Mean and Median

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psm12se: Master | Next Rank: 500 Posts; Posts: 109; Joined: Sun Oct 21, 2012 5:10 amFollowed by: 1 member

by psm12se » Sun Mar 03, 2013 6:55 am

Last month 15 homes were sold in Town X. The average(arithmetic mean)sales price of the homes was $150,000 and the median sale price was $130,000. 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.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Mar 03, 2013 7:49 am

psm12se wrote:Last month 15 homes were sold in Town X. The average(arithmetic mean)sales price of the homes was $150,000 and the median sale price was $130,000. 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.

Let's looks at one possible scenario and see which answer choices we can eliminate.

Aside: To make things simpler, let's divide all of the prices by 1000.

First, we'll use a nice rule that says: sum of all values = (mean)(number of values)
So, the sum of all 15 prices = ($150)(15) = $2250.

If the median is $130, then the middlemost value is $130

So, one possible scenario is:
130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 430

Aside: To find the last value (430), I took the sum of all 15 numbers (2250) and subtracted (14)(130)

Notice that this scenario tells us that II and III need not be true (since our scenario does not conform to either one).

Since answer choices B, C, D and E all include either II or III, we can eliminate them.

This leaves us with A, which must be the correct answer.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Sun Mar 03, 2013 11:58 pm

Brent@GMATPrepNow wrote:
psm12se wrote:Last month 15 homes were sold in Town X. The average(arithmetic mean)sales price of the homes was $150,000 and the median sale price was $130,000. 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.
Let's looks at one possible scenario and see which answer choices we can eliminate.

Aside: To make things simpler, let's divide all of the prices by 1000.

First, we'll use a nice rule that says: sum of all values = (mean)(number of values)
So, the sum of all 15 prices = ($150)(15) = $2250.

If the median is $130, then the middlemost value is $130

So, one possible scenario is:
130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 130, 430

Aside: To find the last value (430), I took the sum of all 15 numbers (2250) and subtracted (14)(130)

Notice that this scenario tells us that II and III need not be true (since our scenario does not conform to either one).

Since answer choices B, C, D and E all include either II or III, we can eliminate them.

This leaves us with A, which must be the correct answer.

Cheers,
Brent

very well explained

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Mar 04, 2013 4:17 am

I posted a similar explanation here:

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