Let x be the number and y be divisor. a is the quotient when x is divided by y and b is the quotient when 2x is divided by y.

x=ay+24------(1)
2x=by+11----(2)

Multiply (1) by 2 and solve for y,

0 = y(2a-b)+37

37 / (b - 2a) = y.

Since y=37 is a prime number, b= 39 and a=1.

IMO D, y=37.

x=37*1 + 24 = 61. 61 divided by 37, remainder =24
2x = 122 divided by 37, remainder =11

sanju09 wrote: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) 12
(B) 13
(C) 35
(D) 37
(E) 59

Let's start with some common sense:

when you divide by a number x, the biggest possible remainder is (x-1). So, if we get a remainder of 24, x must be at least 25... eliminate (A) and (B).

Now let's just backsolve:

(C) 35

To get a remainder of 24, we can pick 24 as our original number.
24*2 = 48. 48/35 = 1 rem13... wrong!

(D) 37

To get a remainder of 24, we can pick 24 as our original number.
24*2 = 48. 48/37 = 1rem11... bingo! Choose (D).