GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 05 Apr 2020, 16:16

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A set of 25 different integers has a median of 50 and a

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

19 Mar 2012, 14:46
15
81
00:00

Difficulty:

65% (hard)

Question Stats:

58% (01:35) correct 42% (01:34) wrong based on 1126 sessions

### HideShow timer Statistics

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

Any idea how to solve this question please?

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert
Joined: 02 Sep 2009
Posts: 62498
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

19 Mar 2012, 23:14
25
29
enigma123 wrote:
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

Any idea how to solve this question please?

Consider 25 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{25}$$.

The median of a set with odd number of elements is the middle number (when arranged in ascending or descending order), so the median of given set is $$x_{13}=50$$;

The range of a set is the difference between the largest and the smallest numbers of a set, so the range of given set is $$50=x_{25}-x_{1}$$ --> $$x_{25}=50+x_{1}$$;

We want to maximize $$x_{25}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-12=50-12=38$$ and thus the maximum value of $$x_{25}$$ is $$x_{25}=38+50=88$$.

The set could be {38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 88}

Hope it's clear.
_________________
Intern
Joined: 03 Feb 2012
Posts: 45
Location: United States (WI)
Concentration: Other
Schools: University of Wisconsin (Madison) - Class of 2014
GMAT 1: 680 Q46 V38
GMAT 2: 760 Q48 V46
GPA: 3.66
WE: Marketing (Manufacturing)

### Show Tags

19 Mar 2012, 17:36
4
1
3
If 25 different integers have a median of 50, then the 13th largest integer in the set is 50 - 12 less than 50, 12 greater than 50 or { 12 different integers less than 50, 50, 12 different integers greater than 50 }.

To get to "the greatest possible integer in the set" - you need to first find the highest possible set of integers in 12 integers less than 50. This is {38, 39, ..., 48, 49}.

So 38 is the low point for the range of 50, leaving you with a high point of 88. The set could be many variations of {38, 39, ... , 50, 11 integers greater than 50 and less than 88, 88}
##### General Discussion
Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

20 Mar 2012, 01:46
I think Bunuel , you meant "We want to maximize $$x_{25}$$, hence we need to minimize $$x_{1}$$. I still don't understand how did you get the below:

Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-12=50-12=38$$
_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert
Joined: 02 Sep 2009
Posts: 62498
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

20 Mar 2012, 01:54
3
2
enigma123 wrote:
I think Bunuel , you meant "We want to maximize $$x_{25}$$, hence we need to minimize $$x_{1}$$. I still don't understand how did you get the below:

Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-12=50-12=38$$

Since $$x_{25}=50+x_{1}$$ then in order to maximize $$x_{25}$$ we need to maximize $$x_{1}$$, so everything is correct there.

As for the next part: $$median=x_{13}=50$$ and since all terms must be distinct integers then the maximum value of $$x_{1}$$ is 50-12=38: $$x_{1}=38$$, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, $$median=x_{13}=50$$. As you can see $$x_{1}$$ cannot possibly be more than 38.

Hope it's clear.
_________________
Intern
Joined: 13 Sep 2011
Posts: 3
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

03 Apr 2012, 03:10
1
1
I am not a quant genius, but a basic learner. However, I found an answer to this question after passing through different hurdles virtually....I worked on the following question to get the answer for this one, because both are similar:

A set of 13 different integers has a median of 30 and a range of 30. What is the greatest possible integer that could be in this set?

A)36

B)43

C)54

D)57

E)60

I considered the below set of values to get the maximum value of the number in a set:

30, 30, 30, 30, 30, 30, 30, 35, 40, 45, 50, 55, 60.

Hence, median = range = 30
Therefore, the maximum value is 60.

I believe, we can apply the same thought process in the actual question and answer it. I am open to feedback. Please do let me know if I have gone wrong anywhere.
Intern
Joined: 19 Aug 2011
Posts: 20
Concentration: Finance, Entrepreneurship
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

03 Apr 2012, 03:25
smileforever41 wrote:
I considered the below set of values to get the maximum value of the number in a set:

30, 30, 30, 30, 30, 30, 30, 35, 40, 45, 50, 55, 60.

Hence, median = range = 30
Therefore, the maximum value is 60.

I believe, we can apply the same thought process in the actual question and answer it. I am open to feedback. Please do let me know if I have gone wrong anywhere.

You missed the word 13 different integers
Intern
Joined: 27 Feb 2012
Posts: 35
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

Updated on: 04 Apr 2012, 01:32
3
1
smileforever41:
In the style of the legend Bunuel:

Consider 13 numbers in ascending order to be $$x_1, x_2, x_3, ..., x_{13}$$.

The median of a set with odd number of elements is the middle number (when arranged in ascending or descending order), so the median of given set is $$x_{7}=30$$;

The range of a set is the difference between the largest and the smallest numbers of a set, so the range of given set is $$30=x_{13}-x_{1}$$ --> $$x_{13}=30+x_{1}$$;

We want to maximize $$x_{13}$$, hence we need to maximize $$x_{1}$$ (remember the restriction of range). Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-6=30-6=24$$ and thus the maximum value of $$x_{13}$$ is $$x_{13}=24+30=54$$.

