Logical Deduction Problems Flashcards

Exactly three of the five statements below are true. Statement 3 says 'Statement 1 is false.' If Statement 1 is true, how many of statements 2–5 must be true?

Answer: 2

If Statement 1 is true, then Statement 3 is false; with 3 total true among 5 and statements 1 and 3 accounting for one true and one false, exactly 2 more from statements 2, 4, 5 must be true.

A is older than B. C is younger than A but older than B. D is older than C. Who is the youngest?

Answer: B

The order from oldest to youngest is D, A, C, B — making B the youngest.

Only employees with a badge can enter the server room. Kevin entered the server room. What must be true?

Answer: Kevin has a badge

Since entry requires a badge and Kevin entered, he must have a badge.

Some painters are musicians. All musicians practice daily. Which conclusion is valid?

Answer: Some painters practice daily

The painters who are musicians must also practice daily, so some painters practice daily.

If a number is divisible by 6, it is divisible by both 2 and 3. The number 18 is divisible by 6. Which statement must be true?

Answer: 18 is divisible by 2 and 3

By direct application of the given rule, 18 divisible by 6 means it is divisible by both 2 and 3.

Four boxes are stacked: Red is above Green. Blue is below Green. Yellow is above Red. What is the order from top to bottom?

Answer: Yellow, Red, Green, Blue

Yellow is above Red, Red is above Green, Green is above Blue — giving Yellow, Red, Green, Blue from top to bottom.

Either the project is on time or the budget is overspent. The project is on time. What can you conclude about the budget?

Answer: The budget may or may not be overspent

An inclusive OR means both conditions could be true simultaneously, so the budget may still be overspent.