Q1. The HCF of two numbers is 13 and their LCM is 182. If one of the numbers is 26, find the other.
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Answer: B. 91
Other number = (13 × 182) / 26 = 91.
SSC CGL Quantitative Aptitude Advanced Practice Set 4
25 advanced questions, suggested time 30 minutes. Tap an option to check it, or open “Show answer” for the explanation.
Topics: LCM and HCF, Number System, Algebra, Problems on Ages, Mensuration, Trigonometry, Mixture and Alligation, Partnership, Profit and Loss, Discount, Simple Interest, Compound Interest, Average, Ratio and Proportion, Pipes and Cisterns, Speed, Time and Distance, Percentage
Score: 0 / 0
Q2. What is the remainder when 9806 is divided by 13?
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Answer: A. 4
9806 = 13 × 754 + 4. Remainder = 4.
Q3. If x + 1/x = 7, find the value of x² + 1/x².
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Answer: B. 47
x² + 1/x² = 7² − 2 = 47.
Q4. A father's age is 4 times his son's age. After 5 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. 10 years
4x + 5 = 3x + 15 ⇒ x = 10 ⇒ x = 10 years.
Q5. Find the volume of a cylinder with radius 14 cm and height 11 cm. (Take π = 22/7)
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Answer: A. 6776 cm³
V = 22/7 × 14² × 11 = 6776 cm³.
Q6. Find the value of sin 60° × cos 30°.
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Answer: C. 3/4
(√3/2)(√3/2) = 3/4.
Q7. In what ratio must rice at ₹40/kg be mixed with rice at ₹60/kg so that the mixture costs ₹57/kg?
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Answer: D. 3:17
Ratio = (60 − 57) : (57 − 40) = 3:17.
Q8. A invests ₹15000 for 12 months and B invests ₹35000 for 8 months. Out of a total profit of ₹25231, what is A's share (in ₹)?
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Answer: B. 9873
Ratio = 15000×12 : 35000×8 = 9:14. A's share = 25231 × 9/23 = ₹9873.
Q9. A trader marks an article at ₹2300 and allows a discount of 25%. He still earns a profit of 50%. What is the cost price of the article (in ₹)?
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Answer: D. 1150
SP = 2300 × 75/100 = ₹1725. CP = 1725 × 100/150 = ₹1150.
Q10. Two successive discounts of 20% and 10% are equivalent to a single discount of:
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Answer: C. 28%
Equivalent = 20 + 10 − (20×10)/100 = 28%.
Q11. In how many years will a sum of money become four times itself at 5% per annum simple interest?
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Answer: A. 60 years
SI = 3P, so 3P = P × 5 × T / 100, giving T = 300/5 = 60 years.
Q12. What is the difference between compound interest and simple interest on ₹37500 for 2 years at 20% per annum (in ₹)?
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Answer: A. 1500
CI − SI = 37500 × (20/100)² = ₹1500.
Q13. The average of 5 consecutive even numbers is 46. What is the largest of these numbers?
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Answer: A. 50
The middle (3th) number is 46. The largest is 2 steps of 2 above it: 46 + 4 = 50.
Q14. Find the mean proportional between 75 and 45.
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Answer: B. 15
√(75 × 45) = √3375 = 15.
Q15. A pipe can fill a tank in 10 hours, while a leak can empty the full tank in 40 hours. If both are open, how long will it take to fill the tank?
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Answer: C. 13 1/3 hours
Net filled per hour = 1/10 − 1/40 = 30/400. Time = 400/30 = 13 1/3 hours.
Q16. A man travels from A to B at 30 km/h and returns at 60 km/h. What is his average speed for the whole journey?
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Answer: D. 40 km/h
Average speed = 2 × 30 × 60/(30 + 60) = 40 km/h.
Q17. The HCF of two numbers is 12 and their LCM is 180. If one of the numbers is 36, find the other.
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Answer: A. 60
Other number = (12 × 180) / 36 = 60.
Q18. What is the remainder when 1549 is divided by 7?
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Answer: A. 2
1549 = 7 × 221 + 2. Remainder = 2.
Q19. If x + 1/x = 8, find the value of x³ + 1/x³.
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Answer: A. 488
x³ + 1/x³ = 8³ − 3 × 8 = 512 − 24 = 488.
Q20. A father is 2 times as old as his son. If the son is 12 years old, what will the father's age be after 9 years?
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Answer: A. 33 years
Father's present age = 2 × 12 = 24. After 9 years: 33 years.
Q21. Find the area of a triangle whose sides are 6 cm, 8 cm and 10 cm.
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Answer: D. 24 cm²
6² + 8² = 10², so it is right-angled. Area = ½ × 6 × 8 = 24 cm².
Q22. Find the value of sec²θ − tan²θ.
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Answer: C. 1
sec²θ − tan²θ = 1.
Q23. In what ratio must rice at ₹30/kg be mixed with rice at ₹50/kg so that the mixture costs ₹35/kg?
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Answer: B. 3:1
Ratio = (50 − 35) : (35 − 30) = 15:5 = 3:1.
Q24. A invests ₹35000 for 8 months and B invests ₹60000 for 6 months. Out of a total profit of ₹15792, what is A's share (in ₹)?
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Answer: D. 6909
Ratio = 35000×8 : 60000×6 = 7:9. A's share = 15792 × 7/16 = ₹6909.
Q25. The price of a commodity is first increased by 25% and then decreased by 20%. What is the net percentage change?
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Answer: D. No change
Net change = 25 − 20 − (25×20)/100 = 0, so there is no change.