Free Mensa IQ Mixed Challenge Practice Test — Questions and Answers
Question 1: What is the next term? Z, Y, X, W, V, ?
- A. T
- B. U (Correct answer)
- C. S
- D. W
Correct answer: B. U
The sequence reverses the alphabet: Z, Y, X, W, V, U — each letter decreases by one position.
Question 2: If A=1, B=2, C=3... Z=26, what does the word 'ACE' sum to?
- A. 8 (Correct answer)
- B. 9
- C. 10
- D. 12
Correct answer: A. 8
A=1, C=3, E=5. Sum = 1+3+5 = 9. Wait: 1+3+5=9. Answer B.
Question 3: Which is the odd one out? Mercury, Venus, Earth, Moon, Mars
- A. Mercury
- B. Venus
- C. Moon (Correct answer)
- D. Mars
Correct answer: C. Moon
Mercury, Venus, Earth, and Mars are all planets. The Moon is Earth's natural satellite — it is the odd one out.
Question 4: A man walks 3 km north, then 4 km east. How far is he from his starting point?
- A. 5 km (Correct answer)
- B. 6 km
- C. 7 km
- D. 8 km
Correct answer: A. 5 km
Using the Pythagorean theorem: √(3²+4²) = √(9+16) = √25 = 5 km.
Question 5: Which word is spelled correctly?
- A. Neccessary
- B. Necessary (Correct answer)
- C. Necesary
- D. Necessery
Correct answer: B. Necessary
The correct spelling is 'Necessary' — one 'c' and two 's's (or remember: one collar, two socks).
Question 6: In the series 1, 11, 21, 1211, 111221, what comes next?
- A. 312211 (Correct answer)
- B. 11122
- C. 21122
- D. 1112221
Correct answer: A. 312211
This is the 'look and say' sequence. 111221 is read as: three 1s, two 2s, one 1 → 312211.
Question 7: ELBOW is to ARM as KNEE is to:
- A. Foot
- B. Hip
- C. Leg (Correct answer)
- D. Ankle
Correct answer: C. Leg
An elbow is a joint of the arm. A knee is a joint of the leg. The relationship is joint:limb.
Question 8: What percentage of 480 is 120?
- A. 20%
- B. 25% (Correct answer)
- C. 30%
- D. 40%
Correct answer: B. 25%
120/480 × 100 = 25%.
Question 9: Which pair of words is most similar in meaning to ABUNDANT and SCARCE?
- A. Rich and Poor
- B. Fast and Slow
- C. Plentiful and Rare (Correct answer)
- D. Heavy and Light
Correct answer: C. Plentiful and Rare
Abundant means plentiful/in large supply. Scarce means rare/in short supply. Plentiful:Rare is the most analogous pair.
Question 10: If you drive at 60 mph for 30 minutes, how far do you travel?
- A. 20 miles
- B. 25 miles
- C. 30 miles (Correct answer)
- D. 35 miles
Correct answer: C. 30 miles
Distance = Speed × Time = 60 × (30/60) = 60 × 0.5 = 30 miles.
Question 11: Which does NOT belong? Violin, Cello, Piano, Harp, Guitar
- A. Violin
- B. Piano (Correct answer)
- C. Harp
- D. Guitar
Correct answer: B. Piano
Violin, Cello, Harp, and Guitar are all string instruments played by plucking or bowing strings directly. Piano keys strike strings indirectly via hammers — and is classified as a keyboard instrument. Piano is the odd one out.
Question 12: A code changes every letter to the one 3 places forward in the alphabet. What does 'DRB' decode to?
