Test: Logical Deduction - CAT MCQ

• Premise: Only if it rains, the garden will not be watered.
• Logic: The watering of the garden is contingent on the absence of rain. Therefore, if it doesn't rain, the garden will be watered.
• Correct Answer: (b) BD
• Detailed Reasoning: Option BD states that the garden was watered (B) and it did not rain (D). According to the given premise, the absence of rain allows for the garden to be watered, making BD the correct combination. AC implies a direct causal relationship that is not supported by the premise, as the premise only establishes a condition under which the garden will not be watered, not when it will be.

Let's analyze the options based on the statement:

• A. The student studied diligently.

  • According to the statement, if the student studied diligently (A), then they will not fail (D).
  • Therefore, A implies D: AD.

• B. The student did not study diligently.

  • If the student did not study diligently (B), we don't have enough information from the statement to conclude whether they will fail or not.

• C. The student failed.

  • If the student failed (C), we don't have enough information from the statement to conclude whether they studied diligently or not.

• D. The student did not fail.

  • According to the statement, if the student studied diligently (A), then they will not fail (D).
  • Therefore, A implies D: AD.

Based on the implications derived from the statement:

• Option 4: AD
  • A (The student studied diligently) implies D (The student did not fail).
  • This matches our analysis.

Therefore, the correct answer is: AD.

• Premise: Either the project is completed on time, or the team works overtime.
• Logic: The completion of the project on time and the team working overtime are presented as mutually exclusive but exhaustive conditions.
• Correct Answer: (c) DA
• Detailed Reasoning: Option DA correctly reflects that if the project is completed on time (A), there is no need for the team to work overtime, hence the team does not work overtime (D). This answer aligns with the logic of mutual exclusivity given in the premise.

• Premise: You cannot access the VIP lounge unless you are a gold member.
• Logic: Being a gold member is a necessary condition for accessing the VIP lounge.
• Correct Answer: (b) CD
• Detailed Reasoning: The premise clearly stipulates that without gold membership (C), access to the VIP lounge is not granted (D). This relationship indicates that gold membership is a prerequisite for lounge access, thus supporting the answer CD.

• Premise: Only if the software is updated, the computer will run smoothly.
• Logic: The smooth operation of the computer is contingent upon the software being updated.
• Correct Answer: (a) AB
• Detailed Reasoning: The relationship established by the premise is that for the computer to run smoothly (B), a necessary condition is that the software must be updated (A). Therefore, AB is the correct combination that aligns with the given logic.

• Premise: If the alarm goes off, John will wake up.
• Logic: The alarm going off is a sufficient condition for John waking up.
• Correct Answer: (a) AB
• Detailed Reasoning: Given that the alarm's ringing (A) suffices for John's awakening (B), AB represents a correct application of the premise. However, it's essential to note that while AB aligns with the premise, other factors could also wake John, which means B does not necessarily imply A.

• Premise: Either the code is correct, or the system will crash.
• Logic: The correctness of the code and the system crashing are presented as mutually exclusive outcomes.
• Correct Answer: (a) AC
• Detailed Reasoning: If the code is correct (A), it ensures that the system will not crash (C), fitting the premise's logic that these events are mutually exclusive. Thus, AC is the correct pairing, indicating that code correctness prevents system crashes.

• Premise: You can only win the game if you score more than 50 points.
• Logic: Scoring more than 50 points is a necessary condition for winning the game.
• Correct Answer: (a) AB
• Detailed Reasoning: This premise establishes a clear condition where scoring above a certain threshold (B) is required to achieve a win (A). AB is the correct choice as it directly applies the given condition for winning.

• Premise: If a product passes the quality check, it will be shipped.
• Logic: Passing the quality check is a sufficient condition for the product to be shipped
• Correct Answer: (a) AB
• Detailed Reasoning: The premise posits that the quality check's approval (A) directly leads to the product being shipped (B), demonstrating a clear cause-and-effect relationship. If a product is shipped (B), it can be inferred that it passed the quality check (A), making AB the correct combination under the premise. However, the converse (a product not being shipped) implies a failure in the quality check (CD), but AB as the answer best fits the logical structure provided.

• Premise: Only if the team collaborates effectively will the project be successful.
• Logic: Effective collaboration is a necessary and sufficient condition for the project's success.
• Correct Answer: (a) AB
• Detailed Reasoning: This premise establishes a definitive condition where the project's success (B) hinges entirely on the team's effective collaboration (A). Thus, AB directly reflects the premise's requirement that for a project to be deemed successful, the underlying condition of effective teamwork must be met. Conversely, if the project was not successful (C), it directly implies that the team did not collaborate effectively (D), reinforcing the importance of teamwork for project success.