GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Jan 2019, 08:47

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • The winners of the GMAT game show

     January 22, 2019

     January 22, 2019

     10:00 PM PST

     11:00 PM PST

    In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
  • Key Strategies to Master GMAT SC

     January 26, 2019

     January 26, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

Last month 15 homes were sold in Town X. The average (arithmetic mean)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
User avatar
Joined: 13 Dec 2009
Posts: 224
Reviews Badge
Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 19 Apr 2010, 05:05
23
99
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

55% (01:00) correct 45% (01:06) wrong based on 1584 sessions

HideShow timer Statistics

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

_________________

My debrief: done-and-dusted-730-q49-v40

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52386
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 19 Apr 2010, 05:44
54
68
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: A (I only).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Kaplan GMAT Instructor
User avatar
Joined: 21 Jun 2010
Posts: 70
Location: Toronto
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 03 Jul 2010, 16:27
14
6
If we understand medians, use reasoning (instead of pure algebra), and have good technique, then we can answer this question very quickly.

Median just refers to the middle number in a sequence of ordered numbers. So, the median here: {3, 3, 3} is 3 even though all the numbers are 3.

We are told that the median is 130k. So, the 8th house sold for 130k. But the 1st through 7th houses may also have sold for 130k. Eliminate III; eliminate C and E.

We can also easily eliminate II. We could have 8 houses that sold for 130k or less; the rest can sell for well above 150k. Eliminate B and D.

The answer must be choice A, and there is no need to evaluate I.

Note that my approach was essentially the same as badgerboy's: start with the choices you can more easily prove untrue. The alternative is to start with the roman numerals that show up most frequently. Of course, another alternative is to use pure algebra, and for some people (I don't think many but some) that may well be more efficient.
General Discussion
Manager
Manager
User avatar
Joined: 13 Dec 2009
Posts: 224
Reviews Badge
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 19 Apr 2010, 06:04
1
Thanks for the quick response Bunuel. The answer is correct. :)

Great explanation, I'm just not able to digest how to attack such a problem in future. Also, the difficult part is how to identify the worst case scenario here? Why cant we take other different values instead of 8 values being 130 and the remaining 7 values at minimum?
_________________

My debrief: done-and-dusted-730-q49-v40

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52386
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 19 Apr 2010, 06:48
10
6
sidhu4u wrote:
Thanks for the quick response Bunuel. The answer is correct. :)

Great explanation, I'm just not able to digest how to attack such a problem in future. Also, the difficult part is how to identify the worst case scenario here? Why cant we take other different values instead of 8 values being 130 and the remaining 7 values at minimum?


We have: \(x_1\leq{x_2}\leq{x_3}\leq{x_4}\leq{x_5}\leq{x_6}\leq{x_7}\leq{x_8=130}\leq{x_9}\leq{x_{10}}\leq{x_{11}}\leq{x_{12}}\leq{x_{13}}\leq{x_{14}}\leq{x_{15}}\).

We are trying to make statement I false, which says: At least one of the homes was sold for more than $165,000. More than 165 can be terms from \(x_9\) to \(x_{15}\). Basically worst case scenario here means minimizing the value of \(x_{15}\) (finding the least possible value of \(x_{15}\)). How can we do that?

First we should maximize the values from \(x_1\) to \(x_7\) (by increasing/maximizing these terms, the lowest terms, we are decreasing/minimizing the highest terms). Their max values can be \(130=x_8\) (as \(x_8\) is the median value and the terms from \(x_1\) to \(x_7\) can not be more than this value).

Next: to minimize \(x_{15}\) we should make terms from \(x_9\) to \(x_{15}\) be the same.

As in solution the least possible value of \(x_{15}\) is \(\approx{173}\), thus values less then 165 are not possible. So at least one home was sold for more than $165.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
Joined: 24 Aug 2007
Posts: 738
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 24 May 2010, 07:04
We are discussing the worst scenario here. In addition, we are not given a lower limit and upper limit on the sale price of the homes.

What if some houses are below $130K?

Can someone explain more on this?
_________________

Want to improve your CR: http://gmatclub.com/forum/cr-methods-an-approach-to-find-the-best-answers-93146.html
Tricky Quant problems: http://gmatclub.com/forum/50-tricky-questions-92834.html
Important Grammer Fundamentals: http://gmatclub.com/forum/key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52386
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 24 May 2010, 07:14
1
1
ykaiim wrote:
We are discussing the worst scenario here. In addition, we are not given a lower limit and upper limit on the sale price of the homes.

