Comprehension
A scientist will perform six experiments - P, R, T, X, Y, and z - during a three-month period, August through October. In each of the three months, exactly two of the experiments will be performed. Each experiment will start on the first day of a month and be completed during that month, The order in which the experiments are performed will also be governed by the following restrictions:
R must be performed in August or in September.
T must be performed in September or in October.
T cannot be performed in the same month in which X is performed.
X must be performed in an earlier month than the month in which Z is performed.
Question: 1
Which of the following can be the schedule for the six experiments?
Which of the following can be the schedule for the six experiments?
Show Hint
When checking options, go through the rules systematically. Start with the most concrete rules (like R must be in Aug/Sep) to eliminate choices quickly.
Updated On: Oct 1, 2025
- Aug: P, R | Sep: T, X | Oct: Y, Z
- Aug: R, T | Sep: X, Y | Oct: P, Z
- Aug: R, X | Sep: T, Y | Oct: P, Z
- Aug: X, Y | Sep: P, Z | Oct: R, T
- Aug: Y, Z | Sep: R, T | Oct: P, X
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
This is an "acceptable schedule" question. We need to check each option against the rules until we find one that is valid.
Step 2: Detailed Explanation:
- (A) Aug: P, R | Sep: T, X | Oct: Y, Z: This violates Rule 3, as T and X are in the same month (September).
- (B) Aug: R, T | Sep: X, Y | Oct: P, Z: This violates Rule 2, as T is in August, but it must be in September or October.
- (C) Aug: R, X | Sep: T, Y | Oct: P, Z: - Rule 1 (R in Aug/Sep): Met, R is in August. - Rule 2 (T in Sep/Oct): Met, T is in September. - Rule 3 (T \(\neq\) X): Met, T is in September, X is in August. - Rule 4 (X \textless Z): Met, X is in August, Z is in October. Since all rules are satisfied, this is a valid schedule.
- (D) Aug: X, Y | Sep: P, Z | Oct: R, T: This violates Rule 1, as R is in October, but it must be in August or September.
- (E) Aug: Y, Z | Sep: R, T | Oct: P, X: This violates Rule 4, as X is in October, which is later than Z in August.
Step 3: Final Answer:
The only schedule that satisfies all the rules is (C).
This is an "acceptable schedule" question. We need to check each option against the rules until we find one that is valid.
Step 2: Detailed Explanation:
- (A) Aug: P, R | Sep: T, X | Oct: Y, Z: This violates Rule 3, as T and X are in the same month (September).
- (B) Aug: R, T | Sep: X, Y | Oct: P, Z: This violates Rule 2, as T is in August, but it must be in September or October.
- (C) Aug: R, X | Sep: T, Y | Oct: P, Z: - Rule 1 (R in Aug/Sep): Met, R is in August. - Rule 2 (T in Sep/Oct): Met, T is in September. - Rule 3 (T \(\neq\) X): Met, T is in September, X is in August. - Rule 4 (X \textless Z): Met, X is in August, Z is in October. Since all rules are satisfied, this is a valid schedule.
- (D) Aug: X, Y | Sep: P, Z | Oct: R, T: This violates Rule 1, as R is in October, but it must be in August or September.
- (E) Aug: Y, Z | Sep: R, T | Oct: P, X: This violates Rule 4, as X is in October, which is later than Z in August.
Step 3: Final Answer:
The only schedule that satisfies all the rules is (C).
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Question: 2
Any of the following experiments can be performed in August EXCEPT
Any of the following experiments can be performed in August EXCEPT
Show Hint
"Cannot be true" or "EXCEPT" questions are often solved by looking at the most restrictive rules, especially those involving relative ordering (like "before" or "after").
Updated On: Oct 1, 2025
- P
- R
- X
- Y
- Z
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The Correct Option is
Solution and Explanation
Step 1: Understanding the Concept:
This question asks which experiment can NEVER be in August. We need to check the rules to see which experiment is forbidden from being in the first month.
