Divide and Conquer a problem into a sub-problem to solve it efficiently
The given information tells you absolutely nothing about the runtime of B. 

As an example, let’s say the solution is a vector of N numbers which can be found in O(n^2 log n) but not in O(n^2), and let B be the problem “What was your input”. Solve the problem in O(n^2 log n), pass the solution to B, get it back in O(n), all consistent with the information you have.