Free Mensa IQ Critical Thinking Practice Test — Questions and Answers
Question 1: All roses are flowers. Some flowers fade quickly. Therefore:
- A. All roses fade quickly
- B. Some roses may fade quickly (Correct answer)
- C. No roses fade quickly
- D. All flowers are roses
Correct answer: B. Some roses may fade quickly
This is a syllogism. We know all roses are flowers, and some flowers fade quickly. It's possible (but not certain) that some of those fading flowers are roses. We cannot conclude all roses fade quickly, only that some roses may.
Question 2: If it is true that 'No X is Y' and 'All Z is X', which must be true?
- A. Some Z is Y
- B. No Z is Y (Correct answer)
- C. All Y is Z
- D. Some X is Z
Correct answer: B. No Z is Y
If no X is Y, and all Z is X, then Z is a subset of X. Since nothing in X is Y, nothing in Z (being part of X) can be Y. Therefore 'No Z is Y' must be true.
Question 3: A study shows students who eat breakfast score higher on tests. A teacher concludes breakfast causes better test scores. What flaw exists in this reasoning?
- A. The sample size is too large
- B. Correlation does not imply causation (Correct answer)
- C. The study used too many variables
- D. Test scores are subjective
Correct answer: B. Correlation does not imply causation
The classic logical flaw: correlation does not imply causation. Students who eat breakfast may also have other habits (better sleep, stable home environment) that cause higher scores. The relationship is correlational, not necessarily causal.
Question 4: Five people sit in a row. Anna is not at either end. Ben is to the right of Anna. Clara is at the leftmost seat. Dana is between Clara and Anna. Who is at the rightmost seat?
- A. Anna
- B. Ben
- C. Eric (Correct answer)
- D. Dana
Correct answer: C. Eric
Clara is at position 1 (leftmost). Dana is between Clara and Anna. So the order so far: Clara(1), Dana(2), Anna(3). Ben is to the right of Anna, so Ben is at 4 or 5. Eric takes the remaining spot. Since Anna is not at an end and Ben must be right of Anna, Ben is at 4 and Eric is at 5 (rightmost).
Question 5: Which argument contains circular reasoning?
- A. The sun rises because the earth rotates
- B. This book is trustworthy because the author says it is accurate (Correct answer)
- C. Exercise improves health because it strengthens the body
- D. Water boils at 100°C because heat increases molecular energy
Correct answer: B. This book is trustworthy because the author says it is accurate
Circular reasoning (begging the question) occurs when the conclusion is used as a premise. 'The book is trustworthy because the author says it is accurate' uses the author's credibility as proof of the author's credibility — the conclusion supports itself.
Question 6: Three friends each prefer a different sport: football, tennis, or swimming. Alex doesn't like water sports. Blake prefers racket sports. Who likes football?
- A. Alex (Correct answer)
- B. Blake
- C. Charlie
- D. Cannot be determined
Correct answer: A. Alex
Blake prefers racket sports = tennis. Alex doesn't like water sports = not swimming. Since Blake has tennis, Alex must choose between football and swimming — but Alex dislikes water sports, so Alex likes football. Charlie likes swimming.
Question 7: What is the logical conclusion if: 'All politicians are public figures' and 'Some public figures are dishonest'?
- A. All politicians are dishonest
- B. Some politicians are public figures
- C. Some politicians may be dishonest (Correct answer)
- D. No politicians are dishonest
Correct answer: C. Some politicians may be dishonest
All politicians are public figures (politicians ⊆ public figures). Some public figures are dishonest. The dishonest public figures may or may not overlap with politicians. Therefore 'some politicians may be dishonest' is the only valid conclusion.
Question 8: A man is looking at a photograph and says, 'Brothers and sisters I have none, but that man's father is my father's son.' Who is in the photograph?
- A. The man himself
- B. The man's father
- C. The man's son (Correct answer)
- D. The man's nephew
Correct answer: C. The man's son
Since he has no brothers or sisters, 'my father's son' = himself. So 'that man's father is me.' Therefore the man in the photograph is his own son.
