The 15 homes in a new development are each to be sold for

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melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pm; Location: Australia / India; Thanked: 37 times; Followed by:2 members

The 15 homes in a new development are each to be sold for

by melguy » Thu Jul 04, 2013 10:34 pm

Hello

Please let me know if there is a shortcut for this problem. I could not do the problem in the test conditions (so i guessed it and moved on) but now while reviewing I was able to do the problem correctly (but took me 4 mins +).

Is there a shortcut that I can use for this and such average problems.

Plz suggest a few similar problems.

Thanks

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Source: Beat The GMAT — Problem Solving | Thu Jul 04, 2013 10:34 pm

CSASHISHPANDAY: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Sat Jun 18, 2011 9:50 pm; Location: New Delhi; Thanked: 35 times; Followed by:3 members; GMAT Score:800

by CSASHISHPANDAY » Thu Jul 04, 2013 10:57 pm

Since the average price of 15 of the homes is $200, then the total price of these homes is 15*$200=$3,000.

The total price of 4 of the homes is 4*$170=$680;
The total price of 5 of the homes is 5*$200=$1,000;

Therefore the total price of the remaining 6 of the homes is $3,000-($680+$1,000)=$1,320. The average price per home is $1,320/6=$220.

Answer: D.

Hope it's clear.

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ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pm; Location: Bangalore, India; Thanked: 97 times; Followed by:26 members; GMAT Score:750

by ganeshrkamath » Thu Jul 04, 2013 11:47 pm

melguy wrote:Hello

Please let me know if there is a shortcut for this problem. I could not do the problem in the test conditions (so i guessed it and moved on) but now while reviewing I was able to do the problem correctly (but took me 4 mins +).

Is there a shortcut that I can use for this and such average problems.

Plz suggest a few similar problems.

Thanks

5 are sold at 200,000
So average of remaining 10 is 200,000.
17*4 + x*6 = 200
x = 132/6
x = 22

So 220,000

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

by GMATGuruNY » Fri Jul 05, 2013 5:00 am

melguy wrote:The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 6 homes?

A. $200,000
B. $210,000
C. $215,000
D. $220,000
E. $230,000

The 5 homes sold for $200 each do not affect the average, since these homes are sold for the average selling price.
Our concern:
The average selling price of THE OTHER 10 HOMES must be $200.

Required sum for the other 10 homes = (number)(average) = 10*200 = 2000.
Sum of the 4 homes sold for $170 each = (number)(average) = 4*170 = 680.
Sum of the remaining 6 homes = 2000-680 = 1320.
Average for the remaining 6 homes = sum/number = 1320/6 = 220.

The correct answer is D.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Thu Apr 05, 2018 4:12 pm

The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 6 homes?

A. $200,000
B. $210,000
C. $215,000
D. $220,000
E. $230,000

The total selling price of the 4 homes is 4 x 170,000 = $680,000, and the total selling price of the 5 homes is 200,000 x 5 = $1,000,000. Thus, the total selling price of these 9 homes is $1,680,000.

The total selling of the all 15 homes is 15 x 200,000 = $3,000,000.

Thus, the total selling price of the remaining 6 homes is 3,000,000 - 1,680,000 = $1,320,000, resulting in a price of 1,320,000/6 = $220,000 per home.

Answer: D

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