Question

Which of the following is an order in which the six magazines can be arranged, from position 1 through position 6?

• A. M, O, P, S, V, T
• B. P, O, S, M, V, T
• C. P, V, T, O, M, S
• D. P, V, T, S, O, M
• E. T, P, V, M, O, S
• A. M occupies position 4.
• B. O occupies position 2.
• C. S occupies position 5.
• D. T occupies position 6.
• J. V occupies position 2.
• A. 1
• B. 2
• C. 4
• D. 5
• O. 6
• A. M occupies position 4 and P occupies position 5.
• B. P occupies position 4 and V occupies position 5.
• C. S occupies position 2 and P occupies position 3.
• D. P occupies position 2.
• T. S occupies position 5.
• A. M
• B. O
• C. P
• D. S
• Y. V
• A. M occupies position 4.
• B. O occupies position 2.
• C. P occupies position 1.
• D. S occupies position 6.
• ^. T occupies position 6.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question asks to identify a valid arrangement of the magazines that satisfies all the given rules. We can test each option against the rules one by one.
Step 2: Detailed Explanation:
Let's check each option:
(A) M, O, P, S, V, T \begin{itemize} \item Rule 1: Position 1 must be P or T. Here it is M. Fails. \end{itemize} (B) P, O, S, M, V, T \begin{itemize} \item Rule 1: P is in position 1. (Ok) \item Rule 2: T is in position 6. (Ok) \item Rule 3: M and O must be consecutive. Here, O is in position 2 and M is in position 4. They are not consecutive. Fails. \end{itemize} (C) P, V, T, O, M, S \begin{itemize} \item Rule 1: P is in position 1. (Ok) \item Rule 2: S is in position 6. (Ok) \item Rule 3: M and O are consecutive ([OM] block in positions 4 and 5). (Ok) \item Rule 4: V and T are consecutive ([VT] block in positions 2 and 3). (Ok) \item All rules are satisfied. This is a valid arrangement. \end{itemize} (D) P, V, T, S, O, M \begin{itemize} \item Rule 1: P is in position 1. (Ok) \item Rule 2: M is in position 6. It must be S or T. Fails. \end{itemize} (E) T, P, V, M, O, S \begin{itemize} \item Rule 1: T is in position 1. (Ok) \item Rule 4: V and T must be consecutive. Here, T is in position 1 and V is in position 3. They are not consecutive. Fails. \end{itemize} Step 3: Final Answer:
Only option (C) satisfies all the rules of the setup. Therefore, it is a possible arrangement.

Answer 2

Step 1: Understanding the Concept:
This question presents a new condition ("If P occupies position 3...") and asks for a conclusion that must logically follow. We need to use this new condition in conjunction with the original rules to determine the fixed position of other magazines.
Step 2: Detailed Explanation:
Let's build the arrangement based on the new condition.
\begin{enumerate} \item Condition: P is in position 3. (\_ \_ P \_ \_ \_) \item Apply Rule 1 (P/T in 1): Since P is not in position 1, T must be in position 1. (T \_ P \_ \_ \_) \item Apply Rule 2 (S/T in 6): Since T is in position 1, it cannot be in position 6. Therefore, S must be in position 6. (T \_ P \_ \_ S) \item Apply Rule 4 ([VT]/[TV] block): Since T is in position 1, V must be in position 2 to form the [TV] block. (T V P \_ \_ S) \item Apply Rule 3 ([MO]/[OM] block): The remaining magazines are M and O. The remaining positions are 4 and 5. Since M and O must be in consecutive positions, they must occupy positions 4 and 5. The order can be either M-O or O-M. \end{enumerate} The complete arrangement is: T(1), V(2), P(3), M/O(4), O/M(5), S(6).
Step 3: Evaluate the Options:
Now we check which of the given options \textit{must} be true based on this deduction.
(A) M occupies position 4. (This could be true, but O could also be in position 4). (B) O occupies position 2. (This is false; V must be in position 2). (C) S occupies position 5. (This is false; S must be in position 6). (D) T occupies position 6. (This is false; T must be in position 1). (E) V occupies position 2. (This is a certain deduction from our steps above. It must be true).
Step 4: Final Answer:
Given that P is in position 3, it is a logical necessity that V must be in position 2. Therefore, option (E) is the correct answer.

