Question

Let a = {1, 3, 5, … 99} 

and b = {2, 4, 6, … 100}

The number of ordered pair (a, b) such that a + b when divided by 23 leaves remainder 2 is ?

Answer 1

a + b = 23λ + 2 

λ = 0, 1, 2, ….

But λ can’t be even

Total = 12 + 35 + 42 + 19 = 108 ordered paris