Mensa IQ Test Mensa IQ Syllogisms and Logical Arguments 3 — Questions and Answers
Question 1: If all roses are flowers and some flowers fade quickly, which is a valid conclusion?
- Some roses fade quickly
- All roses fade quickly
- No roses fade quickly
- Nothing can be concluded about roses fading (Correct answer)
Correct answer: Nothing can be concluded about roses fading
The 'some flowers' that fade may not overlap with roses; the conclusion is indeterminate.
Question 2: All successful students study hard. Tom did not study hard. Therefore:
- Tom is not a successful student (Correct answer)
- Tom is a successful student
- Some successful students don't study hard
- Tom studies sometimes
Correct answer: Tom is not a successful student
Modus tollens: All S→H; ¬H(Tom) → ¬S(Tom). Tom is not a successful student.
Question 3: No cowards are heroes. Some soldiers are cowards. Which conclusion MUST be true?
- Some soldiers are not heroes (Correct answer)
- No soldiers are heroes
- All heroes are soldiers
- Some cowards are soldiers
Correct answer: Some soldiers are not heroes
The coward-soldiers are not heroes (no coward is a hero) → some soldiers are not heroes.
Question 4: All doctors are graduates. All graduates can think critically. Ram is a doctor. Which is true?
- Ram can think critically (Correct answer)
- Ram cannot think critically
- Ram is not a graduate
- Nothing can be inferred about Ram
Correct answer: Ram can think critically
Ram→doctor→graduate→critical thinker by chaining both universals.
Question 5: Either the butler or the maid committed the crime. The maid is innocent. Therefore:
- The butler committed the crime (Correct answer)
- Both are guilty
- Neither is guilty
- The case is unsolvable
Correct answer: The butler committed the crime
Disjunctive syllogism: P∨Q; ¬Q → P. The butler committed the crime.
Question 6: All X are Y. Some Z are not Y. Which conclusion is valid?
- Some Z are not X (Correct answer)
- All Z are X
- No Z are X
- Some X are Z
Correct answer: Some Z are not X
If some Z are not Y, and all X are Y, then those Z cannot be X → some Z are not X.
Question 7: Person A says: 'All parrots are birds and can talk.' Person B counters: 'My parrot cannot talk.' What has Person B identified?
- A counterexample disproving the universal claim (Correct answer)
- An irrelevant point
- A supporting example
- A circular argument
Correct answer: A counterexample disproving the universal claim
One counterexample is sufficient to disprove a universal (all-X) claim.
Mensa IQ Test Mensa IQ Syllogisms and Logical Arguments 3
If all roses are flowers and some flowers fade quickly, which is a valid conclusion?