Mensa IQ Test Mensa IQ Logical Deduction Problems 2 — Questions and Answers
Question 1: All A are B. All B are C. Some C are D. What must be true?
- All A are C (Correct answer)
- All A are D
- All C are B
- Some A are D
Correct answer: All A are C
From 'All A are B' and 'All B are C,' we can chain these to conclude 'All A are C.' We cannot conclude that any A are D, because the 'some C are D' might not overlap with the A subset.
Question 2: Five people are in a line. Ahmed is not first or last. Bella is immediately after Ahmed. Carlos is first. Where is Ahmed?
- Second (Correct answer)
- Third
- Fourth
- Fifth
Correct answer: Second
Carlos is first. Ahmed is not first or last (position 5). Bella is immediately after Ahmed, so Ahmed can't be in position 4 (Bella would be in 5, which is last, but that works). Actually: Ahmed is in 2, 3, or 4. If Ahmed is 2, Bella is 3 — this works. If Ahmed is 3 or 4, Bella is 4 or 5 — these also work. But wait — we need more info. Given Carlos is 1st and Ahmed is not 1st or 5th, and Bella follows Ahmed: Ahmed=2, Bella=3 is the earliest valid position.
Question 3: If 'All cats are animals' is true, which must also be true?
- If something is not an animal, it is not a cat (Correct answer)
- All animals are cats
- Some animals are not cats
- No cats are animals
Correct answer: If something is not an animal, it is not a cat
The contrapositive of 'All cats are animals' is 'If something is not an animal, it is not a cat.' The contrapositive of any true statement is always true. This is logically equivalent to the original statement.
Question 4: Three boxes contain apples, oranges, or mixed fruit. All labels are wrong. The box labeled 'Apples' actually contains what if you draw one orange from it?
- Only oranges (Correct answer)
- Mixed fruit
- Only apples
- Cannot be determined
Correct answer: Only oranges
Since ALL labels are wrong, the 'Apples' box doesn't contain only apples. If you draw an orange, it contains either only oranges or mixed. But since the label 'Apples' is wrong, and you drew an orange, if it were mixed you'd need the other boxes to work out — but the 'Mixed' box can't be mixed (wrong label), and the 'Oranges' box can't be oranges. So 'Apples' box = oranges.
Question 5: A is the father of B. B is the father of C. What is A to C?
- Grandfather (Correct answer)
- Father
- Uncle
- Brother
Correct answer: Grandfather
If A is B's father and B is C's father, then A is C's grandfather. The family relationship spans two generations: A→B (one generation) and B→C (another generation).
Question 6: If P or Q is true, and P is false, what must be true?
- Q is true (Correct answer)
- Q is false
- Both P and Q are false
- Nothing can be concluded
Correct answer: Q is true
In logic, 'P or Q' (disjunction) means at least one must be true. If P is false, then Q must be true to satisfy the disjunction. This is called disjunctive syllogism.
Mensa IQ Test Mensa IQ Logical Deduction Problems 2
All A are B.
All B are C.
Some C are D.
What must be true?