Last month 15 homes were sold in Town X. The Average ( arithmetic mean) sale price of the homes was 150000 and the median sale price was 130000. Which of the following statements must be true?
1. At least one of the homes was sold for more than 165,000
2. At least one of the homes was sold for more than 130,000 and less than 150,000
3. At least one of the homes was sold for less than 130,000
A. 1
B. 2
C. 3
D. 1 and 2
E 1 and 3
GMAT Forum
5 postsPage 1 of 1
- jstern31
- Course Students
- Posts: 6
- Joined: Fri Mar 12, 2010 8:59 am
- jstern31
- Course Students
- Posts: 6
- Joined: Fri Mar 12, 2010 8:59 am
- rohit801
- Course Students
- Posts: 21
- Joined: Tue Jan 03, 2006 1:57 pm
Re: Last month 15 homes were sold in Town X.
Last month 15 homes were sold in Town X. The Average ( arithmetic mean) sale price of the homes was 150000 and the median sale price was 130000. Which of the following statements must be true?
1. At least one of the homes was sold for more than 165,000
2. At least one of the homes was sold for more than 130,000 and less than 150,000
3. At least one of the homes was sold for less than 130,000
OK- so, let's see what we can deduce from the question stem:
The price of the 8th home, in ascending order of the values, is 130K [median of 15 numbers]. There are seven house prices on either side of ths value. Now, the Mean of 15 houses=150K. What can we deduce:
Sum of all 15 prices = 15*150K = 2250K. Let's try to MAXIMIZE the values of the first seven houses so that we can get some info the MINIMUM value of the last seven houses. The MAX value of each of the first seven can be 130K [if it were higher, then 130 couldn't be the median.]. So, we get 7*130K= 910K. Then, the AVG of the last 7 houses is: (2250K-910K-130K)/7 ~ over 170K. [ you can do the math].
This means-" At least one of the homes was sold for more than 165,000" must be true. It could be that ALL sold for the 170Kish value but even if one were below 170ish, then at least one would have to be OVER 170ish to maintain the Average.
This should give you some headstart to figure out that only A must be true; other options, don't NEED to be true.
Hope that helps.
1. At least one of the homes was sold for more than 165,000
2. At least one of the homes was sold for more than 130,000 and less than 150,000
3. At least one of the homes was sold for less than 130,000
OK- so, let's see what we can deduce from the question stem:
The price of the 8th home, in ascending order of the values, is 130K [median of 15 numbers]. There are seven house prices on either side of ths value. Now, the Mean of 15 houses=150K. What can we deduce:
Sum of all 15 prices = 15*150K = 2250K. Let's try to MAXIMIZE the values of the first seven houses so that we can get some info the MINIMUM value of the last seven houses. The MAX value of each of the first seven can be 130K [if it were higher, then 130 couldn't be the median.]. So, we get 7*130K= 910K. Then, the AVG of the last 7 houses is: (2250K-910K-130K)/7 ~ over 170K. [ you can do the math].
This means-" At least one of the homes was sold for more than 165,000" must be true. It could be that ALL sold for the 170Kish value but even if one were below 170ish, then at least one would have to be OVER 170ish to maintain the Average.
This should give you some headstart to figure out that only A must be true; other options, don't NEED to be true.
Hope that helps.
- tanishsr1013
- Forum Guests
- Posts: 2
- Joined: Tue Jul 13, 2010 5:27 am
Re: Last month 15 homes were sold in Town X.
Hi all,
What is the correct answer to the question? Is there any other method of solving or shortcut to this question, as I also solved this as 'rohit801' solved and reached the same answer "Only 1 is true".
-regards,
Tanish S.
What is the correct answer to the question? Is there any other method of solving or shortcut to this question, as I also solved this as 'rohit801' solved and reached the same answer "Only 1 is true".
-regards,
Tanish S.
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
5 posts Page 1 of 1