Definitely E.
We know:
tulips > maples
some sycamores > maples
maples > some sycamores
all maples > dogwoods
so we know
tulips / [some] sycamores > maples > dogwoods / [some] sycamores
Important: We have no info on the relation of tulips to sycamores or dogwoods to sycamores.
A) Some dogwoods are as old as the youngest tulip trees.
This is impossible. If all tulips are older than maples and all dogwoods are younger than maples, no dogwoods could be as old as tulip trees. Eliminate.
B) Some dogwoods are as old as the youngest sycamores.
This is possible but we are looking for a must be true. The oldest dogwood could be 1 year old and the youngest sycamore 6 years old, and we could still fulfill the terms of the question. Eliminate.
C) Some sycamores are not as old as the oldest dogwoods.
Again, this is possible, but it doesn't need to be true to fulfill the terms of the problem. Eliminate.
D) Some tulip trees are not as old as the oldest sycamore.
Once again, this is possible. Some tulip trees could be younger than the oldest sycamore, we have no info as to the relation between tulips and sycamores. But it is equally possible that all tulip trees are older than the oldest sycamore. Eliminate.
E) Some sycamores are not as old as the youngest tulip trees.
This is the only one that must be true. Since the youngest tulip trees are still older than maple trees, and there are some sycamores that are younger than maple trees, this condition must be true according to the passage.