Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 12 Oct 2008
Posts: 486

Tom, Jane, and Sue each purchased a new house. The average
[#permalink]
Show Tags
09 Oct 2009, 23:27
Question Stats:
63% (01:02) correct 37% (00:52) wrong based on 1675 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.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 48110

Re: Average
[#permalink]
Show Tags
09 Oct 2009, 23:53
reply2spg 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. 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 Answer B.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Senior Manager
Joined: 18 Sep 2009
Posts: 325

Re: Average
[#permalink]
Show Tags
10 Oct 2009, 08:50
good explanation ,thaank you very much



SVP
Joined: 29 Aug 2007
Posts: 2419

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....
_________________
Verbal: http://gmatclub.com/forum/newtotheverbalforumpleasereadthisfirst77546.html Math: http://gmatclub.com/forum/newtothemathforumpleasereadthisfirst77764.html Gmat: http://gmatclub.com/forum/everythingyouneedtoprepareforthegmatrevised77983.html
GT



Intern
Affiliations: CA  India
Joined: 27 Oct 2009
Posts: 44
Location: India
Schools: ISB  Hyderabad, NSU  Singapore

Re: mean n median
[#permalink]
Show Tags
05 Nov 2009, 23:29
Mean and one of the values out of 3 values are same, hence median has to be equal to mean.
Ans. is B.



Manager
Joined: 30 May 2008
Posts: 58

Re: Average
[#permalink]
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
Answer B. 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?



Math Expert
Joined: 02 Sep 2009
Posts: 48110

Re: Average
[#permalink]
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
Answer B. 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.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 12 Sep 2011
Posts: 13

Re: Average
[#permalink]
Show Tags
06 Sep 2012, 11:38
Bunuel wrote: reply2spg 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. 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 Answer B. 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 360250 and shows examples, this Issa much more intuitive when you pair it with a bell curve, thank you thank you thank uou



Manager
Joined: 24 Mar 2010
Posts: 70

Re: mean n median
[#permalink]
Show Tags
04 Dec 2012, 11:53
kalpeshchopada7 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? Could someone answer this please
_________________
 Stay Hungry, stay Foolish 



Intern
Joined: 07 May 2011
Posts: 33

Re: mean n median
[#permalink]
Show Tags
04 Dec 2012, 19:55
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: kalpeshchopada7 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? Could someone answer this please



Manager
Joined: 24 Mar 2010
Posts: 70

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: kalpeshchopada7 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? Could someone answer this please 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. ??? Awaiting your views?
_________________
 Stay Hungry, stay Foolish 



Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 219
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 succeedMichael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+



Manager
Joined: 04 Mar 2013
Posts: 76
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
reply2spg 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. 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



Intern
Joined: 21 Dec 2013
Posts: 24
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."



Intern
Joined: 28 May 2014
Posts: 16

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



Intern
Joined: 04 Feb 2014
Posts: 14

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?



Current Student
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
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: statisticsmadeeasyallinonetopic203966.html



Intern
Joined: 15 Aug 2015
Posts: 3
Location: United States
WE: Analyst (Consumer Products)

Re: Tom, Jane, and Sue each purchased a new house. The average
[#permalink]
Show Tags
01 Sep 2015, 19:12
Mean = 120, what is the Median? T+J+S = 120/3 > T+J+S = 360
1.) T = 110 Test Extreme Cases: If T = 110, J = 1, S = 249 .... Median = 110 If T = 110, J = 125, S = 125 .... Median = 125 So, Insuff.
2.) J = 120 Test Extreme Cases: If J = 120, T = 120, S = 120 .... Median = 120 If J = 120, T = 100, S = 140 .... Median = 120 If J = 120, T = 15, S = 125 .... Median = 120
As you can see, the Median will always equal 120 when one of the values is equal to 120.
So, Suff.
Answer = B, only statement 2.



Intern
Joined: 09 Jan 2017
Posts: 6

Re: Tom, Jane, and Sue each purchased a new house. The average
[#permalink]
Show Tags
22 Jul 2017, 03:06
Hi,
The answer is B
Concept involved :
Median of a no. is For odd no. of digits in the series the middle term will be the median of the no.
e.g. 3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29
When we put those numbers in order we have:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56
There are fifteen numbers. Our middle is the eighth number:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56
The median value of this set of numbers is 23
for the even set of no.s the median is the average of the middle terms.
3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29
When we put those numbers in order we have:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
In this example the middle numbers are 21 and 23.
To find the value halfway between them, add them together and divide by 2:
21 + 23 = 44 then 44 ÷ 2 = 22
So the Median in this example is 22.



Senior Manager
Joined: 29 Jun 2017
Posts: 492
GPA: 4
WE: Engineering (Transportation)

Re: Tom, Jane, and Sue each purchased a new house. The average
[#permalink]
Show Tags
17 Aug 2017, 03:33
1) toms house is 110,000 $ mean is 120,000 sum/N = mean sum =360,000 as n=3 now toms is 110,000 which means jane and sue has total of 250,000 value either J or S can be 120,000 or 130,000 or vice versa which changes median.. A and D gone 2) jane is 120,000 T+S =240,000 max can be 120,000 in this case all will be 120,000 and in other cases one is less than 120,000 and other is more than 120,000 in that case also median is same 120,000 hence B is sufficient.
_________________
Give Kudos for correct answer and/or if you like the solution.




Re: Tom, Jane, and Sue each purchased a new house. The average &nbs
[#permalink]
17 Aug 2017, 03:33



Go to page
1 2
Next
[ 21 posts ]



