Question

A number when divided by a divisor leaves a remainder of $24$. When twice the original number is divided by the same divisor the remainder is $11$. What is the value of the divisor?

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

Answer 1

The correct option is D $37$

Solution -

Let numbers be x

Let divisor be d

$x=md+14$ $2x=nd+11$

then

$2md+48=nd+11$

$37=(n-2m)d$

$d=\frac{37}{n-2m}$

37 is prime number

then $n-2m=37$ or $1$

$d=1,37$

D is correct