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

It is currently 27 Aug 2014, 11:02

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 numbers has an average of 50. If the largest

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 25 Aug 2011
Posts: 195
Location: India
GMAT 1: 730 Q49 V40
WE: Operations (Insurance)
Followers: 1

Kudos [?]: 60 [0], given: 11

GMAT Tests User
A set of numbers has an average of 50. If the largest [#permalink] New post 12 Mar 2012, 21:38
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

48% (02:05) correct 52% (02:14) wrong based on 27 sessions
A set of numbers has an average of 50. If the largest element is 5 greater than 3 times the smallest element and if the median equals the mean . what is largest possible value in the set

A. 85
B. 86
C. 88
D. 91
E. 92

If median = mean does’nt it imply an evenly spaced set?
[Reveal] Spoiler: OA
Expert Post
1 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2038
Followers: 491

Kudos [?]: 2016 [1] , given: 30

Re: set [#permalink] New post 13 Mar 2012, 09:29
1
This post received
KUDOS
Expert's post
Hi, there. I'm happy to help with this. :)

This is a diabolically evil question, much much harder than anything the GMAT will ask you. In addition to that, the question is flawed. What is the source of this extremely poor question?

First, to answer your parenthetical question --- mean = median does not imply evenly spaced. Evenly-spaced is an extremely special condition -- if that's true, it's also true that mean - median, but there are scads of sets with mean = median that don't have this special condition.

In this question, we want a set that satisfies two conditions:
1) mean = median = 50
2) the largest element is 5 greater than 3 times the smallest element

Here are some sets that satisfy those conditions:
{27, 28, 50, 59, 86}
{29, 29, 50, 50, 92}
{30, 30, 45, 50, 50, 50, 95}
{33, 34, 36, 37, 50, 51, 52, 53, 104}

So, I was able to create a set that satisfies this condition with a highest value of 104. I am sure I could make sets with higher values, but I don't know how high could go (possibly 152?) (Notice, BTW, all of those set have mean = median, and none are evenly spaced, or even close)

The point is: the question, as posed, does not contain the correct answer among the answer choices. It may be that the author intended further restrictions (e.g. only five elements, elements are integers, all elements are distinct, etc etc.) that have not been stated. It is the mark of a poor question when the author has in mind further conditions that are not explicitly stated. The GMAT will never do that to you.

So, don't worry about this particular question ---- and in fact, you might be suspicious of any other question you got from that source. Here's a more GMAT-like question about median:

http://gmat.magoosh.com/admin/questions/845

When you submit your answer to that question, the next page will have a video explanation.

Does everything I've set here make sense? Please let me know if you have any further questions.

Mike :)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Senior Manager
Senior Manager
avatar
Joined: 12 Mar 2012
Posts: 370
Concentration: Operations, Strategy
Followers: 2

Kudos [?]: 99 [0], given: 31

Re: A set of numbers has an average of 50. If the largest [#permalink] New post 14 Mar 2012, 01:07
Before reading the post from mike i tried to solve by rejecting options i.e.

3x+5 the largest in the set

only B and E are possible and among those E is higher so marked that

@mike
its a nice analysis;
_________________

Practice Practice and practice...!!

If my reply /analysis is helpful-->please press KUDOS
If there's a loophole in my analysis--> suggest measures to make it airtight.

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4687
Location: Pune, India
Followers: 1079

Kudos [?]: 4844 [0], given: 163

Re: A set of numbers has an average of 50. If the largest [#permalink] New post 14 Mar 2012, 02:33
Expert's post
devinawilliam83 wrote:
A set of numbers has an average of 50. If the largest element is 5 greater than 3 times the smallest element and if the median equals the mean . what is largest possible value in the set

A. 85
B. 86
C. 88
D. 91
E. 92

If median = mean does’nt it imply an evenly spaced set?


Mike has already given a great analysis of this question. Let me add one more bit here:

The question says 'a set of numbers', not integers so a member of the set can be 49.9999.
The limiting value of the smallest number is 50. As long as the smallest number is a tiny bit less than 50, you can have the greatest number a tiny bit less than 50*3 + 5 = 155.

I would have respected this question much more if instead, they had asked "which of the following numbers cannot be in the set?" and had provided 155 or a greater value as an option.

And the median = mean condition doesn't hold much relevance (to create a median of 50, you can add any number of 50s to the set).

Also, for an evenly spaced set, mean = median but not vice versa.
e.g.
2, 3, 4, 4, 7 - mean = median = 4
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: A set of numbers has an average of 50. If the largest   [#permalink] 14 Mar 2012, 02:33
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic A certain set of numbers has an average (arithmetic mean) of jabgars 5 21 Oct 2013, 19:13
18 Experts publish their posts in the topic A set of numbers contains 7 integers and has an average Joy111 19 15 May 2012, 00:36
Set S has a range of p and the largest number in set S is v metallicafan 4 09 Apr 2012, 12:13
Which set(s) has the largest standard deviation? seekmba 7 29 Aug 2010, 15:43
A set has 16 numbers. If a number is three times the average johnycute 4 09 Nov 2006, 01:28
Display posts from previous: Sort by

A set of numbers has an average of 50. If the largest

  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®.