Step 2: Detailed Explanation:
The most relevant rule is Rule 4: "X must be performed in an earlier month than the month in which Z is performed."
- This means X must come before Z in the sequence of months. - If Z were in August (the earliest month), there would be no earlier month available for X to be performed in. - Therefore, Z cannot be in August.
To confirm the others are possible in August, we can refer to the valid schedule from question 1: - Aug: R, X | Sep: T, Y | Oct: P, Z - This shows R and X can be in August. We can also easily construct a schedule with P and Y in August. For example: - Aug: P, Y | Sep: R, X | Oct: T, Z. This is valid. So, P, R, X, and Y can all be in August.
Step 3: Final Answer:
Z is the only experiment that cannot be performed in August due to the rule that X must precede it.
This question asks which experiment can NEVER be in August. We need to check the rules to see which experiment is forbidden from being in the first month.
Step 2: Detailed Explanation:
The most relevant rule is Rule 4: "X must be performed in an earlier month than the month in which Z is performed."
- This means X must come before Z in the sequence of months. - If Z were in August (the earliest month), there would be no earlier month available for X to be performed in. - Therefore, Z cannot be in August.
To confirm the others are possible in August, we can refer to the valid schedule from question 1: - Aug: R, X | Sep: T, Y | Oct: P, Z - This shows R and X can be in August. We can also easily construct a schedule with P and Y in August. For example: - Aug: P, Y | Sep: R, X | Oct: T, Z. This is valid. So, P, R, X, and Y can all be in August.
Step 3: Final Answer:
Z is the only experiment that cannot be performed in August due to the rule that X must precede it.
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Question: 3
If T is performed in September, which of the following must be true?
If T is performed in September, which of the following must be true?
Show Hint
For "must be true" questions, try to find a counterexample for each option. If you can build a single valid schedule where the statement is false, then it doesn't "must be true." The correct answer will be the one for which no counterexample is possible.
Updated On: Oct 1, 2025
- P is performed in August.
- R is performed in September.
- X is performed in August.
- Y is performed in September.
- Z is performed in October.
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
This is a conditional question. We add the new information (T is in September) to our rules and deduce what must necessarily follow.
Step 2: Detailed Explanation:
1. New Condition: T is in September.
2. Rule 3 (T \(\neq\) X): Since T is in September, X cannot be in September.
3. Rule 4 (X \textless Z): X must be performed in an earlier month than Z.
4. Combining these, X cannot be in September. If X were in October, there would be no later month for Z. Therefore, X must be in August.
5. Let's check the other options to see if they are necessarily true. - If X is in August and T is in September, then Z must be in October to satisfy X \textless Z. So (E) is also true. Let's re-read the question. - Ah, a subtlety. X must be in an earlier month. So if X is in August, Z can be in September or October. If X is in September, Z must be in October. - Let's re-do the deduction. 1. T is in September. 2. By Rule 3, X is not in September. 3. X cannot be in October, because then there would be no later month for Z (Rule 4). 4. Therefore, X must be in August. This makes option (C) a necessary truth.
6. Now let's re-evaluate (E) based on this. If X is in August, Z can be in September or October. If Z is in September, the September experiments would be T and Z. This is a possible scenario (e.g., Aug: R, X | Sep: T, Z | Oct: P, Y). Since Z does not HAVE to be in October, (E) is not a "must be true".
7. Let's check the other options. - (A) P can be in October. (See the valid scenario just constructed). - (B) R can be in August. (See the valid scenario). - (D) Y can be in August or October. (See the valid scenario).
Step 3: Final Answer:
Given that T is in September, X cannot be in September. To satisfy the condition that X is before Z, X must be in August.
This is a conditional question. We add the new information (T is in September) to our rules and deduce what must necessarily follow.
