Question

Write whether every positive integer can be of the form $4q+2$, where $q$ is an integer.

• A. Yes
• B. No
• C. Ambiguous
• D. Data Insufficient

Answer 1

Answer: (B)

No, all positive integers cannot be written in the form of $4q+2$
Because, $4q+2=2(2q+1)$
Therefore, $4q+2$ is an even number.
So, we can't write odd numbers in the form $4q+2$ (where $q$ is an integer)
Also $2q+1$ is an odd number, hence the maximum power of $2$ that divides $4q+1$ is $1$. Therefore, we can't represent the numbers divisible by $4$ this form.