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

It is currently 22 Oct 2014, 19:26

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

Last month 15 homes were sold in Town X. The average

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 27 Oct 2009
Posts: 152
Location: Montreal
Schools: Harvard, Yale, HEC
Followers: 1

Kudos [?]: 14 [0], given: 18

Last month 15 homes were sold in Town X. The average [#permalink] New post 08 Oct 2010, 13:58
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

54% (02:32) correct 46% (01:14) wrong based on 56 sessions
Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?

I. At least one of the homes was sold for more than $165,000.
II. At least one of the homes was sold for more than $130,0000 and less than $150,000
III. At least one of the homes was sold for less than $130,000.

A. I only
B. II only
C. III only
D. I and II
E. I and III

OPEN DISCUSSION OF THIS QUESTION IS HERE: last-month-15-homes-were-sold-in-town-x-the-average-128477.html

MODERATOR
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Jun 2013, 04:12, edited 2 times in total.
Edited the question
Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23381
Followers: 3607

Kudos [?]: 28803 [3] , given: 2849

Re: 15 homes in town X [#permalink] New post 08 Oct 2010, 14:01
3
This post received
KUDOS
Expert's post
Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?

I. At least one of the homes was sold for more than $165,000.
II. At least one of the homes was sold for more than $130,0000 and less than $150,000
III. At least one of the homes was sold for less than $130,000.

A. I only
B. II only
C. III only
D. I and II
E. I and III

Note that we are asked which MUST be true.

Given: {x_1}+{x_2}+...+{x_7}+({x_8=130})+{x_9}+...+{x_{15}}=15*150=2250

Let's start with the first one and try to make it false.

I. At least one of the homes was sold for more than $165,000.

Worst case scenario, when x_{15} has the least value (trying to make it less than 165), would be when x_1=x_2=x_3=x_4=x_5=x_6=x_7=x_8=130=max, and x_9=x_{10}=x_{11}=x_{12}=x_{13}=x_{14}=x_{15}=min:
8*130+7x=2250 --> x_{min}\approx{173}.

So we got that I is always true: At least one of the homes was sold for more than $165,000 (as for the worst case scenario we got that least value of x_{15}>165).

But if we take the scenario which we considered: x_1=x_2=x_3=x_4=x_5=x_6=x_7=x_8=130, and x_9=x_{10}=x_{11}=x_{12}=x_{13}=x_{14}=x_{15}\approx{173} we can see that II and III with this scenario are false. So II and III are not always true.

Answer: I only.

More at: gmatprep-2010-statistics-92909.html

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

Retired Moderator
avatar
Joined: 03 Aug 2010
Posts: 247
Followers: 2

Kudos [?]: 30 [0], given: 41

Re: 15 homes in town X [#permalink] New post 24 Dec 2010, 00:35
why 3rd is wrong ? because if the median is 130000 , atleast a few elements shoulce be below it

pls help
_________________

http://www.gmatpill.com/gmat-practice-test/

Amazing Platform

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23381
Followers: 3607

Kudos [?]: 28803 [0], given: 2849

Re: 15 homes in town X [#permalink] New post 24 Dec 2010, 00:59
Expert's post
hirendhanak wrote:
why 3rd is wrong ? because if the median is 130000 , atleast a few elements shoulce be below it

pls help


Not necessarily.

If a set has odd number of terms the median of a set is the middle number when arranged in ascending or descending order;
If a set has even number of terms the median of a set is the average of the two middle terms when arranged in ascending or descending order.


So, for a set with odd number of elements the median is just the middle number: it's not necessary for any number of terms in a set to be more or less than the median. Consider the set {1, 1, 1,} --> median=1 or the set {1, 1, 2} --> median=1 no term is less than 1...

So if we take: x_1=x_2=x_3=x_4=x_5=x_6=x_7=x_8=130=median, and x_9=x_{10}=x_{11}=x_{12}=x_{13}=x_{14}=x_{15}\approx{173} we can see that III is wrong with this scenario, so it's not always true.

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

2 KUDOS received
Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 929
Followers: 11

Kudos [?]: 199 [2] , given: 123

Reviews Badge
Re: Mean / Median Question from GMAT Prep Test 1 [#permalink] New post 11 Mar 2011, 17:40
2
This post received
KUDOS
Median means 7 prices were above the median and 7 below the median.

I. At least one of the homes was sold for more than $165,000.
Total sales = 150K * 15 = 2250K

Lets say all the seven homes above the median were sold for 165K

Hence
165K * 7 + 130K * 8 = 1159K + 1040K = 2199K - Not high enough. Hence one home MUST have been above 165K


A, D and E left.


II. At least one of the homes was sold for more than $130,000 and less than $150,000.


This is not true you can have the mean 150K even when 7 numbers are below 130K and 7 numbers are above 150K. I will not solve this scenario since this is intuitive.


III. At least one of the homes was sold for less than $130,000.

This is not true since we can have 8 numbers at 130K and 7 numbers above 130K and have the mean 150K. I will not solve this scenario since this is intuitive.

D and E out. A remains.


CDM770234 wrote:
Can someone help me solve the following GMAT Prep Test 1 question:

23. Last month 15 homes were sold in town X. The average (Arithmetic Mean) price was $150,000 and the median sale price was $130,000. Which of the following statements must be true?

I. At least one of the homes was sold for more than $165,000.
II. At least one of the homes was sold for more than $130,000 and less than $150,000.
III. At least one of the homes was sold for less than $130,000.

The answer choices are:

A. I only
B. II only
C. III only
D. I and II
E. I & III

I do not agree/understand the official answer! :?
Intern
Intern
avatar
Joined: 17 Dec 2010
Posts: 9
Followers: 0

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

Re: 15 homes in town X [#permalink] New post 17 Mar 2011, 08:49
Thanks, gmat1220!

I saw that this question was already posted with detailed analysis. Unfortunately, my search did not find it.

Thanks for responding in spite of that, gmat1220!
Re: 15 homes in town X   [#permalink] 17 Mar 2011, 08:49
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Last month 15 homes were sold in Town X. The average meesawoosa 3 12 May 2009, 16:38
Last month 15 homes were sold in town X. the average sale sondenso 9 06 Apr 2008, 01:00
Last month 15 homes were sold in Town X. The average avenger 4 06 Oct 2007, 17:13
Last month 15 homes were sold in Town X. The average sale briks123 2 23 Jul 2007, 07:28
Last month 15 homes were sold in Town X. The average ( LM 2 23 Jun 2007, 01:47
Display posts from previous: Sort by

Last month 15 homes were sold in Town X. The average

  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®.