A number when divided by a divisor left reminder 23. When twice of the number was divided by the same divisor, reminder was 11. what is the divisor?

Let's denote the number as 'a' and the divisor as 'd'.

From the problem, we know that:

1. a = kd + 23 (where k is some integer)
2. 2a = ld + 11 (where l is another integer)

We can substitute the first equation into the second to get:

2(kd + 23) = ld + 11 2kd + 46 = ld + 11 2kd - ld = 11 - 46 (d(2k - l)) = -35

Since both k and l are integers, (2k - l) is also an integer. Let's denote it as m. So, we have:

d * m = -35

The only pairs of integers (d, m) that satisfy this equation are (-1, 35), (-5, 7), (-7, 5), (-35, 1), (1, -35), (5, -7), (7, -5), and (35, -1).

However, since a divisor cannot be negative, the only possible values for the divisor 'd' are 1, 5, 7, and 35.

Without additional information, we cannot determine which of these four values is the correct divisor.