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Free Mensa IQ Word Problems and Applied Math Practice Test Flashcards

35 cards from real MENSA practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 20 Free Mensa IQ Word Problems and Applied Math Practice Test flashcards as text

  1. A store offers a 20% discount on an item that originally costs $150. What is the sale price?

    Answer: B. $120

    Discount = 20% × $150 = $30. Sale price = $150 - $30 = $120.

  2. If 5 workers can build a wall in 8 days, how many days will it take 10 workers (at the same rate)?

    Answer: B. 4 days

    Inverse proportion: more workers = fewer days. 5×8 = 10×d, so d = 40/10 = 4 days.

  3. A tank fills in 4 hours through pipe A and empties in 6 hours through pipe B. If both pipes are open, how long to fill the empty tank?

    Answer: C. 12 hours

    Pipe A fills 1/4 per hour. Pipe B empties 1/6 per hour. Net rate = 1/4 - 1/6 = 3/12 - 2/12 = 1/12. Time = 12 hours.

  4. A car travels 240 km in 3 hours. At the same speed, how long to travel 400 km?

    Answer: B. 5 hours

    Speed = 240/3 = 80 km/h. Time = 400/80 = 5 hours.

  5. A shop buys an item for $80 and sells it for $100. What is the profit percentage?

    Answer: B. 25%

    Profit = $20. Profit% = (Profit/Cost) × 100 = (20/80) × 100 = 25%.

  6. If the length of a rectangle increases by 50% and the width decreases by 50%, what happens to the area?

    Answer: B. Decreases by 25%

    Original area = LW. New area = 1.5L × 0.5W = 0.75LW. The area decreases by 25%.

  7. Three friends split a restaurant bill of $72 equally, then each leaves a $4 tip. How much did each person pay in total?

    Answer: C. $28

    Bill per person = 72/3 = $24. With $4 tip: $24 + $4 = $28 each.

  8. A cyclist completes 3/4 of a race in 45 minutes. How long will the full race take at the same pace?

    Answer: B. 60 min

    3/4 race = 45 min. Full race = 45 ÷ (3/4) = 45 × (4/3) = 60 minutes.

  9. A population of bacteria doubles every 30 minutes. If you start with 100 bacteria, how many will there be after 2 hours?

    Answer: C. 1,600

    2 hours = 120 minutes = 4 doublings. 100 × 2⁴ = 100 × 16 = 1,600.

  10. If 30% of students are boys and there are 42 girls, how many students are there total?

    Answer: B. 60

    Girls = 70% of total. 42 = 0.70 × total. Total = 42/0.70 = 60 students.

  11. A train leaves City A at 9 AM going 80 km/h. Another train leaves City B (300 km away) at 10 AM going 70 km/h toward City A. When do they meet?

    Answer: C. 12:00 PM

    By 10 AM, Train A has traveled 80 km, leaving 220 km. Combined speed = 150 km/h. Time = 220/150 = 1.467 hrs ≈ 1 hr 28 min from 10 AM = ~11:28. Closest answer is 11:30 AM. Actually: 220/150 = 1h 28 min, so 11:28. Wait — let's recheck: Train A at 10 AM is at km 80, Train B at km 300 from A, gap = 220 km. Rate = 80+70=150 km/h. Time = 220/150 = 88/60 hours = 88 min. 10 AM + 88 min = 11:28 AM. Closest: 11:30 AM.

  12. What is 15% of 240?

    Answer: B. 36

    15% of 240 = 0.15 × 240 = 36.

  13. A rope is cut into two pieces in the ratio 3:5. If the shorter piece is 12 meters, how long is the rope?

    Answer: C. 32 m

    Shorter piece (3 parts) = 12 m. Each part = 4 m. Total parts = 3+5 = 8. Total rope = 8 × 4 = 32 m.

  14. John can do a job in 6 days, Mary in 12 days. How long will it take them working together?

    Answer: B. 4 days

    John's rate = 1/6, Mary's rate = 1/12. Combined = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4. Time = 4 days.

  15. A map has a scale of 1:50,000. If two cities are 6 cm apart on the map, how far apart are they in reality?

    Answer: B. 3 km

    Real distance = 6 × 50,000 = 300,000 cm = 3,000 m = 3 km.

  16. If you invest $1,000 at 5% simple annual interest, how much will you have after 4 years?

    Answer: A. $1,200

    Simple interest = Principal × Rate × Time = $1,000 × 0.05 × 4 = $200. Total = $1,000 + $200 = $1,200.

  17. A container holds 120 liters. It is filled to 3/4 capacity. How many more liters are needed to fill it completely?

    Answer: C. 30 L

    Current level = 3/4 × 120 = 90 L. Space remaining = 120 - 90 = 30 L.

  18. Two numbers are in ratio 2:3 and their sum is 50. What is the larger number?

    Answer: C. 30

    Total parts = 2+3 = 5. Each part = 50/5 = 10. Larger number = 3 × 10 = 30.

  19. A house was bought for $200,000 and sold for $250,000. What is the percentage profit?

    Answer: B. 25%

    Profit = $50,000. Profit% = (50,000/200,000) × 100 = 25%.

  20. If 1/3 of a number is 27, what is 2/5 of that number?

    Answer: A. 32.4

    If 1/3 = 27, then the number = 81. 2/5 × 81 = 162/5 = 32.4.