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?
Answer: C
Let the number be N and the divisor be D. We have \(N = Dk + 24\). Now consider twice the number, 2N. \(2N = 2(Dk + 24) = 2Dk + 48\). When 2N is divided by D, the remainder is the same as the remainder of \(48 \div D\). We are given that this remainder is 11. So, \(48 = Dm + 11\) for some integer m. This means \(D \times m = 37\). Since 37 is a prime number, its only factors are 1 and 37. The divisor D must be greater than the remainder (24), so D must be 37.