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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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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]

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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]

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12 Jun 2009, 12:01
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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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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]

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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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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]

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09 Aug 2014, 02:58
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Re: A set of 15 different integers has median of 25 and a range [#permalink]

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18 Aug 2015, 08:34
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Re: A set of 15 different integers has median of 25 and a range [#permalink]

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18 Aug 2015, 21:27
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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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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Senior Manager Joined: 17 Jun 2015 Posts: 270 GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37 GMAT 3: Q V Followers: 3 Kudos [?]: 22 [1] , given: 165 Re: A set of 15 different integers has median of 25 and a range [#permalink] ### Show Tags 28 Dec 2015, 06:33 1 This post received KUDOS 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 _________________ Fais de ta vie un rêve et d'un rêve une réalité EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8597 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 400 Kudos [?]: 2570 [1] , given: 166 Re: A set of 15 different integers has median of 25 and a range [#permalink] ### Show Tags 28 Dec 2015, 16:47 1 This post received KUDOS Expert's post 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. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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

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29 Dec 2015, 12:49
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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.

GMAT assassins aren't born, they're made,
Rich

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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20 Apr 2016, 17:56
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
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Re: A set of 15 different integers has median of 25 and a range [#permalink]

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26 Oct 2016, 23:08
nookway wrote:
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

-------------------------------------------------------------------------------------------------------------------------------------

Haven't you made the assumption that the integers in the set are consecutive integers whereas the question does not specify that they are consecutive?
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Re: A set of 15 different integers has median of 25 and a range [#permalink]

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27 Oct 2016, 16:13
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

We are given that there are 15 different integers in a set with a median of 25 and a range of 25. We must determine the greatest possible integer that could be in the set. To determine this integer, we need to first determine the greatest possible value of the least integer from the set.

Since there are 15 total integers in the set, there are 7 integers before the median and 7 integers after the median if we list them in order. We must also keep in mind that each integer is different. Thus, the first 8 integers including the median are the following:

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

Since the range of this set is 25, the greatest number in this set must be 25 more than the smallest integer in the set, and thus the largest number in the set is 18 + 25 = 43.

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

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27 Oct 2016, 17:37
Hi Mitty,

Since the question asks for the LARGEST POSSIBLE integer that could be in the set of numbers, we have to tailor our work around a certain 'math idea' - since we have a range of 25, to get the largest possible integer, we need the smallest integer in the set to be as big as possible. Working 'backwards' from the median - and keeping in mind that all of the values are distinct - the numbers BELOW the median would have to be consecutive. In that way, we could make the smallest number as big as possible.

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Set of 15 different integers [#permalink]

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10 Nov 2016, 19:44
Set of 15 different integers has a median of 25 and a range of 25, what is the greatest possible integer that could be in this set?
A.32
B.37
C. 40
D. 43
E. 50

My answer is E, which is wrong please explain how.
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Re: Set of 15 different integers [#permalink]

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spc11 wrote:
Set of 15 different integers has a median of 25 and a range of 25, what is the greatest possible integer that could be in this set?
A.32
B.37
C. 40
D. 43
E. 50

Let's tackle this one step at a time.

First, we have 15 different integers.
We can let these 15 spaces represent the 15 numbers written in ascending order: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

If the median is 25, we can add this as the middle value: _ _ _ _ _ _ _ 25 _ _ _ _ _ _ _
Notice that 7 of the remaining numbers must be greater than 25 and the other 7 remaining number must be less than 25.

Since, we are told that the range is 25, we know that the greatest number minus the smallest number = 25

Now notice two things:
1) Once we know the value of the smallest number, the value of the greatest number is fixed.
For example, if the smallest number were 10, then the greatest number would have to be 35 in order to have a range of 25
Similarly, if the smallest number were 12, then the greatest number would have to be 37 in order to have a range of 25

2) If we want to maximize the value of the greatest number, we need to maximize the value of the smallest number.

So, how do we maximize the value of the smallest number in the set?
To do this, we must maximize each of the 7 numbers that are less than the median of 25.

Since the 15 numbers are all different, the largest values we can assign to the numbers less than the median of 25 are as follows:
18 19 20 21 22 23 24 25 _ _ _ _ _ _ _ (this maximizes the value of the smallest number)

If 18 is the maximum value we can assign to the smallest number, and if the range of the 15 numbers is 25, then greatest number must equal 43 (since 43 - 18 = 25)

So, the numbers are as follows: 18 19 20 21 22 23 24 25 _ _ _ _ _ _ 43 (the missing numbers don't really matter here)

This means the answer is 43
[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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10 Nov 2016, 20:28
spc11 wrote:
Set of 15 different integers has a median of 25 and a range of 25, what is the greatest possible integer that could be in this set?
A.32
B.37
C. 40
D. 43
E. 50

My answer is E, which is wrong please explain how.

Merging topics. Please search before posting.
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Re: A set of 15 different integers has median of 25 and a range [#permalink]

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10 Nov 2016, 20:38
Thanks a ton Bunnel!

GMATPrepNow wrote:
spc11 wrote:
Set of 15 different integers has a median of 25 and a range of 25, what is the greatest possible integer that could be in this set?
A.32
B.37
C. 40
D. 43
E. 50

Let's tackle this one step at a time.

First, we have 15 different integers.
We can let these 15 spaces represent the 15 numbers written in ascending order: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

If the median is 25, we can add this as the middle value: _ _ _ _ _ _ _ 25 _ _ _ _ _ _ _
Notice that 7 of the remaining numbers must be greater than 25 and the other 7 remaining number must be less than 25.

Since, we are told that the range is 25, we know that the greatest number minus the smallest number = 25

Now notice two things:
1) Once we know the value of the smallest number, the value of the greatest number is fixed.
For example, if the smallest number were 10, then the greatest number would have to be 35 in order to have a range of 25
Similarly, if the smallest number were 12, then the greatest number would have to be 37 in order to have a range of 25

2) If we want to maximize the value of the greatest number, we need to maximize the value of the smallest number.

So, how do we maximize the value of the smallest number in the set?
To do this, we must maximize each of the 7 numbers that are less than the median of 25.

Since the 15 numbers are all different, the largest values we can assign to the numbers less than the median of 25 are as follows:
18 19 20 21 22 23 24 25 _ _ _ _ _ _ _ (this maximizes the value of the smallest number)

If 18 is the maximum value we can assign to the smallest number, and if the range of the 15 numbers is 25, then greatest number must equal 43 (since 43 - 18 = 25)

So, the numbers are as follows: 18 19 20 21 22 23 24 25 _ _ _ _ _ _ 43 (the missing numbers don't really matter here)

This means the answer is 43
[Reveal] Spoiler:
D

RELATED VIDEO
Re: A set of 15 different integers has median of 25 and a range   [#permalink] 10 Nov 2016, 20:38

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