Answer 3

Step 1: Understanding the Concept:
This question introduces a new condition that combines with the original rules to limit the possibilities. We need to find the possible positions for T under this new constraint.
Step 2: Key Deductions from the New Condition:
\begin{enumerate} \item Original Rule 3: M and O are consecutive ([MO]/[OM]). \item Original Rule 4: V and T are consecutive ([VT]/[TV]). \item New Condition: O and T are consecutive ([OT]/[TO]). \end{enumerate} Combining these three block rules, we can deduce a larger structure. O must be next to M and T. T must be next to O and V. This forces a 4-magazine chain: M-O-T-V or its reverse V-T-O-M. In both cases, O and T are internal to the block.
Step 3: Placing the 4-Magazine Block:
This [MOTV/VTOM] block must be placed in the 6 available positions. The two remaining magazines are P and S. Let's test the possible placements of the 4-magazine block. \begin{itemize} \item Placement 1: Block in positions 1-4. The magazine in position 1 would be M or V. This violates Rule 1, which requires P or T in position 1. So this placement is not allowed. \item Placement 2: Block in positions 3-6. The magazine in position 6 would be V or M. This violates Rule 2, which requires S or T in position 6. So this placement is not allowed. \item Placement 3: Block in positions 2-5. This is the only remaining possibility. Positions 1 and 6 are left open for P and S. \end{itemize} Step 4: Determining the Final Arrangement and T's Position:
With the 4-magazine block in positions 2-5, we must satisfy Rules 1 and 2 for the remaining slots. \begin{itemize} \item For position 1, Rule 1 requires P or T. Since T is inside the block (in position 3 or 4), P must be in position 1. \item For position 6, Rule 2 requires S or T. Since T is inside the block, S must be in position 6. \end{itemize} The only valid arrangement structure is: P, [4-magazine block], S.
Now let's see where T can be: \begin{itemize} \item If the block is M-O-T-V in positions 2-5, then T is in position 4. (Arrangement: P, M, O, T, V, S) \item If the block is V-T-O-M in positions 2-5, then T is in position 3. (Arrangement: P, V, T, O, M, S) \end{itemize} So, under this condition, T can be in position 3 or position 4.
Step 5: Final Answer:
Looking at the options, only position 4 is listed. Since we have proven that T can be in position 4, this is the correct answer.

Answer 4

Step 1: Understanding the Concept:
This is a "can be true" question, which asks us to find a possible scenario that is consistent with all the rules. The rules are: (1) P/T in 1; (2) S/T in 6; (3) M and O are a block; (4) V and T are a block. We test each option to see if a valid arrangement can be constructed.
Step 2: Detailed Explanation:
Let's test each option:
(A) M occupies position 4, P occupies position 5. `(_ _ _ M P _)` \begin{itemize} \item From Rule 3 ([MO] block), if M is in 4, O must be in 3. The arrangement becomes `(_ _ O M P _)`. \item From Rule 1 (P/T in 1), since P is in 5, T must be in 1. The arrangement becomes `(T _ O M P _)`. \item From Rule 4 ([VT] block), since T is in 1, V must be in 2. The arrangement becomes `(T V O M P _)`. \item The only magazine left is S, and the only position left is 6. The final arrangement is T, V, O, M, P, S. \item This arrangement is valid: T is in 1 (Rule 1 ok), S is in 6 (Rule 2 ok), OM are in 3-4 (Rule 3 ok), TV are in 1-2 (Rule 4 ok). \item Since a valid arrangement can be constructed, this option \textit{can be true}. \end{itemize} (B) P occupies 4, V occupies 5. `(_ _ _ P V _)` \begin{itemize} \item From Rule 4 ([VT] block), if V is in 5, T must be in 4 or 6. Position 4 is taken by P, so T must be in 6. `(_ _ _ P V T)`. \item From Rule 1 (P/T in 1), since T is in 6, P must be in 1. This contradicts the condition that P is in 4. Impossible. \end{itemize} (C) S occupies 2, P occupies 3. `(_ S P _ _ _)` \begin{itemize} \item From Rule 1 (P/T in 1), since P is in 3, T must be in 1. `(T S P _ _ _)`. \item From Rule 2 (S/T in 6), since T is in 1, S must be in 6. This contradicts the condition that S is in 2. Impossible. \end{itemize} (D) P occupies position 2. `(_ P _ _ _ _)` \begin{itemize} \item From Rule 1 (P/T in 1), since P is in 2, T must be in 1. `(T P _ _ _ _)`. \item From Rule 4 ([VT] block), since T is in 1, V must be in 2. This contradicts the condition that P is in 2. Impossible. \end{itemize} (E) S occupies position 5. `(_ _ _ _ S _)` \begin{itemize} \item From Rule 2 (S/T in 6), since S is not in 6, T must be in 6. `(_ _ _ _ S T)`. \item From Rule 4 ([VT] block), since T is in 6, V must be in 5. This contradicts the condition that S is in 5. Impossible. \end{itemize} Step 3: Final Answer:
Only the conditions in option (A) allow for the construction of a valid arrangement that does not violate any rules. Therefore, (A) is the correct answer.

