A car dealer purchased 10 cars for a total of $1000,000. If the range

chondro48, nick1816 Please attempt the question

Hi all,

The maximum possible value of a car (Nmax) happens if 9 cars are priced at (Nmax-50,000) each and a car is priced at Nmax as follows:
--> 9*(Nmax-50,000) + Nmax = 1,000,000
--> Nmax = 145,000

Similarly, the minimum possible value of a car (Nmin) happens if 9 cars are priced at (Nmin + 50,000) each and a car is priced at Nmin as follows:
--> 9*(Nmin+50,000) + Nmin = 1,000,000
--> Nmin = 55,000

Finally, let us calculate the difference:
-->Nmax - Nmin = 145,000 - 55,000
-->Nmax - Nmin = 90,000

Answer is (E)
+1 kudo if this explanation enlightens you

Total sum of prices of cars= 1,000,000

Maximum possible value when range is 50,000 => 9 cars should fall below average to make the 10th car of very high value.
Therefore 9*5,000 = 45,000 . Reducing the price of 9 cars by 5000 from average (1,000,000/10 = 100,000) and increasing the price of 1 car by adding 45,000 to average will give the desired scenario

Maximum possible value = average + 45,000 = 100,000+45,000 = 145,000

For minimum possible value, we need to do the exact opposite. =>9 cars should fall above average making the value of 10th car as low as possible maintaining the difference of 50,000.
105,000 is obtained by adding 5000 to the average. Since above average value would hold for 9 cars; 105000 holds for 9 cars . 9* 5000 = 45,000 which means that the 10th car that is supposed to have the minimum possible value would be 1,000,000 - (9*10500) = 1,000,000 - 945,000 = 55,000

Highest possible value - Lowest possible value = 145,000 - 55,000 = 90,000 - (Option E)

I do not understand the question. The wording is not clear. You say range price is $50,000, isn't the range= max - min? Ther word range is confusing with what requested in the question.

Hi

The definition of a range in a set is maximum - minimum, is't right? How come is the range is 50,000 then becomes 90000.

Do you have any other definition of a range with a set?

Posted from my mobile device

Any similar question?

Posted from my mobile device

Any similar question?

Posted from my mobile device

Hi,

Your definition of range is correct, but that is not the question.

It is asking for the maximum-minimum POSSIBLE values with a fixed range.

Consider the below example:

A father has to split $100 between his 4 sons with a fixed range of 20 between the highest and lowest amounts.

he has the below options:

40-20-20-20

(or)

30-30-30-10

or even

35-35-15-15

On all above occasions you will see the range as 20; but when you check the maximum - minimum value - it will be 40 (from the 1st split) - 10 (from the second split) = 30.

Hope this helps

Mo2men

What if I could have asked,
What is the difference between minimum max & maximum max?

We have a fixed range of $50,000 and we are moving that range around average of $100,000 so that min & max values change around the average. But there is a limit to max and there is a corresponding limit to min values.
Since there are several max and min values possible satisfying conditions of average = $100,000 and range = $50,000, there is a maximum of max and minimum of min values. The question asks the difference between them.

In a particular case, range = max - min
But what if the question asks about maximum possible and minimum possible values, then the answer is to be derived from 2 extreme cases as discussed in solutions.
Maximum possible value of a car = $145,000
Minimum possible value of a car = $55,000
Difference = $90,000
But this is not a single case, but 2 separate cases
1st in which maximum max value is found
2nd in which minimum min value is found.

What is the source of this question? Thank you.