rocket7 wrote:
So does that mean that this set does not contain any -ve integers? I am assuming it can not but why?

The set cannot have negative integers because of the given data points.
The median is 25 so the middle element is 25.
The range is 25 so greatest - smallest = 25
We know that 25 is there in the set so the smallest element can certainly not be less than 0 since the range of the entire set is 25.
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A set of 15 different integers has median of 25 and a range  [#permalink]

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24 Nov 2018, 15:56
A video explanation can be found here:

Median is 25. In a set of 15 integers, the median will be the 8th number (take 15 – 1, then divide that by 2. You have seven numbers to left of the median and seven to the right.)

Maximum value of the “greatest” possible integer would equal maximum value of the “least” possible integer, plus 25.

Since all integers are different, least possible integer is 15 - 7 = 18.

Maximum possible integer is therefore 18 + 25 = 43
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Re: A set of 15 different integers has median of 25 and a range  [#permalink]

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25 Dec 2018, 11:28
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

WLOG (without loss of generality) we may assume that:

$$a = {x_1} < {x_2} < \ldots < {x_7} < {x_8} = 25 < {x_9} < \ldots < {x_{14}} < {x_{15}} = a + 25\,\,\,\,\,{\text{ints}}$$

Considering this powerful structure, the problem is trivialized:

$$?\,\, = \,\,\left( {a + 25} \right)\,\,\max \,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,a\,\,\max$$

$$a\,\,\max \,\,\,\,\, \Leftrightarrow \,\,\,\,\left( {{x_7},{x_6},{x_5},{x_4},{x_3},{x_2},{x_1} = a} \right) = \left( {24,23,22,21,20,19,18} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,a\,\,\max \,\, = \,\,18\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = 43$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: A set of 15 different integers has a median of 25 and a  [#permalink]

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08 Oct 2019, 08:12
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Re: A set of 15 different integers has a median of 25 and a   [#permalink] 08 Oct 2019, 08:12

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