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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]

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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, 01:15, 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]

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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]

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The correct answer is D.

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]

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New post 18 May 2011, 00:11
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]

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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.







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]

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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]

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

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

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Hi All,

When it comes to maximizing or minimizing a value in a group of numbers, you have to think about what the other numbers would need to be to accomplish your goal.

Here, we have a group of 15 DISTINCT (meaning DIFFERENT) integers with a median of 25 and a RANGE of 25. That range will dictate how large the largest value can be.

With a median of 25, we know that 7 numbers are LESS than 25 and 7 numbers are GREATER than 25:

_ _ _ _ _ _ _ 25 _ _ _ _ _ _ _

To maximize the largest value, we need to maximize the smallest value. Here's how we can do it:

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

With 18 as the smallest value, and a range of 25, the largest value would be 43.

Final Answer:
[Reveal] Spoiler:
D


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

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The largest in the set minus the smallest in the set should be 25
All the integers are different

Use the options. If 50 is the largest and the range is 25, the smallest is 25, which could have been if the integers were allowed to be same in the set.


Next option to check is 43. 43 - 25 = 18. Can 18 be a part of the set and at the same time there are no repetitions and 25 is the median? Yes

18, 19, 20, 21, 22, 23, 25, 6 more numbers, 43

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

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Hi hdwnkr,

Excellent use of TESTing THE ANSWERS! While that approach isn't nearly as useful overall as TESTing VALUES or the frequent 'math' approaches that will always be an option, it WILL be applicable at least a handful of times on Test Day. Having that approach in your skill-set will help you to quickly (and correctly) solve those few questions and move on with confidence.

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

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EMPOWERgmatRichC wrote:
Hi hdwnkr,

Excellent use of TESTing THE ANSWERS! While that approach isn't nearly as useful overall as TESTing VALUES or the frequent 'math' approaches that will always be an option, it WILL be applicable at least a handful of times on Test Day. Having that approach in your skill-set will help you to quickly (and correctly) solve those few questions and move on with confidence.

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Thanks a lot for the encouragement. Much appreciated! :) Helps when I am just days away from the D Day
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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 20 Apr 2016, 18:56
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

25 is the median
numbers are different
it means there are 7 different numbers to the right and 7 different numbers to the left. to maximize the last one, we need to maximize the lowest one so that the range would be 25.
now...
7th number - 24
6th number - 23
5th number - 22
4th number - 21
3rd number - 20
2nd number - 19
1st number - 18

18+25 = 43

answer - D
Re: A set of 15 different integers has median of 25 and a range   [#permalink] 20 Apr 2016, 18:56
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