Question

Which of the following is not the form of an odd integer?​

• A. $2n+1$
• B. $2(n+1)$
• C. $2n+3$
• D. $3(2n+1)$

Answer 1

The correct option is B $2(n+1)$

We know that $a=bq+r$, where $0\le r<b$

$2n+1⟹$
Let $a=2n+1$, from this we can conclude that on dividing $a$ with $2$, we get $1$ as the remainder. So, we can say that this is an odd number.

$2(n+1)⟹$
Let $a=2(n+1)$, from this we can conclude that on dividing $a$ with $2$, we get $0$ as the remainder. So, we can say that this is an even number.

$2n+3⟹$
Let $a=2n+3=2n+2+1=$$2(n+1)+1=2m+1)$ (taking $n+1=m$), from this we can conclude that on dividing $a$ with $2$, we get $1$ as the remainder. So, we can say that this is an odd number.

$3(2n+1)⟹$
Let $a=3(2n+1)=6n+3=$$2(3n+1)+1=2m+1$, (taking $3n+1=m$) from this we can conclude that on dividing $a$ with $2$, we get $1$ as the remainder. So, we can say that this is an odd number.