It is currently 19 Oct 2017, 04:45

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Tom, Jane, and Sue each purchased a new house. The average

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

### Hide Tags

Director
Joined: 12 Oct 2008
Posts: 539

Kudos [?]: 592 [1], given: 2

Tom, Jane, and Sue each purchased a new house. The average [#permalink]

### Show Tags

09 Oct 2009, 23:27
1
KUDOS
38
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

59% (01:05) correct 41% (00:53) wrong based on 1601 sessions

### HideShow timer Statistics

Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was \$120,000. What was the median price of the three houses?

(1) The price of Tom’s house was \$110,000.
(2) The price of Jane’s house was \$120,000.
[Reveal] Spoiler: OA

Kudos [?]: 592 [1], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128829 [9], given: 12183

### Show Tags

09 Oct 2009, 23:53
9
KUDOS
Expert's post
16
This post was
BOOKMARKED
Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was \$120,000. What was the median price of the three houses?

(1) The price of Tom’s house was \$110,000.
(2) The price of Jane’s house was \$120,000.

[Reveal] Spoiler:
OA B IMO C

We have three prices: a, b and c. (a+b+c)/3=120
The median price would be: the second biggest.
a<=b<=c --> median price b.

(1) One of the prices is 110, less than average of 120. It's possible 110 to be a or b price, so insufficient.

(2) One of the prices is 120 equals to average. It must be the b price, as it's not possible this price to be lowest or highest because it's equals to the average, only 2 cases a<120<c or a=b=c=120

_________________

Kudos [?]: 128829 [9], given: 12183

Senior Manager
Joined: 18 Sep 2009
Posts: 356

Kudos [?]: 588 [0], given: 2

### Show Tags

10 Oct 2009, 08:50
good explanation ,thaank you very much

Kudos [?]: 588 [0], given: 2

SVP
Joined: 29 Aug 2007
Posts: 2472

Kudos [?]: 843 [0], given: 19

Re: mean n median [#permalink]

### Show Tags

05 Nov 2009, 23:29
kirankp wrote:
Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was \$120,000. What was the median price of the three houses?

(1) The price of Tom’s house was \$110,000.
(2) The price of Jane’s house was \$120,000.

Did not you get B?
If one of the house is equal to mean, then it is the median because other 2 houses (both) cannot be > 120,000 or < 120,000. The wrost case, is one is < 120,000 and the other is >120,000.

So B is suff....
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

Kudos [?]: 843 [0], given: 19

Intern
Affiliations: CA - India
Joined: 27 Oct 2009
Posts: 45

Kudos [?]: 779 [0], given: 5

Location: India
Schools: ISB - Hyderabad, NSU - Singapore
Re: mean n median [#permalink]

### Show Tags

05 Nov 2009, 23:29
1
This post was
BOOKMARKED
Mean and one of the values out of 3 values are same, hence median has to be equal to mean.

Ans. is B.

Kudos [?]: 779 [0], given: 5

Manager
Joined: 30 May 2008
Posts: 74

Kudos [?]: 138 [0], given: 26

### Show Tags

21 Apr 2012, 01:53
Bunuel wrote:
We have three prices: a, b and c. (a+b+c)/3=120
The median price would be: the second biggest.
a<=b<=c --> median price b.

(1) One of the prices is 110, less than average of 120. It's possible 110 to be the a or b price, so insufficient.

(2) One of the prices is 120 equals to average. It must be the b price, as it's not possible this price to be lowest or highest because it's equals to the average, only 2 cases a<120<c or a=b=c=120

if one of the price is 110, aka not avg 120, wouldn't it be "a"? Since there are 3 numbers, average is 120, anything less than average will be "a"? How can 110 possibly be b?

Kudos [?]: 138 [0], given: 26

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128829 [0], given: 12183

### Show Tags

21 Apr 2012, 02:04
catty2004 wrote:
Bunuel wrote:
We have three prices: a, b and c. (a+b+c)/3=120
The median price would be: the second biggest.
a<=b<=c --> median price b.

(1) One of the prices is 110, less than average of 120. It's possible 110 to be the a or b price, so insufficient.

(2) One of the prices is 120 equals to average. It must be the b price, as it's not possible this price to be lowest or highest because it's equals to the average, only 2 cases a<120<c or a=b=c=120

if one of the price is 110, aka not avg 120, wouldn't it be "a"? Since there are 3 numbers, average is 120, anything less than average will be "a"? How can 110 possibly be b?

Try to construct different scenarios, you'll see that it's not that hard:

Sum is 120*3=360.
110+120+130=360;
100+110+150=360.
_________________

Kudos [?]: 128829 [0], given: 12183

Intern
Joined: 12 Sep 2011
Posts: 13

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

### Show Tags

06 Sep 2012, 11:38
Bunuel wrote:
Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was \$120,000. What was the median price of the three houses?

(1) The price of Tom’s house was \$110,000.
(2) The price of Jane’s house was \$120,000.

[Reveal] Spoiler:
OA B IMO C

We have three prices: a, b and c. (a+b+c)/3=120
The median price would be: the second biggest.
a<=b<=c --> median price b.

