Question

Which of the following could be the pairs of skaters who skate in each set, from set 1 through set 4?

• A. Set 1: Fiona, Ravi | Set 2: Jill, Toby | Set 3: Gloria, Shigeru | Set 4: Heidi, Vernon
• B. Set 1: Gloria, Shigeru | Set 2: Heidi, Ravi | Set 3: Fiona, Toby | Set 4: Jill, Vernon
• C. Set 1: Heidi, Shigeru | Set 2: Gloria, Ravi | Set 3: Jill, Vernon | Set 4: Fiona, Toby
• D. Set 1: Heidi, Toby | Set 2: Gloria, Shigeru | Set 3: Jill, Ravi | Set 4: Fiona, Vernon
• E. Set 1: Jill, Vernon | Set 2: Heidi, Ravi | Set 3: Gloria, Shigeru | Set 4: Fiona, Toby
• A. Vernon skates in set 2.
• B. Shigeru skates in set 4.
• C. Ravi skates in set 3.
• D. Jill skates in set 4.
• J. Heidi skates in set 3.
• A. Fiona skates with Ravi.
• B. Gloria skates with Ravi.
• C. Gloria skates with Shigeru.
• D. Gloria skates with Vernon.
• O. Jill skates with Vernon.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a "could be true" or "acceptable arrangement" question. We must check each option against the rules until we find one that is valid.
Step 2: Detailed Explanation:


[(A)] (Fiona, Ravi), (Jill, Toby), (Gloria, Shigeru), (Heidi, Vernon).
Violates Rule 3 (Jill cannot skate with Toby).
[(B)] (Gloria, Shigeru), (Heidi, Ravi), (Fiona, Toby), (Jill, Vernon).
Violates Rule 2 (Fiona must be in set 1 or 4, but she is in set 3).
[(C)] (Heidi, Shigeru), (Gloria, Ravi), (Jill, Vernon), (Fiona, Toby).
F in 4 ✓, R before V ✓, J with V ✓, but Rule 4 is violated (Shigeru must be with Fiona or Gloria, not Heidi).
[(D)] (Heidi, Toby), (Gloria, Shigeru), (Jill, Ravi), (Fiona, Vernon).
- Rule 1: Ravi(3) before Vernon(4).
- Rule 2: Fiona in set 4.
- Rule 3: Jill is with Ravi, not Toby.
- Rule 4: Shigeru with Gloria.
All conditions satisfied.
\fbox{% \parbox{\dimexpr\linewidth-2\fboxsep-2\fboxrule}{ Final Answer: Option (D) is the only valid arrangement. }} % Correct Answer Correct Answer: (D) Set 1: Heidi, Toby | Set 2: Gloria, Shigeru | Set 3: Jill, Ravi | Set 4: Fiona, Vernon % Solution Solution:
Step 1: Checking the Rules against Option (D)
The proposed schedule is: - Set 1: Heidi and Toby - Set 2: Gloria and Shigeru - Set 3: Jill and Ravi - Set 4: Fiona and Vernon
Let's check each rule: 1. Ravi skates in an earlier set than Vernon does (R \textless V): Ravi is in set 3, Vernon is in set 4. \(3 \textless 4\), so this rule is satisfied. 2. Fiona skates in either set 1 or set 4: Fiona is in set 4. This rule is satisfied. 3. Jill does not skate with Toby: Jill skates with Ravi in set 3. This rule is satisfied. 4. Shigeru skates with either Fiona or Gloria: Shigeru skates with Gloria in set 2. This rule is satisfied.
Step 2: Conclusion
Since the arrangement in option (D) satisfies all four constraints, it is a possible schedule. Other options can be eliminated as they violate one or more rules (e.g., (A) violates Rule 3, (B) violates Rule 2, (C) violates Rule 4).

Answer 2

Step 1: Apply the Condition
We are given that Gloria and Toby are paired in Set 1.
- Set 1: (G, T)
Step 2: Make Deductions

1. From the condition: Set 1 is $(G, T)$.
2. By Rule 4, $S$ must skate with $F$.
3. By Rule 2, $F$ must be in Set 1 or 4. Set 1 is already taken, so $(S, F)$ must be in Set 4.
4. Remaining men: $R, V$. By Rule 1 ($R < V$), Ravi must be in Set 2 and Vernon in Set 3.
5. Remaining women: $H, J$. They must pair with $R$ and $V$, giving two possible assignments: \[ \text{Set 2: } (H, R), \ (J, V) \quad \text{or} \quad \text{Set 2: } (J, R), \ (H, V) \]
6. Rule 3 (Jill $\neq$ Toby) is already satisfied, since Toby is in Set 1 with Gloria.

Checking the options:
 

• (A) Vernon in Set 2: False. Vernon must be in Set 3.
• (B) Shigeru in Set 4: True. This always holds.
• (C) Ravi in Set 3: False. Ravi must be in Set 2.
• (D) Jill in Set 4: False. Jill must be in Set 2 or 3.
• (E) Heidi in Set 3: Possible, but not guaranteed (depends on assignment).

Final Answer: 
\[ \boxed{\text{(B) Shigeru skates in Set 4. This is the only statement that must be true.}} \]

Answer 3

Step 1: Apply the Condition
We are given two pieces of information: - Set 1 woman is Heidi (H). - Set 2 man is Toby (T). This gives us a partial schedule: Set 1: (H, ?), Set 2: (?, T), Set 3: (?, ?), Set 4: (?, ?).
Step 2: Make Deductions
1. Rule 3 (J \(\neq\) T): Jill does not skate with Toby. Since Toby is the man in set 2, Jill cannot be the woman in set 2. 2. Rule 2 (F in 1 or 4): Fiona must be the woman in set 1 or 4. Heidi is the woman in set 1. Therefore, Fiona must be the woman in set 4. - Set 4 woman: F.
3. Placement of Women: We have placed H (set 1) and F (set 4). We know J is not in set 2. The only remaining woman is Gloria (G). The only remaining women's slots are in set 2 and set 3. Since J is not in set 2, G must be in set 2, and J must be in set 3. - Set 1: (H, ?) - Set 2: (G, T) - Set 3: (J, ?) - Set 4: (F, ?)
4. Rule 4 (S with F or G): Shigeru (S) skates with Fiona or Gloria. We have Gloria paired with Toby in set 2. So, Shigeru must be paired with Fiona in set 4. - Set 4 pair: (F, S)
5. Placement of Men: We have placed T (set 2) and S (set 4). The remaining men are Ravi (R) and Vernon (V). They must be the partners for H (set 1) and J (set 3). 6. Rule 1 (R \textless V): Ravi must skate before Vernon. Therefore, R must be in set 1, and V must be in set 3. - Set 1 pair: (H, R) - Set 3 pair: (J, V)
Step 3: Final Schedule and Evaluation
The complete and only possible schedule is: - Set 1: Heidi and Ravi (H, R) - Set 2: Gloria and Toby (G, T) - Set 3: Jill and Vernon (J, V) - Set 4: Fiona and Shigeru (F, S)
Now we check the options to see which one matches our deduced pairings. - (A) Fiona skates with Ravi. False. Fiona skates with Shigeru. - (B) Gloria skates with Ravi. False. Gloria skates with Toby. - (C) Gloria skates with Shigeru. False. Gloria skates with Toby. - (D) Gloria skates with Vernon. False. Gloria skates with Toby. - (E) Jill skates with Vernon. True. This is the pair in set 3.