You have a problem P that you must solve. You have worked out two different divide and conquer algorithms that solve it.
Algorithm X requires solving four subproblems of half the size of the input, and takes quadratic time to put the solutions of the subproblems back together to solve the original instance.
Algorithm Y requires solving you have subproblems of half the size, but the solutions can now be put back together in linear time.
What are the asymptotic complexities of the two algorithms, and which is the asymptotically faster algorithm?