On dividing a certain number by 342, we get 47 as the remainder. What will be the remainder if the same number is divided by 18?

Correct option is A

Ans. (c)
Sol.
Let the number be:
N = 342 × q + 47, for some integer q.
Now we want the remainder when N is divided by 18:
We use the expression:
N = 342q + 47
⇒ N mod 18 = (342q + 47) mod 18
⇒ N mod 18 = (342q mod 18 + 47 mod 18)
Now,
342 ÷ 18 = 19, so 342 ≡ 0 mod 18
And, 47 mod 18 = 11
So,
N mod 18 = 0 + 11 = 11