Deductive Logical Thinking Flashcards

A company has the following policy for project team assignments: 1) All projects must be led by a certified Project Manager. 2) No Project Manager can lead more than two projects simultaneously. 3) Any project with a budget exceeding €500,000 must also include a Senior Financial Analyst. David, a certified Project Manager, is currently leading two projects. One of these projects has a budget of €600,000. Which of the following statements must be true?

Answer: David's €600,000 project team must include a Senior Financial Analyst.

The third rule states that any project with a budget over €500,000 must include a Senior Financial Analyst. Since David is leading a project with a €600,000 budget, this rule applies directly to his project. The other options are possible but not guaranteed; David could be assigned a new project if one of his current ones ends (B), we only know about David's two projects, not the company total (C), and we have no information about other Project Managers (D).

Read the following statements: 1. If the interest rates decrease, the stock market will rally. 2. If the stock market rallies, consumer confidence will increase. 3. This quarter, consumer confidence did not increase. Assuming these statements are true, what can be logically deduced?

Answer: The interest rates did not decrease this quarter.

This is a logical chain of reasoning using the contrapositive. The statements create the sequence: If A (rates decrease), then B (market rallies). If B (market rallies), then C (confidence increases). Therefore, if A, then C. The contrapositive states that if Not C, then Not A. We are told that consumer confidence did not increase (Not C). Therefore, we can definitively conclude that interest rates did not decrease (Not A). We cannot conclude that rates *increased*, only that they did not *decrease*.

In a logistics company, all shipments to Europe are sent via air freight. No shipments sent via air freight are routed through the company's southern hub. Based solely on these two premises, which of the following conclusions is logically certain?

Answer: No shipment to Europe is routed through the southern hub.

The premises establish a clear logical link: Shipments to Europe -> Sent via Air Freight -> NOT Routed through Southern Hub. By combining the start and end of this chain, we can deduce that shipments to Europe are not routed through the southern hub. Option A is a possibility but not a certainty (southern hub shipments could go to non-European destinations, but they don't *have* to). Options C and D introduce information and conclusions not supported by the premises.

A manager is reviewing four employees: Amina, Ben, Chloe, and Daniel. The following is known: - If Amina receives a promotion, then Ben will also receive a promotion. - Chloe and Daniel will receive the same outcome; either both are promoted or neither is promoted. - Ben does not receive a promotion. Given this information, which of the following must be true?

Answer: Amina does not receive a promotion.

This problem requires using the contrapositive of the first statement. The statement is 'If Amina is promoted (A), then Ben is promoted (B)'. The contrapositive is 'If Ben is NOT promoted (Not B), then Amina is NOT promoted (Not A)'. We are told that Ben does not receive a promotion, so we can definitively conclude that Amina does not receive a promotion either. We don't have enough information to determine the outcome for Chloe and Daniel.

A software development team follows these deployment rules: A new feature can be deployed to customers only if it has passed both Quality Assurance (QA) testing and security vulnerability scans. Any feature that fails the security scan must be reworked by the development team and cannot be resubmitted for QA testing for at least 48 hours. Yesterday, the 'Auto-Fill' feature was deployed to customers. What can be deduced from this event?

Answer: The 'Auto-Fill' feature passed the security vulnerability scan.

The first rule states that deployment requires passing *both* QA testing and security scans. Since the 'Auto-Fill' feature was deployed, it must have fulfilled both conditions. Therefore, it necessarily passed the security vulnerability scan. We cannot know if it was reworked at some earlier stage (A), nor do we have information about testing timelines (C) or other features (D).

At a business conference, every attendee from a technology company received a blue lanyard. Every attendee with a blue lanyard was given a ticket to the networking dinner. Maria is an attendee at the conference who was not given a ticket to the networking dinner. What must be true about Maria?

Answer: Maria does not work for a technology company.

This problem presents a deductive chain: Tech Company Attendee -> Blue Lanyard -> Dinner Ticket. The most certain conclusion comes from applying the contrapositive to the entire chain. If an attendee did NOT receive a dinner ticket, they must NOT be a tech company attendee. We can also deduce she did not have a blue lanyard, but the most foundational conclusion based on the entire logical flow is about her company type. We cannot know her actual company (A) or pass type (D).