Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 06 Oct 2015, 11:53

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# GMAT Diagnostic Test Question 21

Author Message
Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 13021
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
Followers: 2918

Kudos [?]: 15193 [1] , given: 3940

GMAT Diagnostic Test Question 21 [#permalink]  06 Jun 2009, 21:59
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
GMAT Diagnostic Test Question 21
Field: word problems (min/max)
Difficulty: 700

A set of 11 different integers has a median of 25 and a range of 50. What is the greatest possible integer that could be in this set?

A. 65
B. 70
C. 75
D. 80
E. 85
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... | Want to know your GMAT Score? Try GMAT Score Estimator
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

Have a blog? Feature it on GMAT Club!

GMAT Club Premium Membership - big benefits and savings

Last edited by bb on 28 Sep 2013, 20:33, edited 1 time in total.
Updated
 Kaplan Promo Code Knewton GMAT Discount Codes Manhattan GMAT Discount Codes
CIO
Joined: 02 Oct 2007
Posts: 1217
Followers: 93

Kudos [?]: 799 [6] , given: 334

Re: GMAT Diagnostic Test Question 20 [#permalink]  08 Jul 2009, 05:56
6
KUDOS
2
This post was
BOOKMARKED
Consider 11 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{11}$$.

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 $$x_{6}=25$$;

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 $$50=x_{11}-x_{1}$$ --> $$x_{11}=50+x_{1}$$;

We want to maximize $$x_{11}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-5=25-5=20$$ and thus the maximum value of $$x_{11}$$ is $$x_{11}=50+20=70$$.

The set could be {20, 21, 22, 23, 24, 25, 26, 27, 26, 29, 70}

_________________

Welcome to GMAT Club!

Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 02 Jul 2013
Posts: 1
Followers: 0

Kudos [?]: 1 [1] , given: 0

Re: GMAT Diagnostic Test Question 21 [#permalink]  20 Nov 2013, 11:24
1
KUDOS
Why must the numbers in the set be different in order to calculate the median?

Couldn't I arrange a set like the following? S={25, 25, 25, 25, 25, 25, 75, 75, 75, 75, 75}?
(Note that after x6, the follwoing numbers could be anything between 26 and 74)

In this way, the median is still 25, but the máximum value of x would now be 75, making "C" the correct answer.

D.
Math Expert
Joined: 02 Sep 2009
Posts: 29750
Followers: 4894

Kudos [?]: 53356 [1] , given: 8155

Re: GMAT Diagnostic Test Question 21 [#permalink]  21 Nov 2013, 00:55
1
KUDOS
Expert's post
peti wrote:
Why must the numbers in the set be different in order to calculate the median?

Couldn't I arrange a set like the following? S={25, 25, 25, 25, 25, 25, 75, 75, 75, 75, 75}?
(Note that after x6, the follwoing numbers could be anything between 26 and 74)

In this way, the median is still 25, but the máximum value of x would now be 75, making "C" the correct answer.

D.

The number is the set must be different because we are told that they are different, check the stem: "A set of 11 different integers has ..."
_________________
Intern
Joined: 19 Jul 2013
Posts: 23
Location: United States
GMAT 1: 340 Q27 V12
GPA: 3.33
Followers: 0

Kudos [?]: 6 [1] , given: 9

Re: GMAT Diagnostic Test Question 20 [#permalink]  05 Jan 2014, 16:45
1
KUDOS
[quote="dzyubam"]Consider 11 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{11}$$.

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 $$x_{6}=25$$;

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 $$50=x_{11}-x_{1}$$ --> $$x_{11}=50+x_{1}$$;

We want to maximize $$x_{11}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-5=25-5=20$$ and thus the maximum value of $$x_{11}$$ is $$x_{11}=50+20=70$$.

The set could be {20, 21, 22, 23, 24, 25, 26, 27, 26, 29, 70}

its clear till since....distict
i was not able to follow after that..??? can u please explain just that area
Math Expert
Joined: 02 Sep 2009
Posts: 29750
Followers: 4894

Kudos [?]: 53356 [1] , given: 8155

Re: GMAT Diagnostic Test Question 20 [#permalink]  05 Jan 2014, 18:03
1
KUDOS
Expert's post
lindt123 wrote:
dzyubam wrote:
Consider 11 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{11}$$.

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 $$x_{6}=25$$;

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 $$50=x_{11}-x_{1}$$ --> $$x_{11}=50+x_{1}$$;

We want to maximize $$x_{11}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-5=25-5=20$$ and thus the maximum value of $$x_{11}$$ is $$x_{11}=50+20=70$$.

The set could be {20, 21, 22, 23, 24, 25, 26, 27, 26, 29, 70}

its clear till since....distict
i was not able to follow after that..??? can u please explain just that area

We know that the median, $$x_6$$, is 25. What is the maximum value of $$x_5$$. Since $$x_5<x_6$$, then the maximum value of $$x_5$$ is 24. Similarly the maximum value of $$x_4$$ is 23, the maximum value of $$x_3$$ is 22, the maximum value of $$x_2$$ is 21 and the maximum value of $$x_1$$ is 20.

Hope it's clear.
_________________
Intern
Joined: 19 Jul 2013
Posts: 23
Location: United States
GMAT 1: 340 Q27 V12
GPA: 3.33
Followers: 0

Kudos [?]: 6 [0], given: 9

Re: GMAT Diagnostic Test Question 20 [#permalink]  05 Jan 2014, 20:51
Bunuel wrote:
lindt123 wrote:
dzyubam wrote:
Consider 11 numbers in ascending order to be $$x_1$$, $$x_2$$, $$x_3$$, ..., $$x_{11}$$.

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 $$x_{6}=25$$;

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 $$50=x_{11}-x_{1}$$ --> $$x_{11}=50+x_{1}$$;

We want to maximize $$x_{11}$$, hence we need to maximize $$x_{1}$$. Since all integers must be distinct then the maximum value of $$x_{1}$$ will be $$median-5=25-5=20$$ and thus the maximum value of $$x_{11}$$ is $$x_{11}=50+20=70$$.

The set could be {20, 21, 22, 23, 24, 25, 26, 27, 26, 29, 70}

its clear till since....distict

i was not able to follow after that..??? can u please explain just that area

We know that the median, $$x_6$$, is 25. What is the maximum value of $$x_5$$. Since $$x_5<x_6$$, then the maximum value of $$x_5$$ is 24. Similarly the maximum value of $$x_4$$ is 23, the maximum value of $$x_3$$ is 22, the maximum value of $$x_2$$ is 21 and the maximum value of $$x_1$$ is 20.

Hope it's clear.

THANX A LOT....IT DID HELP A LOT!!!
Re: GMAT Diagnostic Test Question 20   [#permalink] 05 Jan 2014, 20:51
Similar topics Replies Last post
Similar
Topics:
31 GMAT Diagnostic Test Question 5 26 06 Jun 2009, 20:07
15 GMAT Diagnostic Test Question 4 37 06 Jun 2009, 20:06
21 GMAT Diagnostic Test Question 3 33 06 Jun 2009, 18:33
9 GMAT Diagnostic Test Question 2 26 06 Jun 2009, 18:03
34 GMAT Diagnostic Test Question 1 30 05 Jun 2009, 21:30
Display posts from previous: Sort by

# GMAT Diagnostic Test Question 21

Moderators: WoundedTiger, Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.