Question

A number when divided by a divisor leaves a remainder of $24$, when twice of the original number is divided by the same divisor the remainder is $11$, then find the divisor.

• A. $13$
• B. $59$
• C. $35$
• D. $37$

Answer 1

The correct option is D

$37$

Let $x$ and $d$ be the number and divisor respectively.

According to the Division Algorithm, we get

$Dividend=Divisior\times Quotient+Remainder$

$x=d\times Q_1+24$

According to the given condition, We get

$2x=d\times Q_2+11$

$\Rightarrow 2\left(d\times Q_1+24\right)=d\times Q_2+11$

$\Rightarrow 2d\times Q_1+48=d\times Q_2+11$

$\Rightarrow d\times Q_2-2d\times Q_1=48-11$

$\Rightarrow d(Q_2-2Q_1)=37$

$\Rightarrow d=\frac{37}{(Q_2-2Q_1)}$

Since $37$ is a prime number, then $(Q_2-2Q_1)=37$ or $1$

Therefore, the Divisor, $d=37$ or $1$