GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Nov 2019, 07:52

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A set of 15 different integers has median of 25 and a range

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9803
Location: Pune, India
Re: A set of 15 different integers has median of 25 and a range  [#permalink]

Show Tags

New post 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.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Intern
avatar
Joined: 20 Aug 2018
Posts: 25
A set of 15 different integers has median of 25 and a range  [#permalink]

Show Tags

New post 24 Nov 2018, 15:56
A video explanation can be found here:
https://www.youtube.com/watch?v=z_TK8hXmny0&t=35s

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
_________________
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: A set of 15 different integers has median of 25 and a range  [#permalink]

Show Tags

New post 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.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13630
Re: A set of 15 different integers has a median of 25 and a  [#permalink]

Show Tags

New post 08 Oct 2019, 08:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: A set of 15 different integers has a median of 25 and a   [#permalink] 08 Oct 2019, 08:12

Go to page   Previous    1   2   [ 24 posts ] 

Display posts from previous: Sort by

A set of 15 different integers has median of 25 and a range

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne