Question

A number when divided by $18$ leaves a remainder of $15$. Which of the following could be the remainder when it is divided by $72$?

• A. $33$
• B. $51$
• C. $15$
• D. All of the above

Answer 1

The correct option is D All of the above

Let the number be $n$.

Given when divided by $18$ gives a remainder $15$.

$\Rightarrow n=18x+15$

When $n$ is divided by $72$.

Let the remainder be $m$

$\Rightarrow$ remainder of $\frac{n}{72}=\frac{18x+15}{72}=18\frac{x}{4}+15$

Remainder of a number when divided by 4 can be 0,1,2,3 .

Thus the numbers are $18\left(0\right)+15,18\left(1\right)+15,18\left(2\right)+15,18\left(3\right)+15$ i.e $15,33,51,69$ .

Thus all the numbers in options could be remainders.

$\therefore$ option (D) is correct.