The average (arithmetic mean) of the 5 houses on a certain street is $

A?

AM for 5 houses: 60,000
Total price for 5 houses: 60,000*5 = 300,000

To maximize the price for one house let all remaining four be equal
Let the price for all four houses be 55,000 respectively;
SO total price for four houses = 220,000
The maximum price for the fifth house could be 300,000 - 220,000 = 80,000

Hence option A cannot be the price for a most costly house

Avg=60k
Sum=Avg*No. of obs=60k*5=300k

Now we know the least expensive house costs 55k so max value of a house can be 55k + value left after taking into account 55k (least value of all houses)

Max Value= 300000-(5*55000) + 55000=80000

Therefore, (A) 82000 being greater than 80000 cannot be a possible value of the house

Hi Experts - chetan2u, VeritasKarishma, Bunuel, yashikaaggarwal, generis

For the most expensive house specifically -- what can be the lowest price for the most expensive house ?

How would you calculate that ?

I am getting 62.5 k can be the min price for the most expensive house.

If you see, the question never mention that the price has to be distinct so we can take extreme values.
The total cost of 5 houses are 60,000*5 = 300,000 (Average*No.of houses = Total)

55,000 is the lowest value.
Now if you want one house to be maximum others have to be of least value.
55,000 is the least value we have.
So let's say A house is of X value and rest 4 are of 55,000
55,000*4 = 220,000
The maximum value of A will be 300,000-220,000 = 80,000.
Hence A is the answer.
Or even if you take distinct values.
Let's say 55,000 , 55001, 55002, 55003 as value of 4 houses. Total of four houses will be 220,006. Making the maximum value of 5th house as 79,994.

The key highlight here is " if you are looking forward for minimum value you will maximize rest all, and if maximum value you have to minimize rest"

Posted from my mobile device

If you are looking for the least value of the most expensive, take all the others to be maximum possible.
Now the least expensive is 55000, then the other four can be equal and will be (60000*5-55000)/4=245000/4=61250 each

But say all were different, then we would have taken consecutive values for the 4 most expensive

The answer is the maximum of all the 5 answer choices.

The average (arithmetic mean) of the 5 houses on a certain street is $60,000. If the price of the least expensive house is $55,000, which of the following could NOT be the price of the most expensive house?

A. $82,000
B. $78,000
C. $72,000
D. $65,000
E. $62,500

I agree with the approach explained in the previous post i.e minimizing the value of the 4 houses to figure out the price of the most expensive house.

My question here is, Can we solve this question in under 30 secs if we approach this question more logically.

You are asked to find out which of the following could not be the price of the most expensive house. That means if we choose option B as the answer i.e 78000$. We are saying that 78,000$ cannot be the price of the most expensive house, but we are agreeing to the fact that other answer choices can be the possible price of the most expensive house.

If 78,000$ cannot be the price of the most expensive house, how can a value above that i.e 82,000$ be a possible price of the most expensive house? Is it possible? No, it's not.

So logically approaching this question, the correct answer should be the highest value among the answer choices. No other calculations are needed.

Hence, Option A is the correct answer.

Thanks,
Clifin J Francis,
GMAT Mentor.

Hi chetan2u

Replying to an old thread here. But, can you elaborate on when you said " But say all were different, then we would have taken consecutive values for the 4 most expensive "? How to get the other 4 numbers if all were different?