The set could be {24,25,26,27,28,29,30,38,40,45,47,49,54}

Originally posted by Anonym on 03 Apr 2012, 05:08.
Last edited by Anonym on 04 Apr 2012, 01:32, edited 1 time in total.
Intern
Joined: 18 Jan 2012
Posts: 43
Location: United States
Schools: IIM A '15 (A)
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

15 Aug 2012, 01:55

Hi..I believe that everyone has inadvertently overlooked the fact that the definition an integer includes negative numbers as well.

All The following sets easily satisfy the conditions stated in the problem.. (Median = 50 , Range is 50).

-50,-51,-52............50......100
-150,-51,-52............50.....200
-250,-51,-52............50.....200
Math Expert
Joined: 02 Sep 2009
Posts: 62498
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

15 Aug 2012, 04:54
1
hafizkarim wrote:

Hi..I believe that everyone has inadvertently overlooked the fact that the definition an integer includes negative numbers as well.

All The following sets easily satisfy the conditions stated in the problem.. (Median = 50 , Range is 50).

-50,-51,-52............50......100
-150,-51,-52............50.....200
-250,-51,-52............50.....200

Not so.

First of all set -50,-51,-52............50......100 is not ordered. In ascending order it would be {-52, -51, ..., 50, ..., 100} (assume there are 25 integer in the set). Now, the range of this set is {range}={largest}-{smallest}=100-(-52)=152, not 50.

Hope it's clear.
_________________
Manager
Joined: 07 Sep 2011
Posts: 59
Location: United States
GMAT 1: 640 Q39 V38
WE: General Management (Real Estate)
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

17 Aug 2012, 03:44
1
Hi Bunuel,

Had the question not mentioned "Distinct Integers", we would have taken all first 13 values as 50 and maximum would have been 100". Is my thinking correct?

Bunuel wrote:
hafizkarim wrote:

Hi..I believe that everyone has inadvertently overlooked the fact that the definition an integer includes negative numbers as well.

All The following sets easily satisfy the conditions stated in the problem.. (Median = 50 , Range is 50).

-50,-51,-52............50......100
-150,-51,-52............50.....200
-250,-51,-52............50.....200

Not so.

First of all set -50,-51,-52............50......100 is not ordered. In ascending order it would be {-52, -51, ..., 50, ..., 100} (assume there are 25 integer in the set). Now, the range of this set is {range}={largest}-{smallest}=100-(-52)=152, not 50.

Hope it's clear.
Math Expert
Joined: 02 Sep 2009
Posts: 62498
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

17 Aug 2012, 03:51
manjeet1972 wrote:
Hi Bunuel,

Had the question not mentioned "Distinct Integers", we would have taken all first 13 values as 50 and maximum would have been 100". Is my thinking correct?

Bunuel wrote:
hafizkarim wrote:

Hi..I believe that everyone has inadvertently overlooked the fact that the definition an integer includes negative numbers as well.

All The following sets easily satisfy the conditions stated in the problem.. (Median = 50 , Range is 50).

-50,-51,-52............50......100
-150,-51,-52............50.....200
-250,-51,-52............50.....200

Not so.

First of all set -50,-51,-52............50......100 is not ordered. In ascending order it would be {-52, -51, ..., 50, ..., 100} (assume there are 25 integer in the set). Now, the range of this set is {range}={largest}-{smallest}=100-(-52)=152, not 50.

Hope it's clear.

Absolutely. If we were not told that the integers in the set must be distinct, then all terms from $$x_1$$ to $$x_{13}$$, could be 50 and in this case the greatest integer, which could be in the set, would be $$x_1+\{range\}=50+50=100$$.

Hope it's clear.
_________________
Intern
Joined: 08 Feb 2011
Posts: 11
Re: A set of 15 different integers has a median of 25  [#permalink]

### Show Tags

09 Jan 2013, 17:03
1
The median (middle number in the set) is 25. It is stated that there are 15 different integers in the set, so there will be 7 different integers smaller than 25 and 7 different integers larger than 25 in the set.

To maximize the largest value in this set, we want to maximize the smallest value in the set.
Therefore, the 7 different integers in the set smaller than 25 will be 24, 23, 22, 21, 20, 19, 18.

18 (maximized smallest integer in set) + 25 (range of set) = largest possible integer in the set

Senior Manager
Joined: 27 Jun 2012
Posts: 345
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
Re: A set of 15 different integers has a median of 25  [#permalink]

### Show Tags

09 Jan 2013, 17:23
1
1
Consider first number = x
Last number = x + 25
And we have median (8th number)=25
Series: x,...6 numbers..., 25 , ...6 numbers..., (x+25)

In order to have the "last number" (x+25) as the greatest possible, we have to maximize the "first number" (x) (under 25).

To maximize x, identify Integers under 25 such that they are consecutive in descending order.
i.e. 18, 19, 220, 21, 22, 23, 24, 25

Thus first number $$x=18$$ and largest number$$x + 25 = 18 +25 =43.$$

Hence choice(D) is correct.

