Question

if the average (arithmetic mean) opf five distinct positive integers is 10, what is the difference between the largest possible value of the greatest integer and the least possible value of the greatest of the five integers

Answer 1

Step-by-step explanation:

a-2d a-d a a+d a+2d/5=10

5a=50

a=10

d=4

largest and least diff

a+2d -(a-2d)

a+2d-a+2d

4d

16

Answer 2

Answer:

$4$

Step-by-step explanation:

As per the given information, we have that the average of five distinct positive integers is $10$.

We know that Average $=\frac{Sum of Observations}{Number of Observations}$

Now, let us assume the minimum positive integer value among the five be $x$.

Thus the five distinct positive integers will be $x, x+1, x+2, x+3$ and $x+4$.

The sum of these five positive integers will be

$x+x+1+x+2+x+3+x+4=5x+10=5x+10$

and the given average for these five positive integers is $10$.

Now, as per the formula of Average

$10=\frac{5x+10}{5}$

$50=5x+10\\5x=40\\x=8$

So, the minimum value of positive integer among these five is $8$ and the maximum value of positive integer will be $x+4=8+4=12$.

Thus, the difference between the largest possible value of the greatest integer and the least possible value of the greatest of the five integers

will be $12-8=4$.