Question

For some integer m, every even integer is of the form:

• A. m
• B. m+1
• C. 2m
• D. 2m+1

Answer 1

The correct option is C

2m

Explanation for the correct option:

Option (C): $2m$

Even number: A number that is divisible by $2$is called an even number.

Odd number: A number that is not divisible by $2$and leaves $1$ as the remainder is called an even number.

If we multiply by $2$ with any integer $\mathit{m}$ then we get $2m$, which is also divisible by $2(2m=2xm)$Because $2m$ is divisible by $2$.

Therefore, $2m$ is an even integer.

Hence, for some integer $\mathit{m}$, every even integer is of the form of $2m$.

Explanation for the incorrect options:

Option (A): $\mathit{m}$

Here, given that $\mathit{m}$ is an integer so $\mathit{m}$ can be even or odd

Therefore, it is not the correct option.

Option (B): $\mathit{m}\mathbf{+}\mathbf{1}$

Here, if we take m as an even integer then $\mathit{m}\mathbf{+}\mathbf{1}$ is not an even integer because it is not divisible by $2$.

Therefore, it is also an incorrect option.

Option (D): $\mathbf{2}\mathit{m}\mathbf{+}\mathbf{1}$

Here, if we take $\mathit{m}$ as any integer (odd or even) then $\mathbf{2}\mathit{m}$ always will be an even integer because it is divisible by $2$, and by adding $1$ in $2m$ then $2m+1$ always be an odd integer number.

Therefore, it is also an incorrect option.

Hence, option (C) is the correct answer.