BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

average-median

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 150
Joined: Tue Mar 08, 2011 4:38 am
Thanked: 5 times

average-median

by finance » Tue Aug 09, 2011 6:23 am
15 homes were sold at an average sales price of 150000. The median of the sales price equals 130000. Which of the followings must be true??
I) At least one was sold for more than 165000
II) At least one was sold for more than 130000 and less than 165000.
III) At least was one was sold for less than 130000.

A) I only
B) II only
C) III only
D) I&II
E) I&III
Top
Source: — Problem Solving |
Legendary Member
Posts: 2789
Joined: Tue Jul 26, 2011 12:19 am
Location: Chennai, India
Thanked: 206 times
Followed by:43 members
GMAT Score:640

by GmatKiss » Tue Aug 09, 2011 6:39 am
will choose D
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 461
Joined: Tue May 10, 2011 9:09 am
Location: pune
Thanked: 36 times
Followed by:3 members

by amit2k9 » Tue Aug 09, 2011 7:47 am
i believe this has been discussed many times.

still...

total = 150 * 15 = 2250 (neglecting the 1000's)

now, 14 * 130 = 1820 meaning last number = 2250-1820 = 440 > 165. Hence 1 is true.

more so, 13 * 130 = 1630, meaning if 14th member = 150 then total = 1630 + 150 = 1780

so 2250 - 1780 = 470 > 165. hence 2 is true too.

thus D it is.
For Understanding Sustainability,Green Businesses and Social Entrepreneurship visit -https://aamthoughts.blocked/
(Featured Best Green Site Worldwide-https://bloggers.com/green/popular/page2)
Top
Master | Next Rank: 500 Posts
Posts: 150
Joined: Tue Mar 08, 2011 4:38 am
Thanked: 5 times

by finance » Tue Aug 09, 2011 9:19 am
Amit, thank you for your reply...but I "still.." did not understand why do you multiply 13 by 14. Why do we multiply the median?? BTHW the answer is A.
Top
Junior | Next Rank: 30 Posts
Posts: 20
Joined: Thu Feb 17, 2011 9:13 am
Thanked: 1 times

by sharmishtha_goel » Tue Aug 09, 2011 11:36 am
how do you check the validation for II and III??


If Median is 130K, i.e. is the 8th value, the seven below are < = 130K .
total 2,250K
if 1st 8 are 130K then balance is 2,250- 1040 = 1,210K i.e. averaged over remaining 7 is approx 1,728K.
hence we can conclude validity of I.

Now, if all the remaining seven were 1,728 , how would you validate II?

TIA
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 312
Joined: Tue Aug 02, 2011 3:16 pm
Location: New York City
Thanked: 130 times
Followed by:33 members
GMAT Score:780

by gmatboost » Tue Aug 09, 2011 10:03 pm
sharmishtha_goel is right on.

If we maximize the first 8, at 130K each, the others still need to average 173k, which means at least one is above 165k.

However, if we just set the other 7 exactly to this average, none will be above 130k and below 165k. This option also shows that III is wrong.

The answer is I only.
Greg Michnikov, Founder of GMAT Boost

GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.

Also, check out the most useful GMAT Math blog on the internet here.
Top
Master | Next Rank: 500 Posts
Posts: 150
Joined: Tue Mar 08, 2011 4:38 am
Thanked: 5 times

by finance » Wed Aug 10, 2011 12:39 am
Thank you guys...I now understood it!! Thanx a lot!
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 407
Joined: Tue Jan 25, 2011 9:19 am
Thanked: 25 times
Followed by:7 members

by Ozlemg » Wed Aug 10, 2011 6:15 am
gmatboost wrote:sharmishtha_goel is right on.

If we maximize the first 8, at 130K each, the others still need to average 173k, which means at least one is above 165k.

However, if we just set the other 7 exactly to this average, none will be above 130k and below 165k. This option also shows that III is wrong.

The answer is I only.
Gmatboost could you elaborate little bit more why ii is wrong?
If first 8 is 130 (8*130K) and last 7 is 150K (7*150K), then average is smt 132.22 but not 150?
The more you suffer before the test, the less you will do so in the test! :)
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 142
Joined: Mon Jan 10, 2011 8:03 am
Thanked: 19 times

by krishnasty » Wed Aug 10, 2011 6:52 am
hey guys...
can i have a detailed explanation on how did v arrive at this ans ? or if this has been discussed earlier, i would be glad if sum1 could provide me the link to that post..
---------------------------------------
Appreciation in thanks please!!
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 312
Joined: Tue Aug 02, 2011 3:16 pm
Location: New York City
Thanked: 130 times
Followed by:33 members
GMAT Score:780

by gmatboost » Wed Aug 10, 2011 7:44 am
If first 8 is 130 (8*130K) and last 7 is 150K (7*150K), then average is smt 132.22 but not 150?
Hi Ozlemg,

It cannot be the case that the first 8 are 130 and the last 7 are 150, because we need the OVERALL average to be 150, and as you point out, in this case the overall average is 132. So, this case is not possible.
II) At least one was sold for more than 130000 and less than 165000.
What invalidates II is that I can give a specific example that has the following properties:
1. The overall average is 150k, which needs to be true for any case we consider
2. No house is between 130 and 165 (II claims that some house must be in that range)

This example is to have the first 8 at exactly 130, and to have the other 7 at around 172. None of them are between 130 and 165, so II is not true.

Let me know what you think.
Greg Michnikov, Founder of GMAT Boost

GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.

Also, check out the most useful GMAT Math blog on the internet here.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 407
Joined: Tue Jan 25, 2011 9:19 am
Thanked: 25 times
Followed by:7 members

by Ozlemg » Wed Aug 10, 2011 12:30 pm
gmatboost wrote:
If first 8 is 130 (8*130K) and last 7 is 150K (7*150K), then average is smt 132.22 but not 150?
Hi Ozlemg,

It cannot be the case that the first 8 are 130 and the last 7 are 150, because we need the OVERALL average to be 150, and as you point out, in this case the overall average is 132. So, this case is not possible.
II) At least one was sold for more than 130000 and less than 165000.
What invalidates II is that I can give a specific example that has the following properties:
1. The overall average is 150k, which needs to be true for any case we consider
2. No house is between 130 and 165 (II claims that some house must be in that range)

This example is to have the first 8 at exactly 130, and to have the other 7 at around 172. None of them are between 130 and 165, so II is not true.

Let me know what you think.
I got your point. Your explanation is clear.
Thank you.
The more you suffer before the test, the less you will do so in the test! :)
Top
Post new topic Post Reply
• Page 1 of 1