(1) One of the prices is 110, less than average of 120. It's possible 110 to be a or b price, so insufficient.

(2) One of the prices is 120 equals to average. It must be the b price, as it's not possible this price to be lowest or highest because it's equals to the average, only 2 cases a<120<c or a=b=c=120

You have no idea how long I've been looking for a more well explained answer, thank you so much!!! Everyone else justs calculates the 360-250 and shows examples, this Issa much more intuitive when you pair it with a bell curve, thank you thank you thank uou

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

Manager
Joined: 24 Mar 2010
Posts: 78

Kudos [?]: 79 [0], given: 134

Re: mean n median [#permalink]

### Show Tags

04 Dec 2012, 11:53
Mean and one of the values out of 3 values are same, hence median has to be equal to mean.

Ans. is B.

Is the above a rule general to all sets?

_________________

- Stay Hungry, stay Foolish -

Kudos [?]: 79 [0], given: 134

Intern
Joined: 07 May 2011
Posts: 40

Kudos [?]: 20 [2], given: 11

Re: mean n median [#permalink]

### Show Tags

04 Dec 2012, 19:55
2
KUDOS
By defintion, Median divides the distribution of values such that exactly half lie below the median and half above the median. example, given 2,5,9,50 (notice that to calculate median, the values must first be arranged in ascending order), the median is (5+9)/2=7. meaning below 7 like two values and above 7 lie two values.

By contrast, Mean or average doesn't necessarily do that. It is affected by the magnitude of each value. if one value is extreme, the mean or average shifts towards that extremity. In the above example, the average is about 16. half of the numbers aren't less than this 16, there are three numbers less than 16. similarly, half aren't above 16, only one i.e. 50 is above 16.

When you are told that there are only three values and one of them is actually the mean or the average, what's that really saying? if all three numbers are different, you know that the average has to fall somewhere between the smallest and the biggest number. and we are given that this middle number is 120,000 and also happens to be the mean. it doesn't matter now what the other two numbers are. this becomes an evenly spaced set of three numbers. the smaller the smallest number, the larger the largest number has to be to keep the average 120,000 constant.

So as a rule, you can remember that for any evenly spaced set, the mean is always equal to the median. example, 2,4,6 or 10,20,30,40.

eaakbari wrote:
Mean and one of the values out of 3 values are same, hence median has to be equal to mean.

Ans. is B.

Is the above a rule general to all sets?

Kudos [?]: 20 [2], given: 11

Manager
Joined: 24 Mar 2010
Posts: 78

Kudos [?]: 79 [0], given: 134

Re: mean n median [#permalink]

### Show Tags

04 Dec 2012, 22:31
koisun wrote:
By defintion, Median divides the distribution of values such that exactly half lie below the median and half above the median. example, given 2,5,9,50 (notice that to calculate median, the values must first be arranged in ascending order), the median is (5+9)/2=7. meaning below 7 like two values and above 7 lie two values.

By contrast, Mean or average doesn't necessarily do that. It is affected by the magnitude of each value. if one value is extreme, the mean or average shifts towards that extremity. In the above example, the average is about 16. half of the numbers aren't less than this 16, there are three numbers less than 16. similarly, half aren't above 16, only one i.e. 50 is above 16.

When you are told that there are only three values and one of them is actually the mean or the average, what's that really saying? if all three numbers are different, you know that the average has to fall somewhere between the smallest and the biggest number. and we are given that this middle number is 120,000 and also happens to be the mean. it doesn't matter now what the other two numbers are. this becomes an evenly spaced set of three numbers. the smaller the smallest number, the larger the largest number has to be to keep the average 120,000 constant.

So as a rule, you can remember that for any evenly spaced set, the mean is always equal to the median. example, 2,4,6 or 10,20,30,40.

eaakbari wrote:
Mean and one of the values out of 3 values are same, hence median has to be equal to mean.

Ans. is B.

Is the above a rule general to all sets?

Thanks for the explanation.

So I can generalize that

if a number in a set is equal to the mean, the set is an evenly spaced set and hence the mean = median.

???

_________________

- Stay Hungry, stay Foolish -

Kudos [?]: 79 [0], given: 134

Senior Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 253

Kudos [?]: 125 [0], given: 282

Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Re: mean n median [#permalink]

### Show Tags

27 Dec 2012, 08:25
Yes it is given that 120 is the mean. In statement 2 it says one of the numbers is 120. You can memorize it as a rule or test it on any 3 nos. The median has to be 120. Read bunuel's post too.
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan
Kudos drives a person to better himself every single time. So Pls give it generously
Wont give up till i hit a 700+

Kudos [?]: 125 [0], given: 282

Manager
Joined: 04 Mar 2013
Posts: 87

Kudos [?]: 10 [0], given: 6

Location: India
Concentration: General Management, Marketing
GPA: 3.49
WE: Web Development (Computer Software)
Re: Tom, Jane, and Sue each purchased a new house. The average [#permalink]

### Show Tags

17 Jun 2013, 23:55
Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was \$120,000. What was the median price of the three houses?

