Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?

Answer: Option C

Remainder,
$$\begin{array}{rl}& \frac{1421\times 1423\times 1425}{12}=R\\ & R\Rightarrow \frac{5\times 7\times 9}{12}\end{array}$$

[Here, we have taken individual remainder such as 1421 divided by 12 gives remainder 5, 1423 and 1425 gives the remainder as 7 and 9 on dividing by 12.]

Now, the sum is reduced to,
$$\frac{5\times 7\times 9}{12}=\frac{35\times 9}{12}$$
$$\frac{35\times 9}{12}$$  = Remainder ⇒ -1 × -3 = 3 [Here, we have taken negative remainder.] So, required remainder will be 3.

Note: When, $$\frac{9}{12}$$ it gives positive remainder as 9 and it also give a negative remainder -3. As per our convenience,we can take any time positive or negative remainder.