Question

Question 2
For some integer q. every odd integer is of the form

A) q
B) q + 1
C) 2q
D) 2q + 1

Answer 1

We know that the odd integers are not divisible by 2.

If we take any integer, say a, as the dividend and 2 as the divisor, then by Euclid's division lemma

$a=2q+r$ Where $q$ is the quotient and $0\le r<2$

If a is an even integer, then the possible values of r are just 0.

If a is an odd integer, the possible values of r are just 1.

Thus, any odd integer can be expressed as $2q+1$.

Hence, answer option is D.