Question

When a natural number $N$ is divided by $D$, the remainder is $35$. When $50N$ is divided by $D$, the remainder is $11$. Find $D$.

• A. $1739$
• B. $43$
• C. $47$
• D. Cannot be determined

Answer 1

Answer: (A)

$1739$

Natural number : $N$

divided by : $D$

Remainder $=35$

Let quotient $=q_1,q_2$

$\Rightarrow (N=q_{1}D+35)50$

$\Rightarrow 50N={50q}_1\left(D\right)+35\left(50\right)$ ..... $\left(i\right)$

$\Rightarrow 50N=q_2\left(D\right)+11$..... $\left(ii\right)$

Subtract $\left(ii\right)$ from $\left(i\right)$,

$\Rightarrow 0=D({50q}_1-q_2)+1739\Rightarrow D(q_2-{50q}_1)=1739\Rightarrow D=\frac{1739}{q_2-{50q}_1}$

$\Rightarrow$ $D$ should be $1739$ or a factor of it.