Question

If x represents a whole number, then the expression representing any positive odd integer is

• A. 2x +1
• B. 2x
• C. x+1
• D. 3x + 4

Answer 1

The correct option is A 2x +1

$\text{An odd number is a number which is}\text{one more than, or one less than an}\text{integral multiple of 2}i.e.,\text{Not perfectly}\text{divisible by 2.}\text{e.g. 1, 3 etc}1=2\times 1-1;3=2\times 1+1\therefore \text{No matter what whole number}x\text{is,}2x+1\text{or}2x-1\text{represents an odd integer.}\text{When},x=0\Rightarrow 2x-1=2\times 0-1=-1\text{Hence, the expression}2x-1\text{cannot}\text{always represent a positive odd integer.}\text{Thus, when}x\text{is a whole number,}2x+1\text{is always a positive odd integer.}i.e.,\text{If}x\in W\Rightarrow 2x+1\in I^{+}$