PI Logical Deduction Problems 4 — Questions and Answers
Question 1: In a group of 30 people, 18 like coffee and 15 like tea. At least how many like both?
- 0
- 3 (Correct answer)
- 5
- 13
Correct answer: 3
By inclusion-exclusion: 18 + 15 − 30 = 3, so at least 3 like both.
Question 2: All certified technicians passed the exam. James did not pass the exam. Which statement is valid?
- James is a certified technician
- James is not a certified technician (Correct answer)
- James may still be certified
- The exam does not determine certification
Correct answer: James is not a certified technician
By contrapositive, failing the exam means James is not a certified technician.
Question 3: A box contains red and blue balls. If you draw one ball, the chance it is red is 1/4. There are 12 balls total. How many are red?
- 2
- 3 (Correct answer)
- 4
- 6
Correct answer: 3
1/4 × 12 = 3 red balls.
Question 4: If neither A nor B is true, then C must be true. A is false and B is false. What follows?
- C is false
- C is true (Correct answer)
- C may or may not be true
- A must be true
Correct answer: C is true
Both A and B are false, satisfying the condition, so C must be true.
Question 5: Four people finish a race: Alice, Bob, Carol, Dan. Alice beats Bob. Dan beats Carol. Bob beats Dan. What is the finishing order?
- Alice, Bob, Dan, Carol (Correct answer)
- Alice, Dan, Bob, Carol
- Bob, Alice, Dan, Carol
- Dan, Alice, Bob, Carol
Correct answer: Alice, Bob, Dan, Carol
The order is Alice > Bob > Dan > Carol from the three given relationships.
Question 6: Some X are Y. Some Y are Z. What can definitely be concluded?
- Some X are Z
- No X are Z
- All X are Z
- Nothing definite about X and Z (Correct answer)
Correct answer: Nothing definite about X and Z
Overlapping 'some' statements don't guarantee any overlap between X and Z.
Question 7: A rule states: employees who work overtime get a bonus OR a day off, but not both. Lisa got a bonus. What is true?
- Lisa also gets a day off
- Lisa does not get a day off (Correct answer)
- Lisa may get both
- Lisa did not work overtime
Correct answer: Lisa does not get a day off
The exclusive or means if Lisa got the bonus, she cannot also get a day off.
PI Logical Deduction Problems 4
In a group of 30 people, 18 like coffee and 15 like tea.
At least how many like both?