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

It is currently 04 Sep 2015, 12:03
GMAT Club Tests

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

Of the 5 numbers, the largest number is 4 greater than the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
3 KUDOS received
Intern
Intern
avatar
Joined: 09 Aug 2010
Posts: 6
Followers: 0

Kudos [?]: 3 [3] , given: 0

Of the 5 numbers, the largest number is 4 greater than the [#permalink] New post 10 Aug 2010, 02:05
3
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

28% (02:51) correct 72% (01:32) wrong based on 70 sessions
Of the 5 numbers, the largest number is 4 greater than the median. Is the mean greater than the median?
(1) The largest number plus the median is 34.
(2) The median minus the smallest number is 10

[Reveal] Spoiler:
B

The method i used was too tedious and turned out to be wrong at the end Can someone help me with a easy method / explanation please ?
[Reveal] Spoiler: OA
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29210
Followers: 4753

Kudos [?]: 50354 [2] , given: 7544

Re: median, mode [#permalink] New post 10 Aug 2010, 02:54
2
This post received
KUDOS
Expert's post
amijags wrote:
Of the 5 numbers, the largest number is 4 greater than the median. Is the mean greater than the median?
(1) The largest number plus the median is 34.
(2) The median minus the smallest number is 10

[Reveal] Spoiler:
B

The method i used was too tedious and turned out to be wrong at the end Can someone help me with a easy method / explanation please ?


Hi, and welcome to Gmat Club. Very good question, so +1 for it. Below is a solution:

Le these 5 numbers in ascending order be \(a\), \(b\), \(c\), \(d\), \(e\): \(a\leq{b}\leq{c}\leq{d}\leq{e}\).

Median would be the middle number - \(c\) and the \(mean=\frac{a+b+c+d+e}{5}\).

Given: \(e=c+4\). Question: is \(\frac{a+b+c+d+e}{5}>c\) --> is \(\frac{a+b+c+d+(c+4)}{5}>c\) --> is \(a+b+d+4>3c\)

(1) The largest number plus the median is 34 --> \(e+c=34\) --> \(c=15\) and \(e=19\) --> question becomes: is \(a+b+d+4>45\). Now, if \(a=b=15\) (max values possible for \(a\) and \(b\)) and \(d=19\) (max value possible for \(d\)) then answer would be YES but as min values of \(a\) and \(b\) are not limited at all then the answer could be NO as well. Not sufficient.

(2) The median minus the smallest number is 10 --> \(a=c-10\) --> question becomes: is \(c-10+b+d+4>3c\) --> \(b+d>2c+6\). Now, max value of \(b\) is \(c\) and max value of \(d\) is \(e=c+4\), so max value of LHS (left hand side) would be \(LHS=b+d=c+c+4=2c+4\), which is always less than right hand side: \(RHS=2c+6\). Hence the answer to the question is NO. Sufficient.

Answer: B.

Hope it's clear.
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 09 Aug 2010
Posts: 6
Followers: 0

Kudos [?]: 3 [0], given: 0

Re: median, mode [#permalink] New post 10 Aug 2010, 03:24
Thank you very much

I get deflected at times am going to mark 2 sides henceforth for DS questions
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 2046
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 32

Kudos [?]: 346 [0], given: 355

GMAT ToolKit User
Re: Of the 5 numbers, the largest number is 4 greater than the [#permalink] New post 21 Feb 2014, 04:46
Nice question +1

Just to add a conceptual approach to this one

Statement 1 is insufficient since we can only find the numerical values of the median and the largest number (M=15, L=19) But we still don’t know about the other three numbers. For instance, smallest numbers could be 11 and other two numbers equally spaced giving an evenly spaced set with Median= Mean. We have extra flexibility to place the other two numbers since we are told that the numbers are not necessarily integers.

Statement 2 is a bit more tricky. It says that the smallest number is 10 less than the median. So let's say that the median is 10 and the largest and smallest numbers are 14 and 0 respectively. Now, we will have 2 numbers to the left of 10 and two to the right. Even if we have 10 and 10 to the left and 10 and 10 to the right, the mean will ALWAYS be larger than the median. Therefore B is the correct answer

Hope this helps
Cheers
J
Manager
Manager
avatar
Joined: 18 May 2014
Posts: 63
Location: United States
Concentration: General Management, Other
GMAT Date: 07-31-2014
GPA: 3.99
WE: Analyst (Consulting)
Followers: 0

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

Re: Of the 5 numbers, the largest number is 4 greater than the [#permalink] New post 18 May 2014, 09:35
Because St. 1 tells us : Median is 15.
So the five numbers can be 19, (one number between 19-15), 15, (2 numbers less than 15)

St. 2 gives us a range between the largest and the smallest number.
Now visualize the numbers on the numberline, the largest number is 4 greater than the median, and median in 10 greater than the smallest number. Now the Mean will be in the exact middle of this range. Therefore, it has to be less than the Median. IMO B
Re: Of the 5 numbers, the largest number is 4 greater than the   [#permalink] 18 May 2014, 09:35
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic In a set of 5 numbers, if the largest number is 3 more than rajatr 4 25 Apr 2013, 02:19
Of the 200 numbers, 16.5% are greater than 40, and 33.3% of DeeptiM 2 14 Aug 2011, 13:07
1 A series of 5 numbers is 3, 4, 5, 5, x, is the range greater 144144 2 06 Jun 2011, 10:53
4 Experts publish their posts in the topic Is the number of members of Club X greater than the number seluka 11 15 Dec 2009, 15:16
4 Experts publish their posts in the topic If x is an integer, is the median of 5 numbers shown greater than the gsr 9 21 Oct 2005, 22:49
Display posts from previous: Sort by

Of the 5 numbers, the largest number is 4 greater than the

  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®.