Question 9: Which of the following best identifies the flaw: 'We should not trust John's opinion on the new policy because he dresses oddly.'
- A. False dilemma
- B. Ad hominem (Correct answer)
- C. Straw man
- D. Slippery slope
Correct answer: B. Ad hominem
Ad hominem is attacking the person rather than their argument. Dismissing John's policy opinion based on his appearance is irrelevant to the validity of his argument — this is a classic ad hominem fallacy.
Question 10: If all Bloops are Razzles and all Razzles are Lazzles, are all Bloops definitely Lazzles?
- A. Yes (Correct answer)
- B. No
- C. Only sometimes
- D. Cannot be determined
Correct answer: A. Yes
This is transitive reasoning. Bloops ⊆ Razzles, and Razzles ⊆ Lazzles. Therefore Bloops ⊆ Lazzles. All Bloops are definitely Lazzles.
Question 11: In a room, there are 4 people. Each person shakes hands with every other person exactly once. How many handshakes occur?
- A. 4
- B. 6 (Correct answer)
- C. 8
- D. 12
Correct answer: B. 6
The number of handshakes = combinations of 4 people taken 2 at a time = 4!/(2!×2!) = 6. Each unique pair (A-B, A-C, A-D, B-C, B-D, C-D) = 6 handshakes.
Question 12: What logical error is: 'Either you support this new law or you hate freedom.'
- A. Slippery slope
- B. Appeal to authority
- C. False dilemma (Correct answer)
- D. Hasty generalization
Correct answer: C. False dilemma
This is a false dilemma (false dichotomy) — presenting only two options when more exist. One could support freedom while opposing this specific law for other valid reasons. The argument artificially limits the choices.
Question 13: A clock shows 3:15. What is the angle between the hour and minute hands?
- A. 0°
- B. 7.5° (Correct answer)
- C. 15°
- D. 22.5°
Correct answer: B. 7.5°
At 3:15, the minute hand is at 90° (pointing to 3). The hour hand: at 3:00 it is at 90°, but by 3:15 it has moved 15/60 × 30° = 7.5° further. So the hour hand is at 97.5°. The angle between them = 97.5° - 90° = 7.5°.
Question 14: Tom is taller than Sam. Sam is taller than Mike. Pete is shorter than Mike. Who is the tallest?
- A. Sam
- B. Mike
- C. Tom (Correct answer)
- D. Pete
Correct answer: C. Tom
The height order from the clues: Tom > Sam > Mike > Pete. Tom is the tallest.
Question 15: Which conclusion is valid? Premise 1: If it rains, the ground is wet. Premise 2: The ground is wet.
- A. It rained
- B. It may or may not have rained (Correct answer)
- C. It definitely did not rain
- D. It will rain soon
Correct answer: B. It may or may not have rained
This is the fallacy of affirming the consequent. The ground being wet doesn't confirm rain — a sprinkler could have caused it. The valid conclusion is only that it may or may not have rained.
Question 16: A bat and ball cost $1.10 together. The bat costs $1 more than the ball. How much does the ball cost?
- A. $0.10
- B. $0.05 (Correct answer)
- C. $0.15
- D. $0.20
Correct answer: B. $0.05
Let ball = x. Bat = x + $1. Together: x + (x + 1) = 1.10. So 2x = 0.10, x = $0.05. The ball costs 5 cents. (Many people intuitively say $0.10 but that's wrong — the bat would then cost $1.10 and total $1.20.)
Question 17: Six people are in a race. The positions are 1st through 6th. Maya finished before Jess but after Kyle. Dan finished last. Sam finished before Maya. Who finished first?
- A. Kyle
- B. Sam
- C. Maya
- D. Cannot be determined (Correct answer)
Correct answer: D. Cannot be determined
We know: Kyle > Maya > Jess, and Sam > Maya, and Dan is last. Both Kyle and Sam are before Maya, but their relative order to each other is not specified. Either Kyle or Sam could be first — it cannot be determined from the given clues alone.
Question 18: Which of the following is an example of a hasty generalization?
