Question

For some integer q, every odd integer is of the form ______.

Options

• q

• q + 1

• 2q

• 2q + 1

Answer 1

For some integer q, every odd integer is of the form 2q + 1.

Explanation:

Odd integers are those integers which are not divisible by 2.

Hence, we can say that every integer which is a multiple of 2 must be an even integer

While 1 added to every integer which is multiplied by 2 is an odd integer.

Therefore, let us conclude that,

For an integer ‘q’, every odd integer must be of the form

(2 × q) + 1 = 2q + 1.