Question

A number is divided by $889$ gives a remainder $63$. If the same number is divided by $29$, the remainder will be:

• A. $10$
• B. $5$
• C. $4$
• D. $2$

Answer 1

The correct option is B $5$

Let the number be x

$\Rightarrow x=889k+63$

where k is the quotient

Let required remainder be r

$\Rightarrow x=29l+r$

Now, k, l = 0, 1, 2,_ _ _

As x = 889k + 63

= (870 + 19) k + 63

= 870k + 19k + 63

= (870k + 58) + 19 k + 5

multiples of $29\Rightarrow$ won't

give remainder

Smallest remainder would

be obtained, when k = 0

$\Rightarrow Remainder=5\Rightarrow \left(B\right)$