(1) The price of Tom’s house was \$110,000.
(2) The price of Jane’s house was \$120,000.

[Reveal] Spoiler:
OA B IMO C

here we go, the price of T is 110 this doesn't tell about other two so its not sufficient.

2. the price is 120 also we know mean is 120 so the other two have one > 120 other is < 120 and the median is the middle one which is 120 hence B is fine

first i too marked C but when have seen the QA then got to realize

Kudos [?]: 10 [0], given: 6

Intern
Joined: 21 Dec 2013
Posts: 24

Kudos [?]: 24 [0], given: 21

Concentration: General Management, Technology
WE: Project Management (Computer Software)
Re: mean n median [#permalink]

### Show Tags

07 Mar 2014, 17:50
rajathpanta wrote:
Yes it is given that 120 is the mean. In statement 2 it says one of the numbers is 120. You can memorize it as a rule or test it on any 3 nos. The median has to be 120. Read bunuel's post too.

I think, this ruel (if a number in a set is equal to the mean, the set is an evenly spaced set and hence the mean = median.) is only true if the set has distinct values. For e.g. Mean = Median when set has same values (120, 120, 120) and this set is not evenly spaced.

Can the rule be - "For set of distinct values, if a number in a set is equal to the mean, then it is evenly spaced set and the mean = median."

Kudos [?]: 24 [0], given: 21

Current Student
Joined: 25 Sep 2012
Posts: 287

Kudos [?]: 173 [1], given: 242

Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: Tom, Jane, and Sue each purchased a new house. The average [#permalink]

### Show Tags

31 May 2014, 14:37
1
KUDOS
Hey mods! the answer has not been registered here...
As confirmed by earlier posts, the answer is B

Kudos [?]: 173 [1], given: 242

Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128829 [0], given: 12183

Re: Tom, Jane, and Sue each purchased a new house. The average [#permalink]

### Show Tags

31 May 2014, 16:00
b2bt wrote:
Hey mods! the answer has not been registered here...
As confirmed by earlier posts, the answer is B

Added the OA. Thank you.
_________________

Kudos [?]: 128829 [0], given: 12183

Intern
Joined: 28 May 2014
Posts: 16

Kudos [?]: 2 [0], given: 0

Re: Tom, Jane, and Sue each purchased a new house. The average [#permalink]

### Show Tags

02 Jun 2014, 01:59
Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was \$120,000. What was the median price of the three houses?

(1) The price of Tom’s house was \$110,000.
(2) The price of Jane’s house was \$120,000.

They are asking us for the median house price, out of the group of three houses.

Given information:
(T+J+S)/3= 120,000.

Statement 1 is telling us that T = 110,000. This means that the other two houses has to have a mean of 130,000. This could be any two prices that deviate with the same amount from 130,000.

Statement one is therefore insufficient. We're looking for the house with the median price and that could be 110,000 ->130,000. We're not sure which one it is currently.

Statement 2 gives us that Jane's house is 120,000. This is the same as the mean and even though we might think that we need info on another house, we're actually already done.

Together with the information given in the question stem we've got the following:

(T +120,000+ S)/3=120,000.

(T+S)/2 = 120,000.

If T is above 120,000 then S has to be equally far from 120,000 in the negative direction. This means that either all of the houses has the mean price of 120,000 or:

T=120,000+x
J=120,000
S=120,000-x

Whatever x is(zero included) we still know that the median will be 120,000.

Hence the answer is B.

Kudos [?]: 2 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16678

Kudos [?]: 273 [0], given: 0

Re: Tom, Jane, and Sue each purchased a new house. The average [#permalink]

### Show Tags

07 Jul 2015, 00:09
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 273 [0], given: 0

Intern
Joined: 04 Feb 2014
Posts: 17

Kudos [?]: 1 [0], given: 1

Re: Tom, Jane, and Sue each purchased a new house. The average [#permalink]

### Show Tags

29 Aug 2015, 19:26
Since the list of numbers is odd, would this apply to all odd listed #? Exp. if the average of a,b,c,d,e is 20 and d=20, does that mean that d is the median?

Kudos [?]: 1 [0], given: 1

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2676

Kudos [?]: 1723 [0], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Tom, Jane, and Sue each purchased a new house. The average [#permalink]

### Show Tags

29 Aug 2015, 19:34
kedusei wrote:
Since the list of numbers is odd, would this apply to all odd listed #? Exp. if the average of a,b,c,d,e is 20 and d=20, does that mean that d is the median?

Median is defined as the "middle most term" which in the case of odd numbered set mentioned by you will be 'c' (I am assuming that you wanted to mention this!).

For an even numbered set, the median will be the average of the 2 middle most terms. Example, median of a,b,c,d will be (b+c)/2

For more theory on sets (mean, median, mode etc.) look at: statistics-made-easy-all-in-one-topic-203966.html
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1723 [0], given: 792

Re: Tom, Jane, and Sue each purchased a new house. The average   [#permalink] 29 Aug 2015, 19:34

Go to page    1   2    Next  [ 24 posts ]

Display posts from previous: Sort by

# Tom, Jane, and Sue each purchased a new house. The average

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

 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®.