An athlete has six trophies to place on an empty three-shelf
display case. The six trophies are bowling trophies F, G, and H
and tennis trophies J, K, and L. The three shelves of the display
case are labeled 1 to 3 from top to bottom. Any of the shelves
can remain empty. The athlete's placement of trophies must
conform to the following conditions:
J and L cannot be on the same shelf.
F must be on the shelf immediately above the shelf that L is
on.
No single shelf can hold all three bowling trophies
K cannot be on Shelf 2.
Questions
1. If G and H are on Shelf 2, which of the following must be
true?
- K is on Shelf 1.
- L is on Shelf 2.
- J is on Shelf 3.
- G and J are on the same shelf.
- F and K are on the same shelf.
2. If no tennis trophies are on Shelf 3, which pair of
trophies must be on the same shelf?
- F and G
- L and H
- L and G
- K and J
- G and H
3. If J is on shelf 2, which of the following must also be on
Shelf 2?
- K
- G
- F
- L
- H
4. If Shelf 1 remains empty, which of the following must be
FALSE?
- H and F are on the same shelf.
- There are exactly three trophies on Shelf 2.
- G and H are on the same shelf.
- There are exactly two trophies on Shelf 3.
- G and K are on the same shelf.
5. If L and G are on the same shelf, and if one of the shelves
remains empty, which of the following must be true?
- If H is on Shelf 3, then J is on Shelf 2.
- K and L are on the same shelf.
- If H is on Shelf 2, then J is on Shelf 3.
- F and K are on the same shelf.
- If J is on Shelf 2, then H is on Shelf 1.