Step 2: Detailed Explanation:
1. New Condition: T is in September.
2. Rule 3 (T \(\neq\) X): Since T is in September, X cannot be in September.
3. Rule 4 (X \textless Z): X must be performed in an earlier month than Z.
4. Combining these, X cannot be in September. If X were in October, there would be no later month for Z. Therefore, X must be in August.
5. Let's check the other options to see if they are necessarily true. - If X is in August and T is in September, then Z must be in October to satisfy X \textless Z. So (E) is also true. Let's re-read the question. - Ah, a subtlety. X must be in an earlier month. So if X is in August, Z can be in September or October. If X is in September, Z must be in October. - Let's re-do the deduction. 1. T is in September. 2. By Rule 3, X is not in September. 3. X cannot be in October, because then there would be no later month for Z (Rule 4). 4. Therefore, X must be in August. This makes option (C) a necessary truth.
6. Now let's re-evaluate (E) based on this. If X is in August, Z can be in September or October. If Z is in September, the September experiments would be T and Z. This is a possible scenario (e.g., Aug: R, X | Sep: T, Z | Oct: P, Y). Since Z does not HAVE to be in October, (E) is not a "must be true".
7. Let's check the other options. - (A) P can be in October. (See the valid scenario just constructed). - (B) R can be in August. (See the valid scenario). - (D) Y can be in August or October. (See the valid scenario).
Step 3: Final Answer:
Given that T is in September, X cannot be in September. To satisfy the condition that X is before Z, X must be in August.
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Question: 4
If R is performed in the same month as Z, which of the following can be the pair of experiments performed in October?
If R is performed in the same month as Z, which of the following can be the pair of experiments performed in October?
Show Hint
When a new condition is added, first make all possible deductions from that condition combined with the original rules. This will often fix several elements in place, making the rest of the question much simpler.
Updated On: Oct 1, 2025
- P and X
- P and Y
- R and Z
- T and Y
- X and Y
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
This is a conditional question. We add the condition that R and Z are in the same month and then see what possible pair can occupy the October slots.
Step 2: Detailed Explanation:
1. New Condition: R and Z are in the same month.
2. Rule 1 (R in Aug/Sep): R must be in August or September. Therefore, the RZ pair must be in August or September.
3. Rule 4 (X \textless Z): X must be in an earlier month than Z. - If the RZ pair is in September, X must be in August. - If the RZ pair is in August, this violates Rule 4, as there is no earlier month for X. - Therefore, the RZ pair must be in September, and X must be in August.
4. Summary of fixed experiments: - August: X and one other experiment. - September: R and Z. - October: Two remaining experiments.
5. Rule 2 (T in Sep/Oct): T must be in September or October. September is full with R and Z, so T must be in October.
6. Conclusion about October: One of the experiments in October must be T. The other experiment will be one of the remaining "floater" experiments (P or Y). 7. Checking the options: - (A) P and X: X must be in August. - (B) P and Y: T must be in October. - (C) R and Z: This pair is in September. - (D) T and Y: This is a possible pairing for October. - (E) X and Y: X must be in August.
Step 3: Final Answer:
Based on the deductions, the pair of experiments in October must include T. Option (D), T and Y, is a possible valid pair. A full valid schedule could be: Aug: X, P | Sep: R, Z | Oct: T, Y.
This is a conditional question. We add the condition that R and Z are in the same month and then see what possible pair can occupy the October slots.
Step 2: Detailed Explanation:
1. New Condition: R and Z are in the same month.
2. Rule 1 (R in Aug/Sep): R must be in August or September. Therefore, the RZ pair must be in August or September.
3. Rule 4 (X \textless Z): X must be in an earlier month than Z. - If the RZ pair is in September, X must be in August. - If the RZ pair is in August, this violates Rule 4, as there is no earlier month for X. - Therefore, the RZ pair must be in September, and X must be in August.