- A. I've never been to Paris, therefore Paris doesn't exist
- B. I met two rude people from City X, therefore everyone from City X is rude (Correct answer)
- C. All bachelors are unmarried men
- D. If you litter once, you'll become a criminal
Correct answer: B. I met two rude people from City X, therefore everyone from City X is rude
A hasty generalization draws a broad conclusion from a small or unrepresentative sample. Meeting two rude people and concluding everyone from that city is rude is a classic hasty generalization.
Question 19: What comes next in the logical sequence: 1, 4, 9, 16, 25, ?
- A. 30
- B. 36 (Correct answer)
- C. 35
- D. 49
Correct answer: B. 36
These are perfect squares: 1²=1, 2²=4, 3²=9, 4²=16, 5²=25. The next is 6²=36.
Question 20: If you rearrange the letters CIFAIPC, you get the name of a(n):
- A. Country
- B. Ocean (Correct answer)
- C. City
- D. River
Correct answer: B. Ocean
Rearranging CIFAIPC gives PACIFIC — the name of an ocean (Pacific Ocean).
Question 21: A farmer has 17 sheep. All but 9 die. How many are left?
- A. 8
- B. 9 (Correct answer)
- C. 17
- D. 0
Correct answer: B. 9
'All but 9 die' means 9 survive. The answer is 9. This is a classic trick question testing careful reading.
Question 22: Which number logically replaces the question mark? 2, 6, 12, 20, 30, ?
- A. 40
- B. 42 (Correct answer)
- C. 44
- D. 48
Correct answer: B. 42
The pattern: differences are 4, 6, 8, 10, 12. Each difference increases by 2. So next = 30 + 12 = 42. Alternatively: n(n+1) pattern — 1×2, 2×3, 3×4, 4×5, 5×6, 6×7=42.
Question 23: Three boxes are labeled 'Apples', 'Oranges', and 'Mixed'. All labels are wrong. You pick one fruit from the 'Mixed' box and it's an apple. What does the 'Apples' box contain?
- A. Apples
- B. Oranges (Correct answer)
- C. Mixed fruits
- D. Cannot be determined
Correct answer: B. Oranges
Since all labels are wrong: 'Mixed' = Apples only (you drew an apple). 'Apples' label cannot contain apples (wrong label), and can't be mixed (that's already taken). So 'Apples' = Oranges. 'Oranges' = Mixed.
Question 24: Which fallacy is: 'My grandfather smoked all his life and lived to 95, so smoking isn't that dangerous.'
- A. Straw man
- B. Anecdotal evidence (Correct answer)
- C. Appeal to tradition
- D. False cause
Correct answer: B. Anecdotal evidence
Using a single personal story (anecdote) to counter statistical evidence is the anecdotal evidence fallacy. One exceptional case doesn't override large-scale epidemiological data.
Question 25: If A > B, B > C, and C > D, which of the following must be false?
- A. A > D
- B. D < A
- C. D > A (Correct answer)
- D. B > D
Correct answer: C. D > A
From A > B > C > D, we know A is greater than all others. D is the smallest. Therefore D > A must be false.
Question 26: A is the brother of B. B is the mother of C. D is the father of A. What is D to C?
- A. Father
- B. Uncle
- C. Grandfather (Correct answer)
- D. Brother
Correct answer: C. Grandfather
A is B's brother. B is C's mother. D is A's father. Since A and B are siblings and D is A's father, D is also B's father. B is C's mother, so D (B's father) is C's grandfather.
Question 27: In a class of 30 students, 18 play soccer, 15 play basketball, and 5 play neither. How many play both?
- A. 5
- B. 7
- C. 8 (Correct answer)
- D. 10
Correct answer: C. 8
Students who play at least one sport = 30 - 5 = 25. Using inclusion-exclusion: Both = Soccer + Basketball - At least one = 18 + 15 - 25 = 8.
Question 28: Which of these is NOT a logical fallacy?
- A. Ad hominem
- B. Modus ponens (Correct answer)
- C. Slippery slope
- D. Straw man
Correct answer: B. Modus ponens
Modus ponens is a valid form of deductive reasoning (If P then Q; P; therefore Q). Ad hominem, slippery slope, and straw man are all logical fallacies.
