What is the largest possible integer that can be chosen as one of five distinct positive integers whose average is 10?

Then the other 4 must be as small as possible, and since they are all distinct, the 4 smaller must be

1 , 2, 3, and 4

(1+2+3+4+x)/5 = 10
10+x = 50
x = 40
The largest such number is 40

check by taking any other 4
e.g.
(3+4+5+6+x)/5 = 10
x + 18 = 50
x = 32

PROGRAMMING

To find the largest possible integer, we need to first understand the concept of an average.

The average (also called the arithmetic mean) of a set of numbers is calculated by adding up all the numbers in the set and then dividing the sum by the total count of numbers.

In this case, the average of five distinct positive integers is given as 10. It means that the sum of these five integers is 10 multiplied by the total count, which is 5.

So, 10 * 5 = 50 is the sum of the five integers.

Now, to determine the largest possible integer, let's assume that the other four integers are as small as possible. We want to maximize the largest integer, so we minimize the others.

If we choose the four smallest positive integers as 1, 2, 3, and 4, their sum would be 1 + 2 + 3 + 4 = 10.

To find the largest possible integer, subtract the sum of the four smallest integers from the total sum:

50 - 10 = 40.

Hence, the largest possible integer that can be chosen is 40.