The series would look like this: 18, 19, 220, 21, 22, 23, 24, 25, ... 6 numbers ..., 43
Note that choice (E) with 50 is a TRAP answer for someone who didn't notice the information "different" numbers.
_________________
Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here
Manager
Joined: 18 Oct 2011
Posts: 75
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

10 Jan 2013, 06:58
For these type of questions you know that since we have an odd number of terms in the set - The median is the 13th number. Since we are looking at the greatest possible number that could have a range of 50, we would want to maximize the 12 numbers that precede the median (50). Since all the numbers in the set are different the first term would have to be 38.

For a range of 50, only 88 would satisfy this condition. Answer: D
Director
Joined: 29 Nov 2012
Posts: 675
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

26 Feb 2013, 07:36
Bunuel wrote:
enigma123 wrote:
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

Any idea how to solve this question please?

Consider 25 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{25}$$.

The median of a set with odd number of elements is the middle number (when arranged in ascending or descending order), so the median of given set is $$x_{13}=50$$;

The range of a set is the difference between the largest and the smallest numbers of a set, so the range of given set is $$50=x_{25}-x_{1}$$ --> $$x_{25}=50+x_{1}$$;

We want to maximize $$x_{25}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-12=50-12=38$$ and thus the maximum value of $$x_{25}$$ is $$x_{25}=38+50=88$$.

The set could be {38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 88}

Hope it's clear.

Since the question mentions different we have to pick numbers as close to the median? What would happen if they didn't mention different numbers? so then we assign the value as median?
Manager
Joined: 14 Jan 2013
Posts: 127
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

18 Nov 2013, 15:20
Bunuel wrote:
enigma123 wrote:
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

Any idea how to solve this question please?

Consider 25 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{25}$$.

The median of a set with odd number of elements is the middle number (when arranged in ascending or descending order), so the median of given set is $$x_{13}=50$$;

The range of a set is the difference between the largest and the smallest numbers of a set, so the range of given set is $$50=x_{25}-x_{1}$$ --> $$x_{25}=50+x_{1}$$;

We want to maximize $$x_{25}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-12=50-12=38$$ and thus the maximum value of $$x_{25}$$ is $$x_{25}=38+50=88$$.

The set could be {38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 88}

Hope it's clear.

Why have we taken consecutive integers in this cases?
Math Expert
Joined: 02 Sep 2009
Posts: 62498
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

19 Nov 2013, 01:38
Mountain14 wrote:
Bunuel wrote:
enigma123 wrote:
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

Any idea how to solve this question please?

Consider 25 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{25}$$.

The median of a set with odd number of elements is the middle number (when arranged in ascending or descending order), so the median of given set is $$x_{13}=50$$;

The range of a set is the difference between the largest and the smallest numbers of a set, so the range of given set is $$50=x_{25}-x_{1}$$ --> $$x_{25}=50+x_{1}$$;

We want to maximize $$x_{25}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-12=50-12=38$$ and thus the maximum value of $$x_{25}$$ is $$x_{25}=38+50=88$$.

The set could be {38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 88}

Hope it's clear.

Why have we taken consecutive integers in this cases?

The set could be...
_________________
Director
Joined: 08 Jun 2010
Posts: 675
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

12 May 2015, 04:10
1
Bunuel wrote:
enigma123 wrote:
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

Any idea how to solve this question please?

Consider 25 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{25}$$.

The median of a set with odd number of elements is the middle number (when arranged in ascending or descending order), so the median of given set is $$x_{13}=50$$;

The range of a set is the difference between the largest and the smallest numbers of a set, so the range of given set is $$50=x_{25}-x_{1}$$ --> $$x_{25}=50+x_{1}$$;

We want to maximize $$x_{25}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-12=50-12=38$$ and thus the maximum value of $$x_{25}$$ is $$x_{25}=38+50=88$$.

The set could be {38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 88}

Hope it's clear.

I can not say a word for this wonderful explanation
Manager
Joined: 03 Aug 2015
Posts: 51
Concentration: Strategy, Technology
Schools: ISB '18, SPJ GMBA '17
GMAT 1: 680 Q48 V35
Re: A set of 25 different integers has a median of 50 and a  [#permalink]

### Show Tags

15 Dec 2015, 07:56
Bunuel wrote:
enigma123 wrote:
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

Any idea how to solve this question please?

Consider 25 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{25}$$.

The median of a set with odd number of elements is the middle number (when arranged in ascending or descending order), so the median of given set is $$x_{13}=50$$;

The range of a set is the difference between the largest and the smallest numbers of a set, so the range of given set is $$50=x_{25}-x_{1}$$ --> $$x_{25}=50+x_{1}$$;

We want to maximize $$x_{25}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-12=50-12=38$$ and thus the maximum value of $$x_{25}$$ is $$x_{25}=38+50=88$$.

The set could be {38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 88}

Hope it's clear.

Thanks for the explanation Bunel...

Could you pls share some similar question for practice?

Thanks,
Arun
Re: A set of 25 different integers has a median of 50 and a   [#permalink] 15 Dec 2015, 07:56

Go to page    1   2    Next  [ 31 posts ]

Display posts from previous: Sort by