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

Question

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

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

Bunuel · Accepted Answer

Given that the average price of 15 of the homes is $200, 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.

Carcass · Answer

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

pradeepss · Answer

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

PareshGmat · Answer

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

JeffTargetTestPrep · Answer

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

CrackverbalGMAT · Answer

This is a fairly simple question on Weighted Averages. The fact that the 15 homes have been divided into three groups, each having a different pricing, is a clear give away that the Arithmetic Mean in this case will be the Weighted Average.
 
There are three different groups given in this question with different averages and weights. In such a situation, the weighted average can be calculated as,

A =  \frac{A1 * N1 + A2 * N2 + A3 * N3}{N1 + N2 + N3} , where A1, A2 and A3 represent the respective averages of the 3 groups and N1, N2 and N3 their weights.

The Arithmetic Mean for the 15 houses is given as $200,000 per home. This means that the total price of all the 15 homes is $3000,000.

Note: For easy calculation, it’s advisable to omit the 3 zeroes at the end of all prices mentioned. You can append the 3 zeroes to the final answer.

4 of the homes were sold for $170 each, so the total selling price of these homes = $680.

5 of the homes were sold for $200 each, so the total selling price of these homes = $1000.

The remaining 6 homes need to give us a total of (3000 – 1680) = $1320. Therefore, the average selling price per home for these homes =  \frac{1320}{6}  = 220 or in other words, $220,000.

The correct answer option is D.

Hope that helps!

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

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