What if some houses are below $130K?

Can someone explain more on this?


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#p715101
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 04 Feb 2010
Posts: 150
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 03 Jul 2010, 07:51
1
1
This is my take on this.

Consider the case that the first 8 houses are priced at 130K. The total sale amount is 2250K, and with 8 houses at 130K (1040K), you're left with 1210K for the 7 remaining houses. Dividing this amount by 7 would give you the least prices that you could price these 7 houses. With approx. 172K per house, a house priced above 165K must be a part of the portfolio.

From the above, one can see that number 2 is not necessarily correct. One can have 8 houses at 130K and the rest at the quoted price above.

The third - well, we can satisfy the conditions and not have a house priced below 130K.
Manager
Manager
avatar
Joined: 06 Mar 2010
Posts: 84
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 03 Jul 2010, 09:20
1
Plugin to check the options might well consume time in above questions.
If there is some way in which we can deduce the question in terms of equation and then verify (just like we do in inequality, co-ordinate geometry), then it might consume less time.
I have tried to deduce the data in terms of equation but in the end, I did the same to plugin data to satisfy above conditions.
If someone can deduce the data into equations and solve it without plugin, then it will be less time consuming.
Retired Moderator
avatar
Joined: 03 Aug 2010
Posts: 201
Re: 15 homes in town X  [#permalink]

Show Tags

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52386
Re: 15 homes in town X  [#permalink]

Show Tags

New post 24 Dec 2010, 00:59
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 the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | 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?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 728
Reviews Badge
Re: Mean / Median Question from GMAT Prep Test 1  [#permalink]

Show Tags

New post 11 Mar 2011, 17:40
4
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! :?
Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1810
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 22 Mar 2011, 23:51
3
Onell wrote:
Last month 15 homes were sold in Town X. The average sale price of the houses was $150,000 and the median sales price was $130,000. Which must be true?
At least 1 house sold for > $165,000
At least 1 house sold for > $130,000 but < $150,000
At least 1 home sold for < $130,000
I
II
III
I and II
I and III


Let's work with the numbers dividing everything by 1000.

Total value of the sale = 15*150=2250

Median sale = $130

If we arrange the sale price in ascending order the 8th value would be 130

I.
Let's try to prove it wrong.
x,x,x,x,x,x,x,130,y,y,y,y,y,y,Z

To make Z<=165
x should be as big as possible.
Let's make them all 130*8=1040
Let's make all y as 165
165*6=990

Z = 2250-990-1040=2250-2030=220>165.

Apparently; it's true.

II.
At least 1 house sold for > $130,000 but < $150,000
Not true.
Same example as st1.
130,130,130,130,130,130,130,130,165,165,165,165,165,165,225
Not true.

III.
At least 1 home sold for < $130,000
Not true.
Same example as st1.
130,130,130,130,130,130,130,130,165,165,165,165,165,165,225
Not true.
Not true.

Ans: "A"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Senior Manager
avatar
Joined: 30 Aug 2009
Posts: 270
Location: India
Concentration: General Management
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 01 May 2011, 16:11
1
15 homes can have the following values

8 Homes having value equal to $130k
3 Homes having value equal to $150k
4 Homes having value equal to $190K

With above values median will be $130k and average will be $150k

Statement II and III become not correct/true. So A. I only

no need of checking Statement I :)
Intern
Intern
avatar
Status: Waiting for Decisions
Joined: 23 Dec 2012
Posts: 39
Location: India
Sahil: Bansal
GMAT 1: 570 Q49 V20
GMAT 2: 690 Q49 V34
GPA: 3
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 20 Aug 2013, 08:04
Bunuel wrote:
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: A (I only).



Hi Bunuel,

Why have we not considered the case that some terms from 1-7 are less than 130, 8th term is 130 and then again terms from 9-15 some are between 130- 150 some even above 165.. In that case all three statements will be true...
What am i missing here???


Sahil
Veritas Prep GMAT Instructor
User avatar
Joined: 11 Dec 2012
Posts: 312
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 20 Aug 2013, 08:22
2
bsahil wrote:
Bunuel wrote:

Note that we are asked which MUST be true.



Hi Bunuel,

Why have we not considered the case that some terms from 1-7 are less than 130, 8th term is 130 and then again terms from 9-15 some are between 130- 150 some even above 165.. In that case all three statements will be true...
What am i missing here???


