MCQ
Write whether every positive integer can be of the form $4q + 2, $ where $q$ is an integer :
- AYes
- ✓No
- CAmbiguous
- DData Insufficient
✓
Answer
Correct option: B.
No
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.
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.
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