Q1. What is the smallest 4-digit number exactly divisible by 19?
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Answer: D. 1007
1000 ÷ 19 leaves remainder 12. 1000 + 7 = 1007.
SSC CGL Quantitative Aptitude Intermediate Practice Set 11
25 intermediate questions. Tap an option to check it, or open “Show answer” for the explanation.
Topics: Number System, Average, Problems on Ages, Simplification, Indices and Surds, Speed, Time and Distance, Geometry, Mensuration, Time and Work, Mixture and Alligation, Partnership, Statistics, Percentage, Profit and Loss, Simple Interest
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Q2. A batsman has an average of 36 runs after 13 innings. How many runs must he score in the next innings to raise his average by 1?
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Answer: D. 50
New total = 14 × 37 = 518; old total = 13 × 36 = 468. Runs = 50.
Q3. A father's age is 5 times his son's age. After 13 years, the father will be 3 times as old as his son. What is the son's present age?
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Answer: B. 13 years
5x + 13 = 3x + 39 ⇒ 2x = 26 ⇒ x = 13 years.
Q4. Find the value of 62² − 31².
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Answer: A. 2883
(62 + 31)(62 − 31) = 93 × 31 = 2883.
Q5. What is the largest 4-digit number exactly divisible by 19?
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Answer: C. 9994
9999 ÷ 19 leaves remainder 5. 9999 − 5 = 9994.
Q6. Find the value of (5^4 × 5^2) ÷ 5^2.
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Answer: D. 625
5^(4 + 2 − 2) = 5^4 = 625.
Q7. Two trains of lengths 120 m and 160 m run in the same direction at 60 km/h and 72 km/h. How long will they take to cross each other completely?
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Answer: A. 84 seconds
Relative speed = 12 km/h = 3 1/3 m/s. Time = (120 + 160)/3 1/3 = 84 s.
Q8. What is the measure of each interior angle of a regular polygon with 5 sides?
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Answer: D. 108°
(5 − 2) × 180/5 = 108°.
Q9. Find the total surface area of a solid hemisphere of radius 7 cm. (Take π = 22/7)
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Answer: C. 462 cm²
TSA = 3 × 22/7 × 7² = 462 cm².
Q10. 25 men can complete a work in 18 days. In how many days can 5 men complete the same work?
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Answer: B. 90 days
25 × 18 = 5 × D ⇒ D = 450/5 = 90 days.
Q11. In what ratio must rice at ₹30/kg be mixed with rice at ₹50/kg so that the mixture costs ₹34/kg?
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Answer: D. 4:1
Ratio = (50 − 34) : (34 − 30) = 16:4 = 4:1.
Q12. The diagonals of a rhombus are 48 cm and 14 cm. Find its area.
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Answer: C. 336 cm²
½ × 48 × 14 = 336 cm².
Q13. Find the value of (3^6 × 3^4) ÷ 3^4.
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Answer: A. 729
3^(6 + 4 − 4) = 3^6 = 729.
Q14. A invests ₹25000 for 6 months and B invests ₹20000 for 12 months. Out of a total profit of ₹11193, what is A's share (in ₹)?
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Answer: D. 4305
Ratio = 25000×6 : 20000×12 = 5:8. A's share = 11193 × 5/13 = ₹4305.
Q15. Find the median of: 23, 32, 45, 2, 22, 5, 25, 54, 15.
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Answer: A. 23
In order: 2, 5, 15, 22, 23, 25, 32, 45, 54. Median = 23.
Q16. Find the value of √1681 + 9².
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Answer: C. 122
√1681 = 41; 9² = 81; total = 122.
Q17. Two cities are 270 km apart. Two cars start at the same time from the two cities towards each other at 47 km/h and 25 km/h. After how many hours will they meet?
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Answer: D. 3.75 hours
Time = 270/(47 + 25) = 3.75 hours.
Q18. The price of an item rises from ₹900 to ₹1080. What is the percentage increase?
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Answer: D. 20%
Increase = 1080 − 900 = 180. % increase = 180/900 × 100 = 20%.
Q19. Two trains of lengths 250 m and 140 m run in the same direction at 90 km/h and 108 km/h. How long will they take to cross each other completely?
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Answer: A. 78 seconds
Relative speed = 18 km/h = 5 m/s. Time = (250 + 140)/5 = 78 s.
Q20. The diagonals of a rhombus are 46 cm and 18 cm. Find its area.
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Answer: D. 414 cm²
½ × 46 × 18 = 414 cm².
Q21. A shopkeeper buys a watch for ₹2000 and sells it for ₹2300. Find the profit or loss percentage.
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Answer: B. 15% profit
Profit = |2300 − 2000| = ₹300. Profit% = 300/2000 × 100 = 15%.
Q22. A's salary is 25% more than B's salary. By what percent is B's salary less than A's?
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Answer: A. 20%
Let B = 100, so A = 125. B is less by 25/125 × 100 = 20%.
Q23. At 5% per annum simple interest, a sum earns ₹1750 as interest in 5 years. Find the sum (in ₹).
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Answer: C. 7000
P = 1750 × 100 / (5 × 5) = ₹7000.
Q24. The price of an item rises from ₹950 to ₹1330. What is the percentage increase?
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Answer: A. 40%
Increase = 1330 − 950 = 380. % increase = 380/950 × 100 = 40%.
Q25. The population of a town is 100000. It increases by 20% every year. What will the population be after 2 years?
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Answer: A. 144000
100000 × (120/100)^2 = 144000.