Sahil


Hi Sahil, I have left the only quote from Bunuel's explanation that is needed to answer your question. We are looking for something that must be true, not that can be true.

If something can be true, then come up with any fairy tale explanation you want. Maybe 1 house was 1,000,000 and the others were all 5$. If 14 of the houses are sold for exactly 130,000 but one is sold for 505,000$. This satisfies the situation, but II) and III) do not happen. Thus, we have found a situation where II and III do not occur, and we can eliminate them.

If I'm looking for something that must be true, I cannot find a single example that will negate it. Try as you will with number I), no scenario will satisfy the conditions and not have a house sold for more than 165,000$. The mathematics of the question guarantee it.

Hope this helps!
-Ron
_________________

Ron Awad
Veritas Prep | GMAT Instructor
Save $100 on Veritas Prep GMAT Courses and Admissions Consulting Services
Veritas Prep Reviews

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4600
Location: United States (CA)
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 08 Dec 2017, 10:57
sidhu4u wrote:
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



We are given that 15 homes were sold in Town X last month. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. We can start by reducing $150,000 and $130,000 by dividing each number by 1,000.

We now have that the mean sale price of the homes was $150 and the median sale price was $130. Let’s now analyze the statements to determine which MUST be true.

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

(We can reinterpret Roman numeral I as: At least one of the homes was sold for more than $165.)

To determine whether the above statement MUST be true, let’s see if we can find a scenario in which none of the homes is priced at more than $165. Furthermore, since the median price is $130, let’s create a scenario in which the eighth value of the 15 values (i.e., the middle number) is 130, the first seven values are all 130 and the last seven values are all 165. That is:

130, 130, 130, 130, 130, 130, 130, 130, 165, 165, 165, 165, 165, 165, 165, 165

If this is the case, then the sum would be 130 x 8 + 165 x 7 = 1,040 + 1,155 = 2,195. However, since the average of price of the homes is $150, the sum of the prices of the homes is 150 x 15 = 2,250. This means that at least one of the numbers in the list above has to be changed to a number greater than 165 to make up the difference between 2,195 and 2,250. (For example, since the difference is 55, we can change the last number 165 to 220 to make up this difference.)

So Roman numeral I is correct.

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

(We can reinterpret II as: At least one of the homes was sold for more than $130 and less than $150.)

In the analysis of Roman numeral I, we showed that none of the homes had to be priced between $130 and $165. Roman numeral II is not correct.

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

(We can reinterpret III as: At least one of the homes was sold for less than $130.)

In the analysis of Roman numeral I, we showed that none of the homes had to be priced less than $130. Roman numeral III is not correct.

Answer: A
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3356
Location: Canada
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 20 Apr 2018, 14:05
Top Contributor
sidhu4u wrote:
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


The key word in this question is MUST
So, if it's possible to create a scenario in which the statement is not true, we can eliminate it.

So, let's create a possible scenario and see which answer choices we can eliminate.

Aside: To make things simpler, let's divide all of the prices by 1000.

First, we'll use a nice rule that says: sum of all values = (mean)(number of values)
So, the sum of all 15 prices = ($150)(15) = $2250.

If the median is $130, then the middlemost value is $130

So, one possible scenario is:
130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 430

Aside: To find the last value (430), I took the sum of all 15 numbers (2250) and subtracted (14)(130)

Notice that this scenario tells us that statements II and III need not be true.
Since answer choices B, C, D and E all include either II or III, we can eliminate them.

This leaves us with A, which must be the correct answer.

Cheers,
Brent

RELATED VIDEO FROM OUR COURSE

_________________

Test confidently with gmatprepnow.com
Image

Intern
Intern
avatar
Joined: 30 Sep 2018
Posts: 4
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 04 Jan 2019, 11:17
Thank you for the answer! I like this type of strategy questions to get conclusion from limited information!
Intern
Intern
avatar
B
Joined: 26 Aug 2017
Posts: 14
GMAT ToolKit User
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean)  [#permalink]

Show Tags

New post 04 Jan 2019, 22:38
Hi Bunuel, can I check with you if this is a high 600+ question?
GMAT Club Bot
Re: Last month 15 homes were sold in Town X. The average (arithmetic mean) &nbs [#permalink] 04 Jan 2019, 22:38

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

Last month 15 homes were sold in Town X. The average (arithmetic mean)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.