Question

Every even and odd integers can be represented as ________ and ________

• A. 2q and 2q+1
• B. 3q and 3q+2
• C. 3q and 3q+1
• D. 2q and q+1

Answer 1

The correct option is A 2q and 2q+1

Let 'a' be any positive integer and b=2.
By euclid's division algorithm,
a=bq + r 0 ≤ r < b
a=2q + r 0 ≤ r < 2 or r =0,1
If r=0 , then a=2q+0
a=2q, then a is an even integer
If r=1, then a=2q+1
a=2q+1, then a is an odd integer