4. Summary of fixed experiments: - August: X and one other experiment. - September: R and Z. - October: Two remaining experiments.
5. Rule 2 (T in Sep/Oct): T must be in September or October. September is full with R and Z, so T must be in October.
6. Conclusion about October: One of the experiments in October must be T. The other experiment will be one of the remaining "floater" experiments (P or Y). 7. Checking the options: - (A) P and X: X must be in August. - (B) P and Y: T must be in October. - (C) R and Z: This pair is in September. - (D) T and Y: This is a possible pairing for October. - (E) X and Y: X must be in August.
Step 3: Final Answer:
Based on the deductions, the pair of experiments in October must include T. Option (D), T and Y, is a possible valid pair. A full valid schedule could be: Aug: X, P | Sep: R, Z | Oct: T, Y.
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Question: 5
If T is performed in the month before Z is performed, which of the following is a pair of experiments that can be performed in the same month as each other?
If T is performed in the month before Z is performed, which of the following is a pair of experiments that can be performed in the same month as each other?
Show Hint
For "could be true" questions, your goal is to construct one valid scenario that matches the option. Start with your main deductions, then try to place the pair from the option and see if you can complete the schedule without violating any rules.
Updated On: Oct 1, 2025
- P and R
- P and Y
- R and Y
- R and Z
- X and Y
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The Correct Option is
Solution and Explanation
Step 1: Understanding the Concept:
This is a conditional question. We add the new information "T is performed in the month before Z" and then determine which pair of experiments could possibly be scheduled together. This is a "could be true" question.
Initial Rules Recap: 1. R \(\in\) \{Aug, Sep\} 2. T \(\in\) \{Sep, Oct\} 3. T \(\neq\) X (in the same month) 4. X \textless Z (X is in an earlier month than Z)
Step 2: Applying the New Condition and Deducing the Schedule:
1. New Condition: T is in the month before Z (T \textless Z).
2. Deduction 1: From Rule 2, T is in Sep or Oct. If T were in Oct, there would be no later month for Z. Therefore, T must be in September, and Z must be in October.
3. Deduction 2: From Rule 4 (X \textless Z) and our finding that Z is in Oct, X can be in Aug or Sep. However, Rule 3 states T and X cannot be in the same month. Since T is in Sep, X cannot be in Sep. Therefore, X must be in August.
4. Summary of fixed experiments: The schedule must have X in August, T in September, and Z in October. This gives us the following frame: - August: {X, \_} - September: {T, \_} - October: {Z, \_}
5. Placing remaining experiments: The remaining experiments are P, R, and Y. They must fill the three empty slots. Rule 1 states R must be in Aug or Sep. - Scenario A: R is in August. The August pair is {X, R}. The remaining P and Y fill the slots in Sep and Oct. A possible valid schedule is Aug:{X,R}, Sep:{T,P}, Oct:{Z,Y}. - Scenario B: R is in September. The September pair is {T, R}. The remaining P and Y fill the slots in Aug and Oct. A possible valid schedule is Aug:{X,P}, Sep:{T,R}, Oct:{Z,Y}.
Step 3: Evaluating the Options:
We are looking for a pair that can be performed together. Let's try to build a valid schedule for one of the options. - (A) P and R: In both scenarios above, P and R are in different months. - (B) P and Y: In both scenarios above, P and Y are in different months. - (C) R and Y: In both scenarios above, R and Y are in different months. - (D) R and Z: Z is in October, R must be in August or September. They can't be together. - (E) X and Y: Let's see if this is possible. X must be in August. Let's try to place Y in August as well. - August: {X, Y} - We already deduced T is in Sep and Z is in Oct. - September: {T, \_} - October: {Z, \_} - The remaining experiments are P and R. From Rule 1, R must be in Aug or Sep. August is full, so R must be in September. The September pair becomes {T, R}. - The last experiment, P, must go in the last available slot in October. The October pair becomes {Z, P}. - The full schedule is: Aug:{X,Y}, Sep:{T,R}, Oct:{Z,P}. Let's check all rules. R is in Sep (ok). T is in Sep (ok). T is not with X (ok). X is before Z (ok). - This is a valid schedule. Therefore, X and Y can be performed together.
