Question

For some integers $q$, every odd integer is of the form:

• A. $q$
• B. $q+1$
• C. $2q$
• D. $2q+1$

Answer 1

The correct option is D

$2q+1$

Step 1: Explanation for the correct option:

• Integers are specific type of numbers that includes zero, positive, and negative values. $Z=\{\dots \dots -8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,\dots \dots \}$, where Z is an integer.
• Option D: Since $q$ is an integer; therefore, $2q$ will always be an even integer. The next consecutive number after $2q$ will be $2q+1$, which will be an odd number.

Step 2: Explanation for incorrect options:

• Option A: Since $q$ is an integer; therefore, it can be either odd or even; therefore, option A is incorrect.
• Option B: Given, $q$ is an integer. Assume, $q$ is an odd integer, in that case, $q+1$ will be an even number. Thus, option B is incorrect.
• Option C: As $2q$ is divisible by 2; therefore, it is an even number. Thus, option C is incorrect.

Final Answer: Hence, option D is correct.