Averages&Medians

Expert replies

Akansha: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Wed Sep 01, 2010 10:04 amFollowed by: 20 members; Thanked: 1 times

by Akansha » Thu May 26, 2011 9:43 am

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
a. I
b. II
c. III
d. I and II
e. I and III

OA is A

Like this post

Source: Beat The GMAT — Problem Solving | Thu May 26, 2011 9:43 am

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Thu May 26, 2011 10:19 am

15/2 +1 makes median, hence 8 homes were sold for not more than $130,000 and 7 homes were sold for >$130,000. III) <130,000 isn't right as we know that 8 homes MUST BE not more than $130,000, BUT we don't know if they are less. II) 150,000*15-130,000*8=1,460,000 spread for 7 homes makes not less than 200,000 each home. Thus we don't know for sure if house >130,000 and <150,000. I) We know for sure that at least one house is sold for >165,000. Why actually as explained before 7 homes average beyond the median could be evenly spread with not less than $200,000. And if not 165,000 then even 200,000 could be placed in I).

BUT I sincerely think that this problem can be solved much easier and speedier way if we cut off zeros and put the revised way into solution

Last month 15 homes were sold in Town X. The average sale price of the houses was $15 and the median sales price was $13. Which must be true?

At least 1 house sold for > $16.5
At least 1 house sold for > $13 but < $15
At least 1 home sold for < $13

Akansha 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
a. I
b. II
c. III
d. I and II
e. I and III

OA is A

Success doesn't come overnight!

Like this post

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Thu May 26, 2011 10:21 am

Hi,
Let the 15 prices when placed in increasing order be a1,a2,...a15, where a1<=a2<=...<=a15
median = a8 = 150K
Avg = 150K
Case(I) Let's assume no house is sold above 165K. So, we shall assign maximum possible values to the sales prices.
So, a1=a2=..=a8=130
a9=a10=...=a15=165
now, average = [(130).8+(165).7]/15 = 2195K/15 <150K
so, our assumption that no house is sold above 165K is false
Hence, I must be true

Case(II)
One counter example is a1=a2=..a8 = 130K, a9=a10...=a14=170K,a15=190K
So, II need not be true

Case(III)
The example used in case II should be sufficient to disprove this
So, III need not be true
Hence, answer A

Cheers!

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review