PI - Cognitive Assessment Logical Deduction Problems Questions and Answers — Questions and Answers
Question 1: All systems updated last night are secure. The main accounting system was not updated last night. Which of the following statements must be true?
- The main accounting system is not secure.
- Some systems that are not secure were not updated last night.
- Only systems updated last night are secure.
- No certain conclusion can be drawn about the security of the main accounting system. (Correct answer)
Correct answer: No certain conclusion can be drawn about the security of the main accounting system.
The first statement says that if a system was updated, then it is secure (A -> B). The second statement says the accounting system was not updated (Not A). This scenario is a logical fallacy known as 'denying the antecedent.' We cannot logically conclude anything about the security of the accounting system. It might be secure for other reasons, or it might not be. Therefore, no certain conclusion can be drawn.
Question 2: If the marketing campaign is successful, the product launch will be on time. If the product launch is on time, the quarterly sales targets will be met. The marketing campaign was successful. What can be logically concluded?
- The product launch will be delayed.
- The quarterly sales targets will be met. (Correct answer)
- The marketing campaign was expensive.
- The sales team is performing well.
Correct answer: The quarterly sales targets will be met.
This is a transitive argument. The premises are: If A (successful campaign), then B (on-time launch). If B (on-time launch), then C (targets met). We are told A is true. Therefore, B must be true, and consequently, C must also be true. The quarterly sales targets will be met.
Question 3: Some employees on the third floor are in the finance department. All employees in the finance department have a background in economics. Which conclusion logically follows from these statements?
- All employees on the third floor have a background in economics.
- Some employees on the third floor have a background in economics. (Correct answer)
- All employees with a background in economics are in the finance department.
- No employees on the third floor are in the finance department.
Correct answer: Some employees on the third floor have a background in economics.
We know that there's an overlap between 'employees on the third floor' and 'finance department.' We also know that everyone in the 'finance department' group is also in the 'background in economics' group. Therefore, the part of the 'third floor' group that is in the 'finance' group must also have a background in economics. This means at least some employees on the third floor have a background in economics.
Question 4: There are four project proposals: Alpha, Beta, Gamma, and Delta. The review committee has established the following conditions: If Alpha is approved, then Beta must also be approved. If Gamma is rejected, then Delta must be approved. If the committee approves Alpha but rejects Delta, which of the following must be true?
- Beta is rejected and Gamma is rejected.
- Beta is approved and Gamma is approved. (Correct answer)
- Beta is rejected and Gamma is approved.
- Beta is approved and Gamma is rejected.
Correct answer: Beta is approved and Gamma is approved.
The premises are: 1) If Alpha is approved, Beta is approved. 2) If Gamma is rejected, Delta is approved. We are told Alpha is approved, so based on premise 1, Beta must be approved. We are also told Delta is rejected. Looking at premise 2, if Delta were to be approved, it would be because Gamma was rejected. The contrapositive is: If Delta is *not* approved (i.e., rejected), then Gamma must *not* be rejected (i.e., approved). Therefore, Beta is approved and Gamma is approved.
Question 5: No reports written by interns are distributed to the board. The latest market analysis was distributed to the board. What can be deduced from these facts?
- The latest market analysis was not written by an intern. (Correct answer)
- All reports written by interns are market analyses.
- No interns are allowed to write market analyses.
- The board only reads reports about market analysis.
Correct answer: The latest market analysis was not written by an intern.
The first statement establishes that the group 'reports written by interns' and the group 'reports distributed to the board' are mutually exclusive. Since the latest market analysis is in the 'distributed to the board' group, it cannot possibly be in the 'written by interns' group.
Question 6: Team members must choose to work on either Project Phoenix or Project Griffin, but not both. If a team member has security clearance, they are assigned to Project Phoenix. Mark does not have security clearance. What is the logical conclusion?
- Mark is assigned to Project Griffin.
- Mark is assigned to Project Phoenix.
- Mark is assigned to both projects.
- Mark's project assignment cannot be determined from the information given. (Correct answer)
Correct answer: Mark's project assignment cannot be determined from the information given.
The rule states that if a team member has security clearance (A), then they work on Project Phoenix (B). It does not state what happens if a team member does *not* have security clearance (Not A). Mark not having clearance doesn't automatically place him on Project Griffin; there may be other criteria for assignment not mentioned. Therefore, we cannot logically determine his assignment based only on the rules provided.
PI - Cognitive Assessment Logical Deduction Problems Questions and Answers
All systems updated last night are secure.
The main accounting system was not updated last night.
Which of the following statements must be true?