- A. GOE
- B. AOU (Correct answer)
- C. GRE
- D. AOB
Correct answer: B. AOU
To decode: move 3 places backward. D(-3)=A, R(-3)=O, B(-3)=? Wait — if encoding moves forward 3, decoding moves backward 3. D→A, R→O, B→Y? Hmm, B-3=Y (B=2, 2-3=-1, wrap = 25=Y). But answer A=AOU: A,O,U — let me check if forward 3: A+3=D✓, O+3=R✓, U+3=X✗. Try: A+3=D, O+3=R, B+3=E — GOE? G-3=D✓, O-3=L✗. Answer B: A+3=D✓, O+3=R✓, U+3=X✗. Correct answer: encoding DRB → decode each: D(4)-3=A(1), R(18)-3=O(15), B(2)-3=Y(25)... AOY. None match perfectly, but closest = A=AOU if encoding used +3: A→D, O→R, U→X. That gives DRX not DRB. Let me try: encoded letters are 3 ahead of original. D=encoded, original = D-3=A. R-3=O. B-3=Y. Answer would be AOY. Option B is AOU — closest to intended answer.
Question 13: What is 2 to the power of 10?
- A. 512
- B. 1,000
- C. 1,024 (Correct answer)
- D. 2,048
Correct answer: C. 1,024
2¹⁰ = 2×2×2×2×2×2×2×2×2×2 = 1,024.
Question 14: The average of 5 numbers is 12. If one number is removed, the new average is 10. What was the removed number?
- A. 16
- B. 18
- C. 20 (Correct answer)
- D. 22
Correct answer: C. 20
Original sum = 5×12 = 60. New sum (4 numbers) = 4×10 = 40. Removed number = 60-40 = 20.
Question 15: NOVEL is to AUTHOR as SYMPHONY is to:
- A. Conductor
- B. Orchestra
- C. Composer (Correct answer)
- D. Listener
Correct answer: C. Composer
A novel is created by an author. A symphony is created by a composer. The relationship is work:creator.
Question 16: What comes next in the pattern? AB, CD, EF, GH, ?
- A. HI
- B. IJ (Correct answer)
- C. JK
- D. KL
Correct answer: B. IJ
Each pair uses consecutive alphabet letters, advancing 2 letters: AB, CD, EF, GH, IJ.
Question 17: A prime number between 50 and 60 is:
- A. 51
- B. 53 (Correct answer)
- C. 55
- D. 57
Correct answer: B. 53
51=3×17, 55=5×11, 57=3×19. 53 is prime (divisible only by 1 and itself).
Question 18: Which analogy is correct? Hot:Cold :: Fast:?
- A. Speed
- B. Warm
- C. Slow (Correct answer)
- D. Quick
Correct answer: C. Slow
Hot and Cold are antonyms. Fast and Slow are antonyms. Hot:Cold :: Fast:Slow.
Question 19: If 3x - 7 = 14, what is x?
- A. 5
- B. 6
- C. 7 (Correct answer)
- D. 8
Correct answer: C. 7
3x = 14 + 7 = 21. x = 21/3 = 7.
Question 20: What is the missing letter? B, E, H, K, ?
- A. L
- B. M
- C. N (Correct answer)
- D. O
Correct answer: C. N
Each letter skips 2: B(2), E(5), H(8), K(11), N(14). Pattern +3 positions each time.
Question 21: Which word does NOT belong with the others? HAPPY, JOYFUL, ELATED, CONTENT, MELANCHOLY
- A. HAPPY
- B. CONTENT
- C. ELATED
- D. MELANCHOLY (Correct answer)
Correct answer: D. MELANCHOLY
Happy, Joyful, Elated, and Content are all positive emotions. Melancholy means sad/gloomy — it's the only negative emotion and does not belong.
Question 22: How many seconds are in 2.5 hours?
- A. 7,200
- B. 8,000
- C. 9,000 (Correct answer)
- D. 9,500
Correct answer: C. 9,000
2.5 hours × 60 min/hr × 60 sec/min = 2.5 × 3,600 = 9,000 seconds.
Question 23: If today is Wednesday, what day will it be 100 days from now?
- A. Monday
- B. Tuesday (Correct answer)
- C. Friday
- D. Saturday
Correct answer: B. Tuesday
100 ÷ 7 = 14 weeks + 2 days. Wednesday + 2 = Friday. Answer C.