This is a conditional question. We add the new information "T is performed in the month before Z" and then determine which pair of experiments could possibly be scheduled together. This is a "could be true" question.
Initial Rules Recap: 1. R \(\in\) \{Aug, Sep\} 2. T \(\in\) \{Sep, Oct\} 3. T \(\neq\) X (in the same month) 4. X \textless Z (X is in an earlier month than Z)
Step 2: Applying the New Condition and Deducing the Schedule:
1. New Condition: T is in the month before Z (T \textless Z).
2. Deduction 1: From Rule 2, T is in Sep or Oct. If T were in Oct, there would be no later month for Z. Therefore, T must be in September, and Z must be in October.
3. Deduction 2: From Rule 4 (X \textless Z) and our finding that Z is in Oct, X can be in Aug or Sep. However, Rule 3 states T and X cannot be in the same month. Since T is in Sep, X cannot be in Sep. Therefore, X must be in August.
4. Summary of fixed experiments: The schedule must have X in August, T in September, and Z in October. This gives us the following frame: - August: {X, \_} - September: {T, \_} - October: {Z, \_}
5. Placing remaining experiments: The remaining experiments are P, R, and Y. They must fill the three empty slots. Rule 1 states R must be in Aug or Sep. - Scenario A: R is in August. The August pair is {X, R}. The remaining P and Y fill the slots in Sep and Oct. A possible valid schedule is Aug:{X,R}, Sep:{T,P}, Oct:{Z,Y}. - Scenario B: R is in September. The September pair is {T, R}. The remaining P and Y fill the slots in Aug and Oct. A possible valid schedule is Aug:{X,P}, Sep:{T,R}, Oct:{Z,Y}.
Step 3: Evaluating the Options:
We are looking for a pair that can be performed together. Let's try to build a valid schedule for one of the options. - (A) P and R: In both scenarios above, P and R are in different months. - (B) P and Y: In both scenarios above, P and Y are in different months. - (C) R and Y: In both scenarios above, R and Y are in different months. - (D) R and Z: Z is in October, R must be in August or September. They can't be together. - (E) X and Y: Let's see if this is possible. X must be in August. Let's try to place Y in August as well. - August: {X, Y} - We already deduced T is in Sep and Z is in Oct. - September: {T, \_} - October: {Z, \_} - The remaining experiments are P and R. From Rule 1, R must be in Aug or Sep. August is full, so R must be in September. The September pair becomes {T, R}. - The last experiment, P, must go in the last available slot in October. The October pair becomes {Z, P}. - The full schedule is: Aug:{X,Y}, Sep:{T,R}, Oct:{Z,P}. Let's check all rules. R is in Sep (ok). T is in Sep (ok). T is not with X (ok). X is before Z (ok). - This is a valid schedule. Therefore, X and Y can be performed together.
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Question: 6
If P is performed in the same month as Y, which of the following must be true?
If P is performed in the same month as Y, which of the following must be true?
Show Hint
For a "must be true" question, you must prove that the statement holds in every possible valid scenario that fits the condition. If you can find even one valid counterexample, the statement is not a "must be true." Systematically going through all cases is a reliable method.
Updated On: Oct 1, 2025
- R is performed in the same month as T.
- R is performed in the same month as X.
- T is performed in August.
- X is performed in August.
- Y is performed in October.
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
This is a conditional question asking what must be true if P and Y are scheduled in the same month. We must consider all possible months for the P-Y pair and see what conclusion holds in every case.
Step 2: Detailed Explanation by Cases:
Let's analyze the three possible months for the {P, Y} pair. The other four experiments are R, T, X, Z.
