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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, 15:39
So does that mean that this set does not contain any -ve integers? I am assuming it can not but why?
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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, 20:22
Hi Rocket7,

The question tells us that the RANGE of the numbers is 25... and asks us to find the largest POSSIBLE integer that could be in the set. If you look at the five answer choices - and then subtract 25 from each, you'll see that the SMALLEST number that would correspond to each of those answers would be a positive integer. Thus, the set CANNOT contain any negative numbers.

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

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21 Feb 2018, 00:21
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?

I missed "different" here and so, assumed the first 8 integers to be 25, and arrived at the highest number as 50:(.
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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 median of 25 and a range  [#permalink]

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13 Jan 2019, 06:06
Keeping it simple -

Range = 25
Median = 25
*15 integer NUMBERS that ARE DISTINCT*

Since there are 15 numbers. The median is the 8th number and it is equal to 25.

Range = Largest Number - Smallest number
25 = Largest Number - Smallest number

In other terms -
Largest Number = Smallest number + 25
Now it becomes obvious that to maximize the largest value, the smallest value has to be maximized!

From here the next step is pretty easy as we keep decreasing the values by 1 below the mean.
Re: A set of 15 different integers has median of 25 and a range   [#permalink] 13 Jan 2019, 06:06

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