Question

Which of the following numbers are divisible by \[2\] but not by $4$?
A.$28$
B.$324$
C.$2356$
D.$8026$

Answer 1

Hint: We know that a number is divisible by $2$ if and only if the digit at unit place of the number is divisible by $2$ and that a number will be only divisible by $4$ if and only if the last two digits of the number together are completely divisible by $4$. So check each option for this rule to find the answer.

Complete step-by-step answer:
We have to choose the number which is divisible by \[2\] but not by $4$. We know that a number is divisible by $2$ if and only if the digit at unit place of the number is divisible by $2$ . Check each option for this.
Here, the unit digits of the numbers $28$,$324$,$2356$ and $8026$ are $8,4,6$ and $6$ respectively. All the unit digits are completely divisible by $2$ as they all are multiples of $2$. This means all the numbers are divisible by $2$. Now, we have to find which number is not divisible by $4$.
We know that a number will be only divisible by $4$ if and only if the last two digits of the number together are completely divisible by $4$.
First option has only two digits $28$ which is a multiple of $4$ as $4 \times 7 = 28$ so it is divisible by $4$ .
In second option the last two digits are-$24$ which is also divisible by $4$
In third option, the last two digits are-$56$ which is also divisible by $4$
In the fourth option, the last two digits are-$26$ which is not completely divisible by $4$ as it gives the remainder $2$.
The correct answer is option D.

Note: We can also solve this question by directly dividing each number by $2$ and $4$ respectively. The number which is not completely divided by $4$ will give remainder after division. But this method is a long method so we use the divisibility rule.