Question

Which of the following can be the list of the six people in the order of their offices, from office 1 through office 6?

• A. Q, U, S, T, P, R
• B. R, P, T, S, U, Q
• C. R, S, Q, U, P, T
• D. S, T, Q, P, U, R
• E. T, P, S, R, Q, U
• A. 1
• B. 2
• C. 3
• D. 4
• J. 5
• A. P
• B. R
• C. S
• D. T
• O. U
• A. P is assigned to office 3.
• B. P is assigned to office 4.
• C. S is assigned to office 4.
• D. T is assigned to office 2.
• T. T is assigned to office 3.
• A. 1 or 2
• B. 1 or 6
• C. 2 or 5
• D. 4 or 5
• Y. 4 or 6
• A. P is assigned to office 1.
• B. Q is assigned to office 3.
• C. R is assigned to office 6.
• D. T is assigned to office 5.
• ^. U is assigned to office 4.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
We need to check each proposed arrangement against the four given rules. The correct answer is the one that satisfies all rules simultaneously. Let's list the rules for easy reference: 1. P is next to T (PT or TP block). 2. Q is not next to S. 3. R is in office 1 or 6. 4. S is in a lower office number than U (S ... U).
Step 2: Detailed Explanation:


(A) Q, U, S, T, P, R:

Rule 4 (S ... U): S is in office 3, U is in office 2. This violates the rule. S must be in a lower numbered office than U. VIOLATION.

(B) R, P, T, S, U, Q:

Rule 1 (PT/TP): P and T are in offices 2 and 3, respectively. They are adjacent. Satisfied.
Rule 2 (Q not next to S): S is in office 4, Q is in office 6. They are not adjacent. Satisfied.
Rule 3 (R is 1 or 6): R is in office 1. Satisfied.
Rule 4 (S ... U): S is in office 4, U is in office 5. 4<5. Satisfied.
All rules are satisfied. This is a valid arrangement.

(C) R, S, Q, U, P, T:

Rule 2 (Q not next to S): S is in office 2, Q is in office 3. They are adjacent. VIOLATION.

(D) S, T, Q, P, U, R:

Rule 1 (PT/TP): T is in office 2, P is in office 4. They are not adjacent. VIOLATION.

(E) T, P, S, R, Q, U:

Rule 3 (R is 1 or 6): R is in office 4. VIOLATION.

Step 3: Final Answer:
The only arrangement that satisfies all the rules is (B).

Answer 2

Step 1: We are given that T is assigned to office 6. According to the given rules and the previous analysis, the arrangement of the offices depends on specific constraints that need to be followed step-by-step.

Step 2: Let’s recall the constraints that influence the assignment:

• Rule 1: P is next to T.
• Rule 2: Q cannot be next to S.
• Rule 3: R is assigned either to office 1 or 6.
• Rule 4: S must be assigned to a lower-numbered office than U, and S and U must not be in adjacent offices.

Step 3: Since T is already in office 6, we can start by placing the other people according to the rules:

• By Rule 1, P must be in office 5, since it must be adjacent to T.
• By Rule 3, R must be placed in office 1, as it is the only remaining option for R (since office 6 is already occupied by T).
• Now, we need to place S, Q, and U in offices 2, 3, and 4, ensuring that S is in a lower-numbered office than U.

Step 4: Let’s consider the valid assignments for S, Q, and U:

• If S is placed in office 2, then U must be in office 4 (since S cannot be next to U, and the only remaining valid office for U is 4).
• If S is placed in office 3, U cannot be placed in office 2 or 4 because they would violate the rule that S and U must not be adjacent.

Step 5: Therefore, the only valid option for U is to be placed in office 4. This satisfies all the rules and constraints given in the problem.

Final Answer:
The only valid office for U, given that T is in office 6, is office 4, which corresponds to (D) 4.

Answer 3

Step 1: The initial condition in the problem states that Q is assigned to office 2. Now we need to determine who must be assigned to office 6 given this condition.

Step 2: Let’s recall the rules we are working with:

• Rule 1: P is next to T (P and T must be placed adjacent to each other).
• Rule 2: Q cannot be next to S (Q and S must not be assigned to adjacent offices).
• Rule 3: R must be assigned either to office 1 or 6.
• Rule 4: S must be in a lower-numbered office than U, and S and U cannot be adjacent to each other.

Step 3: Given that Q is assigned to office 2, let’s analyze the remaining offices based on the rules:

• Rule 3: Since Q is in office 2, we know that R can only be assigned to office 1 or 6. The person in office 1 is already assigned, so the only available office for R is 6.
• Rule 1: Since R is now assigned to office 6, P must be assigned to the office next to T. Therefore, T and P must be adjacent, meaning one of them must occupy office 5, and the other office 6. However, as per Rule 3, R is already in office 6, so T cannot be in office 6.

Step 4: Since R is the only person who can be assigned to office 6, the correct answer is (B) R.

Final Answer:
Therefore, the person assigned to office 6 must be R, corresponding to (B).

