The way permissions affect paths is explained in the path_resolution man page: http://linux.die.net/man/2/path_resolution
The only permission on folder A that matters is the search (execute) permission: if you don't have it you can't descend to folder B. Other than that there is no relation between permissions of A and B, for example if A is read-only and B is not, or even if you don't even have read permission to A, you still can create and delete files in B.