Question

For some integer $q$ every odd integer is of the form :

• A. $q$
• B. $q+1$
• C. $2q$
• D. $2q+1$

Answer 1

The correct option is D

$2q+1$

Let, an integer is represented as $q.$

When $q$ is an odd integer,

Suppose $q=5$ then $\left(a\right),\left(d\right)$ are correct because $5$ is already odd and $2q+1=11$is also odd.

When $q$is an even integer,

Suppose $q=6$ then (b), (d) are correct because,

$$\begin{gathered} q+1=7 \\ 2q+1=13 \end{gathered}$$

Therefore. It is clear from both cases $\left(d\right)$ is the only option that is every odd integer is of the form since options $\left(a\right),\left(b\right),\mathrm{and}\left(c\right)$ are incorrect.

Hence, the correct answer is option (d),$(2q+1).$