Mensa IQ Test Mensa IQ Syllogisms and Logical Arguments 5 — Questions and Answers
Question 1: All prime numbers greater than 2 are odd. 7 is a prime number greater than 2. Therefore:
- 7 is odd (Correct answer)
- 7 is even
- 7 is not prime
- No odd numbers are prime
Correct answer: 7 is odd
Modus ponens applied to a mathematical syllogism: 7 satisfies the premise conditions, so 7 is odd.
Question 2: Some musicians are athletes. All athletes are disciplined. Which is valid?
- Some musicians are disciplined (Correct answer)
- All musicians are disciplined
- No musicians are disciplined
- All disciplined people are musicians
Correct answer: Some musicians are disciplined
Darii (AII-1 variant): the musician-athletes are disciplined → some musicians are disciplined.
Question 3: Premises: All frogs are amphibians. No amphibians live in deserts. Which follows?
- No frogs live in deserts (Correct answer)
- Some frogs live in deserts
- All amphibians are frogs
- Some desert animals are frogs
Correct answer: No frogs live in deserts
Celarent: All F→A; No A→D → No F→D.
Question 4: Argument: 'If we ban assault rifles, next they'll ban all guns, then knives, then forks.' This is which fallacy?
- Slippery slope (Correct answer)
- Ad populum
- False dilemma
- Circular reasoning
Correct answer: Slippery slope
Assuming one small step inevitably leads to extreme consequences without evidence is the slippery slope fallacy.
Question 5: No insects have backbones. All beetles are insects. Which is valid?
- No beetles have backbones (Correct answer)
- Some beetles have backbones
- All backboned animals are beetles
- Some insects are beetles
Correct answer: No beetles have backbones
EAE-1 Celarent: No I have B; All Be are I → No Be have B.
Question 6: Premises: If you study, you pass. If you pass, you celebrate. Anna studied. What follows?
- Anna celebrates (Correct answer)
- Anna does not pass
- Anna does not celebrate
- Nothing follows
Correct answer: Anna celebrates
Hypothetical syllogism: study→pass→celebrate; Anna studied → Anna celebrates.
Question 7: All fast cars are expensive. Some red cars are fast. Which is valid?
- Some red cars are expensive (Correct answer)
- All red cars are expensive
- No red cars are expensive
- All expensive cars are red
Correct answer: Some red cars are expensive
The fast red cars are expensive (all fast cars are expensive) → some red cars are expensive.
Mensa IQ Test Mensa IQ Syllogisms and Logical Arguments 5
All prime numbers greater than 2 are odd. 7 is a prime number greater than 2.
Therefore: