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

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The 15 homes in a new development are each to be sold for  [#permalink]

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New post Updated on: 09 Nov 2012, 02:46
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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

Originally posted by bssys on 08 Nov 2012, 13:36.
Last edited by Bunuel on 09 Nov 2012, 02:46, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The 15 homes in a new development are each to be sold for  [#permalink]

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New post 09 Nov 2012, 02:54
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bssys 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


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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New post 08 Nov 2012, 14:09
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This is a classic problem that during your gmat exam makes you out of balance, nervous because you deal with a lot of information.

Ok take control of the question. (I have structured my answer step by step, like a process of thoughts)

First of all we have 15 homes so odd number.

Second this 15 is grouped in 3 blocks or groups whatever you want to say.

Now is the best part: one group is 170 of 4 this is important to take in account the other 5 (strees on this) 200

Now look at the answer choices : A is not possible. out

Now is the moment to attack the question. The best strategy here is a weighted average strategy.

considering the average is more or less in the middle, it follows that the group of 6 is what we are looking for and is between 170 and 200 or after 200. We have 170 200 and 6*x and the average is 200: in some place we have to put 6*x

Now in the average what value has a major "weight" No the group pf 4 with 170 ( value 680) but the 5 houses with 200 (value 1000).

So the average tends to the latter or is after, otherwise we do not have 200 like average. In this kind of problem the last value (in increasing order as we can see) is never the answer because put our value to close at the end point of our weighted average.

So the answer must be D

I hope my explanation is useful
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New post 20 Jan 2013, 00:24
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


This was taken from GMAT prep test, but i didnt know that when you exit out you can not review the correct answers for the test.
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Re: The 15 homes in a new development are each to be sold for  [#permalink]

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New post 20 Jan 2013, 01:13
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jsphcal 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


This was taken from GMAT prep test, but i didnt know that when you exit out you can not review the correct answers for the test.

IMO the answer has to be D.
5 houses are being sold for 200,000. 4 houses are being sold for $30,000 less, resulting in a loss of $120,000. To make the average selling price intact i.e. $200,000, the remaining 6 houses must be sold at such a profit that it compensates for the loss of 120,000. Hence 6x=120,000.
x=20,000.
The 6 houses are sold at $20,000 profit or at $220,000.
+1D
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Re: The 15 homes in a new development are each to be sold for  [#permalink]

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New post 20 Jan 2013, 04:52
jsphcal 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


This was taken from GMAT prep test, but i didnt know that when you exit out you can not review the correct answers for the test.


Merging similar topics. Please refer to the solutions above.
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Re: The 15 homes in a new development are each to be sold for  [#permalink]

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New post 09 Dec 2014, 19:04
Fastest way to do the calculation is as shown below:
Avg = 200
so lets find the deviation from avg for each sale.

i.e for 4 homes its was -30, 5 homes it was 0 and let x be deviation for rest of the 6 homes.

setup a equation: -30*4 + 5*0 + x*6 = 0 <== (basically 0*15) find x = 20 so the homes should be sold for 220,000 of avg to converge to 200,000.

Answer: D


bssys 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

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Re: The 15 homes in a new development are each to be sold for  [#permalink]

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New post 10 Dec 2014, 20:32
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For the sake of calculation, remove the 3 extra zero's from the question as well as answer

\(Answer = \frac{200*15 - 170*4 - 200*5}{6} = \frac{3000 - 1680}{6} = 500 - 280 = 220\)

Answer = D = 220000
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Re: The 15 homes in a new development are each to be sold for  [#permalink]

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New post 06 Jan 2015, 02:53
I also used Paresh's approach - weighted average.

I only wanted to add that it helps to map out the information we have, after we write down the formula for the mean.

M=S/N
Then, looking into the text, we know:
M=200.000
N=15 houses
S= M*N= 3.000.000 total amount of money earned by selling all 15 houses.

This 3.000.000 is comprised of houses sold at a different price, so this is where the concept of the weighted average is used.

4 houses were sold for 170.000
5 houses were sold for 200.000
6 houses were sold for X
---------------------------------
15 houses were sold for 370.000 + X

Using the formula for the mean:
M=S/N
200.000 = (4*170.000 + 5*200.000 + 6*X) / 15
200.000*15 = 1.680.000 + 6X
3.000.000-1.680.000 = 6X
1.320.000 / 6 = X
220.000 = X ANS D
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Re: The 15 homes in a new development are each to be sold for  [#permalink]

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New post 05 Apr 2018, 16:56
bssys 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 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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Re: The 15 homes in a new development are each to be sold for  [#permalink]

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New post 17 Aug 2018, 12:48
Hello,

Such questions can be answered in 30 -45 secs if we master the deviation principle

Assume that average price of each of 6 houses sold is 200,000.
and 4 houses were sold at less than average by 30,000 each= 30000*4=120,000
Now this price of 120,000 must be equally added to the price of each 6 houses to maintain the avg at 200,000
so
200,000+(120,000/6)= 220,000

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Re: The 15 homes in a new development are each to be sold for   [#permalink] 17 Aug 2018, 12:48
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