Question

How many numbers are there between $886$ and $990,$ which are divisible by $12?$

• A. $8$
• B. $9$
• C. $7$
• D. $10$

Answer 1

The correct option is B $9$

For a number to be divisible by $12$, it should be divisible by $3$ and $4$ both simultaneously.

The smallest number, which is greater than $886$ and divisible by $12$ is $888.$

The next number, which is divisible by $12$ is $888+12=900$ and so on.

Hence, numbers greater than $886$ and divisible by 12 can be represented as $888+12n\text{where}n\text{is a whole number}$

Largest number less than $990$ and divisible by 12 is $984$.

Numbers divisible by 12 are :
$888,\mathrm{900.....984}$

To find the position of $984$ in the series:
$\Rightarrow 888+12n=984\Rightarrow 12n=984-888=96\Rightarrow n=\frac{96}{12}=8$

Hence, first number greater than 888 is 900 and $8^{th}$ number greater than 888 is 984.

There are $8$ muliplies of $12$ greater than $888$ and less than or equal to $984.$

Hence, including $888,$ there are $8+1=9$ multiples of $12$ between $886$ and $990.$