- Case 1: {P, Y are in August.} - August: {P, Y} - Rule 1 (R in Aug/Sep): August is full, so R must be in September. - Rule 2 (T in Sep/Oct): T must be in September or October. - The remaining experiments to place are R, T, X, Z in Sep and Oct. We know R is in Sep. - If T is in September, then Sep would be {R, T}. The remaining two experiments, X and Z, would go in October. This violates Rule 4 (X \textless Z), as they would be in the same month. So T cannot be in September. - T must be in October. - The schedule so far: Aug:{P,Y}, Sep:{R,\_}, Oct:{T,\_}. The remaining experiments are X and Z. - To satisfy Rule 4 (X \textless Z), X must go in September and Z must go in October. - The only possible schedule is: Aug:{P,Y}, Sep:{R,X}, Oct:{T,Z}. In this case, R and X are in the same month.
- Case 2: {P, Y are in September.} - September: {P, Y} - Rule 1 (R in Aug/Sep): September is full, so R must be in August. - Rule 2 (T in Sep/Oct): September is full, so T must be in October. - The remaining experiments are X and Z. The open slots are one in August and one in October. - To satisfy Rule 4 (X \textless Z), X must be in August and Z must be in October. - The only possible schedule is: Aug:{R,X}, Sep:{P,Y}, Oct:{T,Z}. In this case, R and X are in the same month.
- Case 3: {P, Y are in October.} - October: {P, Y} - Rule 2 (T in Sep/Oct): October is full, so T must be in September. - Rule 3 (T \(\neq\) X): Since T is in Sep, X cannot be in Sep. X must be in August. - The remaining experiments are R and Z. R must be in Aug or Sep (Rule 1). - If R were in September, Sep would be {T, R}. August would have X and Z. But this violates Rule 4 (X \textless Z). So R cannot be in September. - R must be in August. - The schedule so far: Aug:{X,R}, Sep:{T,\_}, Oct:{P,Y}. The only remaining experiment is Z, which must go in September. - The only possible schedule is: Aug:{R,X}, Sep:{T,Z}, Oct:{P,Y}. In this case, R and X are in the same month.
Step 3: Final Answer:
In all three possible cases, R and X must be performed in the same month. Therefore, statement (B) must be true.
This is a conditional question asking what must be true if P and Y are scheduled in the same month. We must consider all possible months for the P-Y pair and see what conclusion holds in every case.
Step 2: Detailed Explanation by Cases:
Let's analyze the three possible months for the {P, Y} pair. The other four experiments are R, T, X, Z.
- Case 1: {P, Y are in August.} - August: {P, Y} - Rule 1 (R in Aug/Sep): August is full, so R must be in September. - Rule 2 (T in Sep/Oct): T must be in September or October. - The remaining experiments to place are R, T, X, Z in Sep and Oct. We know R is in Sep. - If T is in September, then Sep would be {R, T}. The remaining two experiments, X and Z, would go in October. This violates Rule 4 (X \textless Z), as they would be in the same month. So T cannot be in September. - T must be in October. - The schedule so far: Aug:{P,Y}, Sep:{R,\_}, Oct:{T,\_}. The remaining experiments are X and Z. - To satisfy Rule 4 (X \textless Z), X must go in September and Z must go in October. - The only possible schedule is: Aug:{P,Y}, Sep:{R,X}, Oct:{T,Z}. In this case, R and X are in the same month.
- Case 2: {P, Y are in September.} - September: {P, Y} - Rule 1 (R in Aug/Sep): September is full, so R must be in August. - Rule 2 (T in Sep/Oct): September is full, so T must be in October. - The remaining experiments are X and Z. The open slots are one in August and one in October. - To satisfy Rule 4 (X \textless Z), X must be in August and Z must be in October. - The only possible schedule is: Aug:{R,X}, Sep:{P,Y}, Oct:{T,Z}. In this case, R and X are in the same month.