Question 29: A train travels 60 mph. Another train travels 90 mph in the opposite direction. They are 300 miles apart. In how many minutes will they meet?
- A. 100 min
- B. 120 min (Correct answer)
- C. 150 min
- D. 200 min
Correct answer: B. 120 min
Combined speed = 60 + 90 = 150 mph. Time = 300/150 = 2 hours = 120 minutes.
Question 30: What reasoning error is: 'We've always done it this way, so we shouldn't change it.'
- A. Appeal to nature
- B. Appeal to tradition (Correct answer)
- C. Appeal to authority
- D. Bandwagon fallacy
Correct answer: B. Appeal to tradition
Appeal to tradition argues that something is correct or better simply because it is traditional or has always been done that way. Tradition alone doesn't validate a practice.
Question 31: All even numbers are divisible by 2. 14 is even. Therefore:
- A. 14 may be divisible by 2
- B. 14 is definitely divisible by 2 (Correct answer)
- C. 14 is not divisible by 2
- D. Some even numbers are not divisible by 2
Correct answer: B. 14 is definitely divisible by 2
This is valid deductive reasoning (modus ponens). If all even numbers are divisible by 2, and 14 is even, then 14 is definitely divisible by 2. This follows necessarily from the premises.
Question 32: Five cards are face-down. Card 1 is to the left of Card 3. Card 2 is to the right of Card 4. Card 5 is between Cards 2 and 3. Card 4 is leftmost. What position is Card 1?
- A. Position 1
- B. Position 2 (Correct answer)
- C. Position 3
- D. Position 4
Correct answer: B. Position 2
Card 4 is leftmost = position 1. Card 2 is right of Card 4, so Card 2 is at position 2+. Card 1 is left of Card 3. Card 5 is between Cards 2 and 3. A valid arrangement: 4, 1, 2, 5, 3. Card 1 is at position 2.
Question 33: Mary is twice as old as Ann was when Mary was as old as Ann is now. Mary is 28. How old is Ann?
- A. 14
- B. 21 (Correct answer)
- C. 24
- D. 18
Correct answer: B. 21
Let Ann's current age = A. When Mary was A years old, the age difference (28-A) years ago, Ann was A-(28-A) = 2A-28. Mary is twice that age now: 28 = 2(2A-28) = 4A-56, so 4A = 84, A = 21.
Question 34: Which is the odd one out in terms of logical category? Apple, Carrot, Banana, Grape, Mango
- A. Apple
- B. Carrot (Correct answer)
- C. Banana
- D. Grape
Correct answer: B. Carrot
Apple, Banana, Grape, and Mango are all fruits. Carrot is a vegetable — it's the odd one out.
Question 35: If 'Some A are B' and 'All B are C', which must be true?
- A. All A are C
- B. No A are C
- C. Some A are C (Correct answer)
- D. All C are A
Correct answer: C. Some A are C
Some A are B, and all B are C. The A's that are B are also C (since all B are C). So at least some A (specifically those that are B) must be C.
Question 36: A snail is at the bottom of a 10-foot well. Each day it climbs 3 feet; each night it slides back 2 feet. On which day does it reach the top?
- A. Day 7
- B. Day 8 (Correct answer)
- C. Day 9
- D. Day 10
Correct answer: B. Day 8
Net progress per day/night cycle = 1 foot. After 7 days/nights, snail is at 7 feet. On day 8, it climbs 3 feet from 7 = 10 feet — it reaches the top on Day 8 (before sliding back).
Question 37: All doctors are professionals. Dr. Chen is a doctor. Therefore:
- A. All professionals are doctors
- B. Dr. Chen is a professional (Correct answer)
- C. Some professionals are not doctors
- D. Dr. Chen may not be a professional
Correct answer: B. Dr. Chen is a professional
Valid modus ponens: All doctors are professionals (doctors ⊆ professionals). Dr. Chen is a doctor. Therefore Dr. Chen is a professional. This is a straightforward, valid deductive conclusion.
Free Mensa IQ Critical Thinking Practice Test
All roses are flowers.
Some flowers fade quickly.
Therefore: