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 $2q+1$

We know that integers are positive and negative whole numbers.
$(...,-3,-2,-1,0,1,2,3,...)$
Also, any integer multiplied by $2$ is even.
Example:- $\left(3\right)\times 2=6$ , $\left(7\right)\times 2=14$, $\left(8\right)\times 2=16$ and so on.
If $1$ is added to these even number, it results in a odd number.
Example $6+1=7$, $14+1=15$, $16+1=17$,
If $q$ is any integer, then $2q$ is the set of even numbers and $2q+1$ represents odd numbers.
Ans is: $2q+1$