- Case 3: {P, Y are in October.} - October: {P, Y} - Rule 2 (T in Sep/Oct): October is full, so T must be in September. - Rule 3 (T \(\neq\) X): Since T is in Sep, X cannot be in Sep. X must be in August. - The remaining experiments are R and Z. R must be in Aug or Sep (Rule 1). - If R were in September, Sep would be {T, R}. August would have X and Z. But this violates Rule 4 (X \textless Z). So R cannot be in September. - R must be in August. - The schedule so far: Aug:{X,R}, Sep:{T,\_}, Oct:{P,Y}. The only remaining experiment is Z, which must go in September. - The only possible schedule is: Aug:{R,X}, Sep:{T,Z}, Oct:{P,Y}. In this case, R and X are in the same month.
Step 3: Final Answer:
In all three possible cases, R and X must be performed in the same month. Therefore, statement (B) must be true.
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Question: 7
If X is performed in the month before Y is performed, which of the following must be true?
If X is performed in the month before Y is performed, which of the following must be true?
Show Hint
When faced with ordering constraints, a powerful technique is to test the placement of the most constrained variable (in this case, X). By proving that placing it in certain positions leads to a contradiction, you can deduce its required position.
Updated On: Oct 1, 2025
- P is performed in August.
- R is performed in September.
- T is performed in September.
- X is performed in August.
- Z is performed in October.
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
This is another "must be true" question with a new conditional statement. We need to find a conclusion that is a necessary consequence of the new rule and the original rules.
Step 2: Detailed Explanation:
1. New Condition: X is performed in the month before Y is performed (X \textless Y).
2. Original Rules Reminder: We also know from Rule 4 that X must be performed in a month before Z (X \textless Z).
3. Analysis of X's Position: Let's test the possible months for X. - Can X be in October? No, because it must come before both Y and Z, and there are no months after October. - Can X be in September? Let's assume X is in September. - If X is in September, then according to the new condition (X \textless Y) and the old rule (X \textless Z), both Y and Z must be performed in October. - This means the two experiments in October are {Y, Z}. - Now consider Rule 2: T must be in September or October. October is now full with {Y, Z}. So, T must be in September. - This would mean that the two experiments in September are {X, T}. - However, this violates Rule 3, which states that T and X cannot be performed in the same month. - This creates a contradiction. Therefore, the initial assumption that X can be in September must be false.
4. Conclusion: Since X cannot be in October and X cannot be in September, the only remaining possibility is that X must be performed in August.
Step 3: Final Answer:
The combination of the new condition and the original rules forces X to be in August. Therefore, the statement "X is performed in August" must be true.
This is another "must be true" question with a new conditional statement. We need to find a conclusion that is a necessary consequence of the new rule and the original rules.
Step 2: Detailed Explanation:
1. New Condition: X is performed in the month before Y is performed (X \textless Y).
2. Original Rules Reminder: We also know from Rule 4 that X must be performed in a month before Z (X \textless Z).
3. Analysis of X's Position: Let's test the possible months for X. - Can X be in October? No, because it must come before both Y and Z, and there are no months after October. - Can X be in September? Let's assume X is in September. - If X is in September, then according to the new condition (X \textless Y) and the old rule (X \textless Z), both Y and Z must be performed in October. - This means the two experiments in October are {Y, Z}. - Now consider Rule 2: T must be in September or October. October is now full with {Y, Z}. So, T must be in September. - This would mean that the two experiments in September are {X, T}. - However, this violates Rule 3, which states that T and X cannot be performed in the same month. - This creates a contradiction. Therefore, the initial assumption that X can be in September must be false.
4. Conclusion: Since X cannot be in October and X cannot be in September, the only remaining possibility is that X must be performed in August.
Step 3: Final Answer:
The combination of the new condition and the original rules forces X to be in August. Therefore, the statement "X is performed in August" must be true.
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