Question

The probability that the sum of squares of two non-negative integers is divisible by 5 is

(a) 7/25

(b) 8/25

(c) 9/25

(d) 2/25

Answer 1

Correct option (c) 9/25

Explanation:

Let two non-negative integers be x & y such that x = 5a + α and y = 5b + β where 0 ≤ α, ≤ β

New, x2+ y2 = 25(a2+ b2 ) + 10(aα + bβ)+ α2 + β2

α2 + β2should be divisible by 5

(α ,β) can have ordered pairs as

{(0,0), (1,2), (2,1), (1,3), (3,1), (2,4), (4,2), (3,4), (4,3)} = 9 ways

required probability is 9/25