Answer:
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,
[tex]Average =\frac{\text{Sum of all observation}}{\text{Number of observations}}[/tex]
Since, the average of these 5 numbers = [tex]\frac{x+x+1+x+2+x+3+x+4}{5}[/tex]
[tex]=\frac{5x+10}{5}[/tex]
= 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.
