Q1. How many factors (divisors) does 144 have?
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Answer: B. 15
144 = 2^4 × 3^2; number of factors = 5 × 3 = 15.
SSC CGL Quantitative Aptitude Intermediate Practice Set 9
25 intermediate questions. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Number System, Statistics, Average, Algebra, Simplification, Indices and Surds, Speed, Time and Distance, Mensuration, Time and Work, Percentage, Partnership, Geometry, Simple Interest
Score: 0 / 0
Q2. Find the median of: 19, 27, 26, 53, 6, 35, 55, 22.
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Answer: A. 26.5
In order: 6, 19, 22, 26, 27, 35, 53, 55. Median = 26.5.
Q3. What is the unit digit of 9^82?
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Answer: D. 1
Unit digits of 9^1, ^2, ^3, ^4 are 9, 1, 9, 1. 82 leaves remainder 2 on division by 4, so take the 2nd value in the cycle: 1.
Q4. What is the largest 4-digit number exactly divisible by 29?
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Answer: D. 9976
9999 ÷ 29 leaves remainder 23. 9999 − 23 = 9976.
Q5. A batsman has an average of 34 runs after 12 innings. How many runs must he score in the next innings to raise his average by 3?
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Answer: A. 73
New total = 13 × 37 = 481; old total = 12 × 34 = 408. Runs = 73.
Q6. If a + b = 5 and ab = 10, find a² + b².
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Answer: D. 5
a² + b² = (a + b)² − 2ab = 25 − 20 = 5.
Q7. Find the value of 73² − 40².
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Answer: C. 3729
(73 + 40)(73 − 40) = 113 × 33 = 3729.
Q8. What is the largest 3-digit number exactly divisible by 13?
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Answer: B. 988
999 ÷ 13 leaves remainder 11. 999 − 11 = 988.
Q9. Find the value of (3^4 × 3^6) ÷ 3^5.
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Answer: B. 243
3^(4 + 6 − 5) = 3^5 = 243.
Q10. Two trains of lengths 210 m and 140 m run in the same direction at 54 km/h and 72 km/h. How long will they take to cross each other completely?
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Answer: A. 70 seconds
Relative speed = 18 km/h = 5 m/s. Time = (210 + 140)/5 = 70 s.
Q11. Find the area of a circle of radius 35 cm. (Take π = 22/7)
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Answer: C. 3850 cm²
Area = 22/7 × 35 × 35 = 3850 cm².
Q12. Find the surface area of a sphere of radius 14 cm. (Take π = 22/7)
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Answer: C. 2464 cm²
SA = 4 × 22/7 × 14² = 2464 cm².
Q13. 18 men can complete a work in 26 days. In how many days can 39 men complete the same work?
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Answer: D. 12 days
18 × 26 = 39 × D ⇒ D = 468/39 = 12 days.
Q14. The diagonals of a rhombus are 52 cm and 10 cm. Find its area.
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Answer: C. 260 cm²
½ × 52 × 10 = 260 cm².
Q15. Find the value of (5^3 × 5^8) ÷ 5^4.
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Answer: A. 78125
5^(3 + 8 − 4) = 5^7 = 78125.
Q16. Find the median of: 27, 12, 9, 15, 48.
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Answer: B. 15
In order: 9, 12, 15, 27, 48. Median = 15.
Q17. The population of a town is 60000. It increases by 5% every year. What will the population be after 2 years?
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Answer: A. 66150
60000 × (105/100)^2 = 66150.
Q18. A invests ₹60000 for 9 months and B invests ₹35000 for 6 months. Out of a total profit of ₹16125, what is A's share (in ₹)?
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Answer: A. 11610
Ratio = 60000×9 : 35000×6 = 18:7. A's share = 16125 × 18/25 = ₹11610.
Q19. Each exterior angle of a regular polygon is 36°. How many sides does it have?
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Answer: A. 10
Sides = 360/36 = 10.
Q20. Two cities are 210 km apart. Two cars start at the same time from the two cities towards each other at 42 km/h and 28 km/h. After how many hours will they meet?
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Answer: B. 3 hours
Time = 210/(42 + 28) = 3 hours.
Q21. Two trains of lengths 260 m and 110 m run in the same direction at 36 km/h and 72 km/h. How long will they take to cross each other completely?
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Answer: B. 37 seconds
Relative speed = 36 km/h = 10 m/s. Time = (260 + 110)/10 = 37 s.
Q22. The diagonals of a rhombus are 28 cm and 18 cm. Find its area.
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Answer: B. 252 cm²
½ × 28 × 18 = 252 cm².
Q23. The price of an item rises from ₹550 to ₹770. What is the percentage increase?
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Answer: D. 40%
Increase = 770 − 550 = 220. % increase = 220/550 × 100 = 40%.
Q24. A's salary is 20% more than B's salary. By what percent is B's salary less than A's?
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Answer: D. 16 2/3%
Let B = 100, so A = 120. B is less by 20/120 × 100 = 16 2/3%.
Q25. At 12% per annum simple interest, a sum earns ₹1200 as interest in 2 years. Find the sum (in ₹).
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Answer: B. 5000
P = 1200 × 100 / (12 × 2) = ₹5000.