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

It is currently 21 Aug 2014, 08:05

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A set of 25 integers has a median of 50 and a range of 50

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 12 Oct 2011
Posts: 133
GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
Followers: 3

Kudos [?]: 59 [0], given: 23

A set of 25 integers has a median of 50 and a range of 50 [#permalink] New post 02 Mar 2012, 06:20
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

53% (01:49) correct 47% (00:50) wrong based on 89 sessions
A set of 25 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Sep 2013, 01:04, edited 1 time in total.
Edited the OA.
Expert Post
7 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19038
Followers: 3360

Kudos [?]: 24454 [7] , given: 2677

Re: A set of 25 integers has a median of 50... [#permalink] New post 02 Mar 2012, 06:59
7
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
BN1989 wrote:
A set of 25 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}. The maximum value of x_{1} is the median, so 50, hence the maximum value of x_{25} is x_{25}=50+50=100.

The set could be {50, 50, 50, ..., 50, 100}

Answer: E.

Now, in order the answer to be 88, as given in the OA, the question should state that "A set of 25 different integers has a median of 50..."

In this case 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}

Answer: D.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 31 Mar 2013
Posts: 70
Followers: 0

Kudos [?]: 9 [0], given: 97

CAT Tests
Re: A set of 25 integers has a median of 50 and a range of 50 [#permalink] New post 03 Sep 2013, 00:58
Shouldn't the question actually be "25 different positive integers" then?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19038
Followers: 3360

Kudos [?]: 24454 [0], given: 2677

Re: A set of 25 integers has a median of 50 and a range of 50 [#permalink] New post 03 Sep 2013, 01:05
Expert's post
Re: A set of 25 integers has a median of 50 and a range of 50   [#permalink] 03 Sep 2013, 01:05
    Similar topics Author Replies Last post
Similar
Topics:
19 Experts publish their posts in the topic A set of 25 different integers has a median of 50 and a enigma123 18 19 Mar 2012, 14:46
4 Experts publish their posts in the topic A set of 15 different integers has median of 25 and a range bhushangiri 6 12 Aug 2008, 03:50
A set of 15 diff integers has a median of 25 and a range of dishant007 5 09 Aug 2008, 18:01
The range of a set is 56. Its median number is 50 more than bigpapi 1 19 Nov 2004, 20:30
The range of a set is 56. ITs median number is 50 more than ruhi 5 14 Nov 2004, 13:15
Display posts from previous: Sort by

A set of 25 integers has a median of 50 and a range of 50

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.