Answer 4

Step 1: We are given that Q is assigned to office 1. Now, we need to analyze the validity of each option under this condition.

Step 2: Let’s recall the rules that govern the assignment:

• Rule 1: P is next to T (P and T must be assigned to adjacent offices).
• Rule 2: Q cannot be next to S (Q and S must not be assigned to adjacent offices).
• Rule 3: R must be assigned either to office 1 or 6.
• Rule 4: S must be in a lower-numbered office than U, and S and U cannot be adjacent to each other.

Step 3: Now, let’s consider the validity of each option one by one, given that Q is in office 1:

• (A) P is assigned to office 3: This is possible because P can be assigned to office 3, which is adjacent to office 4. Since T is not yet assigned, this placement of P is valid.
• (B) P is assigned to office 4: This is also possible, as P can be placed in office 4, and T can then be placed in office 5 or 3 to satisfy the rule that P and T must be adjacent.
• (C) S is assigned to office 4: This cannot be true. By Rule 2, Q and S cannot be adjacent, but with Q in office 1, S cannot be assigned to office 2 or 3, which means office 4 is the only option left for S. However, according to Rule 4, S must be in a lower-numbered office than U, and since U would have to be placed in office 5 or 6, this creates a conflict. Thus, this assignment violates the rules.
• (D) T is assigned to office 2: This is possible. T can be assigned to office 2, and P can be assigned to office 3, satisfying the adjacency rule.
• (E) T is assigned to office 3: This is possible as well. T can be assigned to office 3, and P can be assigned to office 4, satisfying the adjacency rule.

Step 4: Conclusion: The only option that cannot be true is **(C) S is assigned to office 4**, because it violates the adjacency rule between Q and S, and the rule that S must be in a lower-numbered office than U.

Final Answer:
Therefore, the correct answer is (C) S is assigned to office 4.

Answer 5

Step 1: We are given that U is assigned to office 3. Now, we need to determine where Q must be assigned, given the constraints of the office assignments.

Step 2: Let’s recall the rules that govern the assignment:

• Rule 1: P is next to T (P and T must be assigned to adjacent offices).
• Rule 2: Q cannot be next to S (Q and S must not be assigned to adjacent offices).
• Rule 3: R must be assigned either to office 1 or 6.
• Rule 4: S must be in a lower-numbered office than U, and S and U cannot be adjacent to each other.

Step 3: Now let’s analyze the placement of Q given that U is assigned to office 3:

• Rule 4: S must be in a lower-numbered office than U, so S cannot be in office 3 or any higher-numbered office. Hence, S could be placed in office 1 or 2.
• Rule 2: Q cannot be placed next to S. So, if S is in office 1, Q cannot be placed in office 2 (since office 1 and office 2 are adjacent). If S is in office 2, Q cannot be placed in office 3, which is adjacent to office 2.

Step 4: Let’s consider the possible placements for Q: - If S is in office 1, Q cannot go to office 2, so Q must go to either office 4 or 6. - If S is in office 2, Q cannot go to office 3, so Q must go to either office 4 or 6. Therefore, in both scenarios, the only valid options for Q are office 4 or office 6.

Final Answer:
Therefore, the correct answer is (E) 4 or 6.

Answer 6

Step 1: We are given that S is assigned to office 2. We need to evaluate which of the following options can be true based on this information.

Step 2: Let’s recall the rules that govern the office assignment:

• Rule 1: P is next to T (P and T must be assigned to adjacent offices).
• Rule 2: Q cannot be next to S (Q and S must not be assigned to adjacent offices).
• Rule 3: R must be assigned either to office 1 or office 6.
• Rule 4: S must be in a lower-numbered office than U, and S and U cannot be adjacent to each other.

Step 3: Now, let’s evaluate the options given that S is assigned to office 2:

• (A) P is assigned to office 1: This is possible. Since S is assigned to office 2, T must be assigned to either office 3 or 1 (due to the adjacency rule between P and T). Thus, P can be assigned to office 1. This is a valid possibility.
• (B) Q is assigned to office 3: This is not possible. According to Rule 2, Q cannot be next to S, but office 3 is adjacent to office 2, so Q cannot be placed in office 3. This is **not valid**.
• (C) R is assigned to office 6: This is possible. By Rule 3, R must be placed either in office 1 or office 6. Since S is already in office 2, office 6 is available for R. This is a valid possibility.
• (D) T is assigned to office 5: This is possible. T could be placed in office 5, with P in office 1 and R in office 6. This assignment satisfies the adjacency condition between P and T. So, this option is valid.
• (E) U is assigned to office 4: This is possible. U could be placed in office 4, with P in office 1 and S in office 2. This placement satisfies all the given rules. This is a valid possibility.

Step 4: After considering all options, the only option that **cannot** be true based on the constraints is **(B) Q is assigned to office 3**. All the other options are valid possibilities when S is in office 2.

Final Answer:
Therefore, the correct answer is (C) R is assigned to office 6.