Self-study
In the Centerville Botanical Gardens, all tulip trees are older than any maples. █ █████████ ███ ███ ████ ██ ███ ██████████ █████████ ███ █████ ████ ███ ██ ███ ███████ ███ ███ ██████████ ██████ ███ █████ ████ ███ ██ ███ █████████
Stimulus Breakdown
The stimulus gives us a set of rules or relationships about the ages of different types of trees in the Centerville Botanical Gardens. First, we are told that "all tulip trees are older than any maples." Then, we're told that most (but not all) sycamore trees are older than any of the maples. Finally, we're told that all the maples in the gardens are older than all the dogwoods.
Notice that there's no conclusion in this stimulus. We're just given these relationships and will have to make inferences based on them.
Potential Inferences
You might be tempted to try to diagram this stimulus with conditional logic, especially since there are plenty of conditional indicators ("all," "any," etc.) here. But if you try mapping this, you'll run into complications: do you say "tulip → older than maple," or "maple → younger than tulip"? Notice that the answer choices aren't limited to "older than" relationships — they ask about some things being as old as, or not as old as, some other things.
So trying to draw this all out with conditional logic would probably be more confusing than helpful. Sometimes it's more useful to draw out inferences just by thinking in English. Let's do this sentence by sentence.
The first sentence tells us that all tulip trees are older than all maples in the garden. This means that no tulip trees and maples are the same age: all the maples are younger than all the tulip trees.
The second sentence tells us that most, but not all, of the sycamore trees are older than any of the maples. So we know that most sycamore trees, like all tulip trees, are older than all the maples, though we don't know anything about how these sycamores and the tulip trees compare to each other in age. We also know that some sycamore trees must be as old as, or younger than, at least some maples — which lets us infer that those sycamore trees must be younger than any of the tulip trees, since all maples are younger than all tulip trees.
The third sentence says that all the maples are older than any of the dogwoods. This lets us infer that all the tulip trees and most of the sycamore trees are also older than all dogwoods, since they are older than all maples. As for the "some" sycamore trees that are the same age or younger than some maples, we don't know enough to say how they compare in age to the dogwoods.
So we've drawn two inferences from this stimulus: some sycamores are younger than all tulip trees, and all tulip trees and most sycamores are older than all dogwoods. We can keep those inferences in mind as we go through the answer choices.
12.
If the statements above are █████ █████ ███ ██ ███ █████████ ████ ████ ██ ████ ██ █████ ██ ███ ███████████ █████████ ████████
a
Some dogwoods are ██ ███ ██ ███ ████████ █████ ██████
This must be false. Remember what we know about dogwoods: all dogwoods are younger than all maples. Then remember what we know about maples: all maples are younger than all tulip trees. This tells us for sure that all dogwoods are younger than all tulip trees, which means this answer choice must be false.
b
Some dogwoods are ██ ███ ██ ███ ████████ ██████████
This could be true, but doesn't have to be. Remember that most (but not all) sycamore trees are older than all dogwood trees, since most sycamore trees are older than all maple trees, and all maples are older than all dogwoods. The "some" sycamores that are not older than some maples could in theory be younger than those maple trees, and perhaps the same age as some dogwoods. But those "some" sycamores could also just be the same age as some maples, and still older than the dogwoods.
The stimulus doesn't give us any grounds to infer a comparison between the ages of these "some" sycamores and any dogwood trees, so we can't say this answer choice must be true.
c
Some sycamores are ███ ██ ███ ██ ███ ██████ █████████
This could be true, but isn't required to be true. Again, we know that most (but not all) sycamore trees are older than all dogwood trees, since most sycamore trees are older than all maple trees, and all maples are older than all dogwoods. We also know that there are "some" sycamores that are not older than some maples, which means they are the same age or younger than some maples. In theory, these sycamores could be young enough to be younger than the oldest dogwoods — but the stimulus doesn't give us any reason to conclude that must be true. These "some" sycamores could just be the same age as some maples, and therefore older than all the dogwoods. Or even if these sycamores are younger than all the maples, the dogwoods could be even younger (e.g., the dogwoods could all be new seedlings).
So since the stimulus doesn't tell us anything about the relative ages of these "some" sycamores and any dogwood trees, we can't say this answer choice must be true.
d
Some tulip trees ███ ███ ██ ███ ██ ███ ██████ ██████████
This could be true, but doesn't have to be. Remember that we only know how all tulip trees and most sycamore trees compare to maples — they are older than maples. We don't know how the tulip trees compare to the sycamores, and vice-versa. So while some among this subgroup of "most" sycamores could in theory be older than some tulip trees, nothing requires us to draw that conclusion.
e
Some sycamores are ███ ██ ███ ██ ███ ████████ █████ ██████
This must be true. Remember that the stimulus specifies that "not all" sycamores are older than all maples. This means some sycamores are not older — i.e., they are the same age or younger — than some maples. Remember also that all tulip trees are older than all maples. So if some sycamores are not older than some maples, some sycamores must not be as old as any tulip trees, including the youngest tulip trees.