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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: A set of 25 different integers has a median of 50 and a range of 50. W [#permalink]

Show Tags

18 Sep 2011, 20:43

dreambeliever 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

I go for D

Given Median = 50 Range = 50

Let Numbers be x1 , x2 , x3 ,.....,x13, .....x24, x25 x13 = 50 x25 - x1 = 50 Now From answer choices, E : let x25 = 100 => x1 = 50 Not possible as we need atleast a difference of 12 between x13 and x1.

Applying the same for all the answer choices we get A, B, C, D are possible. As we are asked abt max possible Ans is D.

Re: A set of 25 different integers has a median of 50 and a range of 50. W [#permalink]

Show Tags

18 Sep 2011, 22:29

2

This post received KUDOS

yes.. i think D too...

i have a different solution though... without looking at the answers...

the total set contains 25 numbers... and the mid-value (median) is 50 which implies the 13th value is 50.

For range to remain 50 and the last digit to be maximum, the first digit must be as close to 50 as possible... the greatest possible number is x1 is 38 (only then will the 13th number be 50)

Re: A set of 25 different integers has a median of 50 and a range of 50. W [#permalink]

Show Tags

19 Sep 2011, 00:26

2

This post received KUDOS

dreambeliever 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

Sol:

50 is the 13th number in the set.

Smallest integer closest to 50= 50-12=38 {: "minus 12" because there must be exactly 12 unique integers smaller than 50(median=50):}

Re: A set of 25 different integers has a median of 50 and a range of 50. W [#permalink]

Show Tags

29 Nov 2014, 23:13

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. _________________

Re: A set of 25 different integers has a median of 50 and a range of 50. W [#permalink]

Show Tags

30 Nov 2014, 05:18

Expert's post

1

This post was BOOKMARKED

dreambeliever 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

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}

Excellent posts dLo saw your blog too..!! Man .. you have got some writing skills. And Just to make an argument = You had such an amazing resume ; i am glad...

So Much $$$ Business school costs a lot. This is obvious, whether you are a full-ride scholarship student or are paying fully out-of-pocket. Aside from the (constantly rising)...

They say you get better at doing something by doing it. then doing it again ... and again ... and again, and you keep doing it until one day you look...

I barely remember taking decent rest in the last 60 hours. It’s been relentless with submissions, birthday celebration, exams, vacating the flat, meeting people before leaving and of...