Question

If x represents a whole number, then which of the following expressions can represent any positive odd integer?

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

Answer 1

The correct option is A 2x +1

An odd number is a number which is one more than, or one less than an integral multiple of 2

For example, 3 is an odd number.

3 can be written as 2 × 1 + 1

(2 × 1 is an integral multiple of 2 here)

So, no matter what whole number x represents, either 2x + 1 or 2x -1 represents an odd integer.

When x = 0, 2x - 1 = 2 × 0 - 1 = -1.

-1 is not a positive number.

Hence, the expression 2x - 1 cannot always represent a positive odd integer.

Thus, when x is a whole number, 2x + 1 is always a positive odd integer.