Question

If \(q\) is a positive integer, which of the following is {not an odd positive integer?}

• A. \(8q+1\)
• B. \(8q+4\)
• C. \(8q+3\)
• D. \(8q+7\)

Hint:

Even \(+\) even \(=\) even, even \(+\) odd \(=\) odd. Any multiple of \(2\) (like \(8q\)) is even.

Answer 1

The Correct Option is B

Step 1: Use parity of multiples of 8.
Since \(q\in\mathbb{Z}^+\), \(8q\) is divisible by \(8\) and hence is even.
Step 2: Check each expression’s parity.
\(8q+1 = \text{even}+1=\text{odd}\).
\(8q+4 = \text{even}+4=even\).
\(8q+3 = \text{even}+3=\text{odd}\).
\(8q+7 = \text{even}+7=\text{odd}\).
Step 3: Conclude.
Only \(8q+4\) is not odd; it is even.