Answer 5

Step 1: Understanding the Concept:
This is a conditional deduction question. We are given a new piece of information (V is in 4) and must determine a specific relationship that results. The question's wording is complex: we need to find T's position, and then find which magazine is in the position numbered one higher than T.
Step 2: Detailed Explanation:
Let's build the arrangement with the new condition: V is in position 4. `(_ _ _ V _ _)` \begin{enumerate} \item Apply Rule 4 ([VT] block): Since V is in 4, T must be adjacent, either in position 3 or 5. \item Case 1: T is in 3. The arrangement is `(_ _ T V _ _)`. \begin{itemize} \item Apply Rule 1 (P/T in 1): T is not in 1, so P must be in 1. `(P _ T V _ _)`. \item Apply Rule 2 (S/T in 6): T is not in 6, so S must be in 6. `(P _ T V _ S)`. \item The remaining magazines, M and O, must fill positions 2 and 5. Rule 3 requires them to be in a consecutive block, but positions 2 and 5 are not consecutive. \item Therefore, Case 1 is impossible. \end{itemize} \item Case 2: T is in 5. The arrangement is `(_ _ _ V T _)`. \begin{itemize} \item Apply Rule 2 (S/T in 6): T is not in 6, so S must be in 6. `(_ _ _ V T S)`. \item Apply Rule 1 (P/T in 1): T is not in 1, so P must be in 1. `(P _ _ V T S)`. \item The remaining magazines, M and O, must fill the consecutive positions 2 and 3. This is allowed by Rule 3. \item The final arrangement must be: P, (M/O), (O/M), V, T, S. \end{itemize} \item This is the only possible outcome. So, if V is in 4, then T must be in 5 and S must be in 6. \end{enumerate} Step 3: Answering the Question:
The question asks: T's position (which is 5) must be "exactly one lower than the position occupied by" which magazine?
This means we are looking for the magazine in position \(5 + 1 = 6\).
From our deduction, the magazine in position 6 is S.
Step 4: Final Answer:
If V is in 4, T must be in 5, which is one position lower than position 6, occupied by S. Therefore, (D) is the correct answer.

Answer 6

Step 1: Understanding the Concept:
This is another conditional deduction question. The new condition connects two existing rules, which should lead to a strong, certain conclusion. We need to find what "must be true" under this new condition.
Step 2: Detailed Explanation:
\begin{enumerate} \item Analyze the Rules and Condition: \begin{itemize} \item Original Rule 4: V and T form a consecutive block ([VT] or [TV]). \item New Condition: S and V form a consecutive block ([SV] or [VS]). \end{itemize} \item Combine the rules: Since V must be next to both T and S, these three magazines must form a 3-magazine super-block: S-V-T or T-V-S. \item Test the position of T: The key to this game is the placement of T, which affects both end positions (1 and 6). \item Can T be in position 1? \begin{itemize} \item If T is in position 1, then from Rule 4, V must be in position 2. \item The combined block must be T-V-S, so S would have to be in position 3. The arrangement starts `T V S _ _ _`. \item However, Rule 2 states that if T is not in position 6, S must be. Since T is in 1, S must be in 6. \item This creates a contradiction: S cannot be in both position 3 and position 6. \item Therefore, T cannot be in position 1. \end{itemize} \item Deduce the occupant of position 1: \begin{itemize} \item According to Rule 1, position 1 must be either P or T. \item We have just proven that T cannot be in position 1. \item Therefore, P must be in position 1. \end{itemize} \end{enumerate} Step 3: Final Answer:
The new condition, when combined with the original rules, makes it impossible for T to be in position 1. Since position 1 must be either P or T, P is forced into position 1. This is a necessary conclusion. Therefore, (C) must be true.
For completeness, a possible arrangement is P, M, O, S, V, T. This satisfies P=1, T=6, [MO] in 2-3, [SV] in 4-5, and [VT] in 5-6.