A number when divided by a divisor leaves a remainder of 30. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor? Select the correct option:
A) 12  B) 13  C) 35  D) 43  E) 59

Rationale: let the number is n , the divisor = d , i will make the two equations - n = xd + 30 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 43 as d is also integer and 43 is a prime number , the d should be 43 to satisfy the above equation . hence answer is ' d '
Answer: D