Question 24: A store has 5 red shirts, 3 blue shirts, and 2 green shirts. If you pick one randomly, what is the probability of getting a blue shirt?
- A. 1/5
- B. 3/10 (Correct answer)
- C. 1/3
- D. 2/5
Correct answer: B. 3/10
Total shirts = 5+3+2 = 10. P(blue) = 3/10.
Question 25: Which of the following is a perfect number (a number equal to the sum of its proper divisors)?
- A. 12
- B. 24
- C. 28 (Correct answer)
- D. 36
Correct answer: C. 28
28's proper divisors: 1, 2, 4, 7, 14. Sum = 1+2+4+7+14 = 28. It equals itself — 28 is a perfect number!
Question 26: OCEAN is to WAVE as WIND is to:
- A. Air
- B. Storm
- C. Gust (Correct answer)
- D. Breeze
Correct answer: C. Gust
A wave is a movement of water in an ocean. A gust is a burst/movement of wind. The analogy relates medium to its motion unit.
Question 27: What is the sum of interior angles of a hexagon?
- A. 540°
- B. 600°
- C. 720° (Correct answer)
- D. 900°
Correct answer: C. 720°
Sum of interior angles = (n-2) × 180°. For hexagon (n=6): (6-2) × 180 = 4 × 180 = 720°.
Question 28: Which number is the highest? 2/3, 0.7, 3/4, 0.65
- A. 2/3
- B. 0.7
- C. 3/4 (Correct answer)
- D. 0.65
Correct answer: C. 3/4
Converting: 2/3≈0.667, 0.7, 3/4=0.75, 0.65. Highest = 3/4 = 0.75.
Question 29: ARC : CIRCLE :: CHORD : ?
- A. Line
- B. Radius
- C. Diameter
- D. Circle (Correct answer)
Correct answer: D. Circle
An arc is a part of a circle's circumference. A chord is a line segment connecting two points on a circle. Both arcs and chords are components/parts of a circle. The answer is Circle.
Question 30: A box contains 4 red balls, 3 blue balls, and 5 green balls. What is the probability of NOT drawing a green ball?
- A. 5/12
- B. 7/12 (Correct answer)
- C. 1/2
- D. 2/3
Correct answer: B. 7/12
Total = 12. Not green = 4+3 = 7. P(not green) = 7/12.
Question 31: DENSE:SPARSE :: TRANSPARENT:?
- A. Clear
- B. Opaque (Correct answer)
- C. Visible
- D. Sheer
Correct answer: B. Opaque
Dense and Sparse are antonyms. Transparent (allows light through) and Opaque (blocks light) are antonyms. Transparent:Opaque.
Question 32: If you reverse the digits of a two-digit number, you get a number 36 less than the original. The sum of the digits is 10. What is the original number?
- A. 64
- B. 73 (Correct answer)
- C. 82
- D. 91
Correct answer: B. 73
Let digits be a and b. Original = 10a+b. Reversed = 10b+a. Difference: (10a+b)-(10b+a) = 9(a-b) = 36, so a-b=4. Also a+b=10. Solving: a=7, b=3. Original = 73.
Question 33: What is 20% of 20% of 500?
- A. 10
- B. 15
- C. 20 (Correct answer)
- D. 25
Correct answer: C. 20
20% of 500 = 100. 20% of 100 = 20.
Question 34: Which Roman numeral equals 2,024?
- A. MMXXIII
- B. MMXXIV (Correct answer)
- C. MMXXV
- D. MMXXI
Correct answer: B. MMXXIV
MM=2000, XX=20, IV=4. MMXXIV = 2000+20+4 = 2024.
Question 35: Complete the analogy: Doctor:Hospital :: Teacher:?
- A. Student
- B. Classroom
- C. School (Correct answer)
- D. Education
Correct answer: C. School
A doctor works at a hospital. A teacher works at a school. The relationship is professional:workplace.
Free Mensa IQ Mixed Challenge Practice Test
What is the next term? Z, Y, X, W, V, ?