The Action:
You have to sequence trophies on Shelves 1, 2, and 3, from top to
bottom.
The Rules:
2) Rule 2 seems to be the most helpful, so let's look at it
first. F must be on the shelf immediately above the shelf that L
is on. You have two basic options. In Option 1 you place F on
Shelf 1 and L on Shelf 2. With Option 2 you put F of Shelf 2 and
L on Shelf 3.
1) In Option 1, we can write next to Shelf 2 "no J," and in
Option 2, we can write next to Shelf 3 "no J."
3) No shelf can hold all three bowling trophies.
4) K can't be on Shelf 2 — that's for either option.
1. B
G and H are on Shelf 2, so if you remember that three bowling
trophies can't be on the same shelf, this tells us that we must
work with Option 1. If you put G and H on Shelf 2 in Option 2,
you'd be breaking Rule 3 — you'd have all 3 bowling trophies on
the same shelf. So you'll have F on Shelf 1, and L, G, and H on
Shelf 2. What must be true? Take a look at B, L is on Shelf 2.
Yes, we just went through the deduction whereby you realize you
must use Option 1 in which F is on Shelf 1 and L is on Shelf 2.
So B is the correct answer.
2. D
Right away we realize that you can't use Option 2 here because
Option 2 already has a tennis trophy on Shelf 3, L, so you will
work with Option 1 — F on the first shelf and L on the second
shelf. You know that neither J nor K can appear on Shelf 2 in
Option 1. J and K are tennis trophies, so if the question
specifies that you can't have a tennis trophy on Shelf 3 and you
can't have these two trophies on Shelf 2, then the only place for
them is on Shelf 1. In other words, K and J must be on the same
shelf, so D is correct.
3. C
This question is directing you to Option 2, because you already
know that J isn't allowed on Shelf 2 in Option 1. With Option 2
you know that F must appear on Shelf 2, so C is correct.
4. D
In only one option can Shelf 1 remain empty, Option 2. The rest
of the question says "Which of the following must be false?"
which means "Which of the following arrangements won't work?"
First, let's look at the basic situation. We have Option 2 and we
have F on 2 and L on 3, and Shelf 1 remains empty. That tells us
that we can do something with J and K. We know in Option 2 that J
can't go on Shelf 3 and Shelf 1 is empty, so the only other place
for it is Shelf 2. We know that K can't be on Shelf 2 and Shelf 1
is emphy, so the only home of K is Shelf 3. So we have Shelf 1
empty, Shelf 2 with F and J, and Shelf 3 with L and K. What to do
with G and H? The only thing we can't do is put them on Shelf 2
because that would violate Rule 3. So if we keep them together we
have to put them on Shelf 3. If we split them up, we can put G on
2 and H of Shelf 3, or vice versa.
A — can we put H and F on the same shelf? Sure, we've already
said we can put one of G and H on Shelf 2 and one on Shelf 3. B —
can we put exactly three trophies on Shelf 2? Sure, we just did
with A. We put F, J, and H together on Shelf 2 and that left us
with L, K, and G together on Shelf 3. C — can we put G and H on
the same shelf? Yes, as long as they're on Shelf 3 and not on
Shelf 2. D — can we put exactly two trophies on Shelf 3? We have
L and K on Shelf 3. To have exactly two trophies on Shelf 3, we
would put both G and H somewhere else and we can't put G and H
together on Shelf 2 because that would violate Rule 3. So D is
our answer here — it's the thing we can't do. E — can we put G
and K on the same shelf? Yes, whether G is alone or together with
H, it's possible to do this.
5. A
This is hard because the if-clause doesn't narrow it down to one
of the two options. L and G can be on the same shelf in both
options, which makes your work more complicated. In both options
there's just one empty shelf — in Option 1 it's Shelf 3, and in
Option 2 it's Shelf 1. Let's see if we can make any more
deductions about both options. In Option 1, if we have to leave
Shelf 3 empty, we can figure out what to do with K and J because
they can't be on Shelf 2 and Shelf 3 is empty, so Shelf 1 has F,
K, and J and Shelf 2 has L and G and the only thing left is H, on
either Shelf 1 or Shelf 2. In Option 2 we know that K can't be on
Shelf 2, and Shelf 1 has to be empty, so the only place for K is
Shelf 3. J can't be on Shelf 3 in Option 2, and Shelf 1 is empty,
so J is on Shelf 2. So we end up with F and J on Shelf 2, L, K,
and G on Shelf 3, and Shelf 1 empty, and H is a floater.
For the answer to be correct, it must be true in both options
— you hit pay dirt right away, because A is correct. It says if H
is on Shelf 3, then J is on Shelf 2. The only way to put H on
Shelf 3 is Option 2, where Shelf 3 is open. You can put H on
Shelf 3, and in Option 2, J is on Shelf 2, so A is correct. B
describes K and L as being on the same shelf, but that's true
only in Option 2. C says if H is on Shelf 2, J is on Shelf 3, but
J is never on Shelf 3. D has F and K on the same shelf; that's
true in Option 1 only and not in Option 2. And E has J on Shelf
2. That's Option 2, but it goes on to say that H is on Shelf 1,
and in Option 2, Shelf 1 is empty. So A is correct.
Other PracticeQs: