Five consecutive positive integers are chosen at random. if the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4?

The remainder would be 1 or 3

Step-by-step explanation:

Consider the 5 consecutive positive integers are,

x,  x + 1,  x + 2,  x + 3,  x + 4,

Since, the average of these 5 numbers =

= x + 2

If x + 2 = odd,

⇒ x = odd - 2 = odd - even = odd

⇒ x + 4 = odd + even = odd

∵ an odd number is represented by '2n + 1'

Where, n = 0, 1, 2, 3, ........

Now, 2n + 1 = 1( mod 4) if n = even

While, 2n + 1 = 3( mod 4) if n = odd,

Hence, when the largest of the five integers is divided by 4 remainder would be 1 or 3.

step-by-step explanation:

step-by-step explanation:

one day the were 5 ducks, and their king told them to multiply their kingdom. so each went their own seperate way and met 4 other ducks on their journey.

when the ducks returned to their kingdom, it was discovered that there were 5 groups of 5 ducks. when the kind counted the number of ducks in total (including the ones he sent out earlier) he counted 25.

therefore 5 times 5 is 25.

the end. : )