SSC CGL 2017 Tier II — Quantitative Abilities — 17 February 2018

Quantitative Abilities

1. 1. What is the unit digit of the sum of first 111 whole numbers?

   • (a) 4
   • (b) 6
   • (c) 5
   • (d) 0
   उत्तर देखें

   उत्तर: (c)

2. 2. How many 100 digit positive number are there?

   • (a) 9 × 1099
   • (b) 9 × 10100
   • (c) 10100
   • (d) 11 × 1098
   उत्तर देखें

   उत्तर: (a)

3. 5. What is the unit digit of (217)413 × (819)547 × (414)624 × (342)812?

   • (a) 2
   • (b) 4
   • (c) 6
   • (d) 8
   उत्तर देखें

   उत्तर: (d)

4. 8. N is the largest two digit number, which when divided by 3, 4 and 6 leaves the remainder 1, 2 and 4 respectively. What is the remainder when N is divided by 5?

   • (a) 4
   • (b) 2
   • (c) 0
   • (d) 1
   उत्तर देखें

   उत्तर: (a)

5. 10. A and B are positive integers. If A + B + AB = 65, then what is the difference between A and B (A, B ≤ 15)?

   • (a) 3
   • (b) 4
   • (c) 5
   • (d) 6
   उत्तर देखें

   उत्तर: (c)

6. 11. What is the value of 143 + 163 + 183 + … + 303?

   • (a) 134576
   • (b) 120212
   • (c) 115624
   • (d) 111672
   उत्तर देखें

   उत्तर: (d)

7. 13. If x + y + z = 0, then what is the value of (3y2 + x2 + z2)/(2y2 – xz)?

   • (a) 2
   • (b) 1
   • (c) 3/2
   • (d) 5/3
   उत्तर देखें

   उत्तर: (a)

8. 14. If P = 7 + 4√3 and PQ = 1, then what is the value of 1/P2 + 1/Q2?

   • (a) 196
   • (b) 194
   • (c) 206
   • (d) 182
   उत्तर देखें

   उत्तर: (b)

9. 15. If a3 + 3a2 + 9a = 1, then what is the value of a3 + (3/a)?

   • (a) 31
   • (b) 26
   • (c) 28
   • (d) 24
   उत्तर देखें

   उत्तर: (c)

10. 16. x, y and z are real numbers. If x3 + y3 + z3 = 13,x + y + z = 1 and xyz = 1, then what is the value of xy + yz + zx?

    • (a) – 1
    • (b) 1
    • (c) 3
    • (d) – 3
    उत्तर देखें

    उत्तर: (d)

11. 17. If (a + b)/c = 6/5 and (b + c)/a = 9/2, then what is the value of (a + c)/b?

    • (a) 9/5
    • (b) 11/7
    • (c) 7/11
    • (d) 7/4
    उत्तर देखें

    उत्तर: (d)

12. 18. If x3 + y3 + z3 = 3(1 + xyz), P = y + z – x, Q = z + x – y and R = x + y – z, then what is the value of P3 + Q3 + R3– 3PQR?

    • (a) 9
    • (b) 8
    • (c) 12
    • (d) 6
    उत्तर देखें

    उत्तर: (c)

13. 19. If x1x2x3 = 4(4 + x1 + x2 + x3), then what is the value of [1/(2 + x1)] + [1/(2 + x2)] + [1/(2 + x3)]?

    • (a) 1
    • (b) 1/2
    • (c) 2
    • (d) 1/3
    उत्तर देखें

    उत्तर: (b)

14. 21. If 3x + 5y + 7z = 49 and 9x + 8y + 21z = 126, then what is the value of y?

    • (a) 4
    • (b) 2
    • (c) 3
    • (d) 5
    उत्तर देखें

    उत्तर: (c)

15. 22. Cost of 4 pens, 6 note books and 9 files is Rs 305. Cost of 3 pens, 4 notebooks and 2 files is Rs 145. What is the cost (in Rs) of 5 pens, 8 notebooks and 16 files?

    • (a) 415
    • (b) 465
    • (c) 440
    • (d) Cannot be determined
    उत्तर देखें

    उत्तर: (b)

16. 23. ABC is a right angled triangle. ∠BAC = 90o and ∠ACB = 60o. What is the ratio of the circum radius of the triangle to the side AB?

    • (a) 1 : 2
    • (b) 1 : √3
    • (c) 2 : √3
    • (d) 2 : 3
    उत्तर देखें

    उत्तर: (b)

17. 25. Triangle ABC is similar to triangle PQR and AB : PQ = 2 : 3. AD is the median to the side BC in triangle ABC and PS is the median to the side QR in triangle PQR. What is the value of (BD/QS)2?

    • (a) 3/5
    • (b) 4/9
    • (c) 2/3
    • (d) 4/7
    उत्तर देखें

    उत्तर: (b)

18. 28. AB and AC are the two tangents to a circle whose radius is 6 cm. If ∠BAC = 60o, then what is the value (in cm) of √(AB2 + AC2)?

    • (a) 6√6
    • (b) 4√6
    • (c) 9√3
    • (d) 8√3
    उत्तर देखें

    उत्तर: (a)

19. 32. The radius of two circles is 3 cm and 4 cm. The distance between the centres of the circles is 10 cm. What is the ratio of the length of direct common tangent to the length of the transverse common tangent?

    • (a) √51 : √68
    • (b) √33 : √17
    • (c) √66 : √51
    • (d) √28 : √17
    उत्तर देखें

    उत्तर: (b)

20. 33. ABC is a triangle. AB = 5 cm, AC = √41 cm and BC = 8 cm. AD is perpendicular to BC. What is the area (in cm2) of triangle ABD?

    • (a) 12
    • (b) 6
    • (c) 10
    • (d) 20
    उत्तर देखें

    उत्तर: (b)

21. 37. एक आयत की लम्बाई तथा चौड़ाई (से.मी. आयत में) क्या है? क्रमशः 8 से.मी. तथा 6 से.मी. हैं। आयत को उसके चार शीर्षों पर इस प्रकार काटा जाता है कि मिलने वाली आकृति एक सम अष्टभुज है। अष्टभुज की भुजा

    • (a) 3(√11) – 7
    • (b) 5(√13) – 8
    • (c) 4(√7) – 11
    • (d) 6(√11) – 9
    उत्तर देखें

    उत्तर: (a)

22. 41. Radius of base of a hollow cone is 8 cm and its height is 15 cm. A sphere of largest radius is put inside the cone. What is the ratio of radius of base of cone to the radius of sphere?

    • (a) 5 : 3
    • (b) 4 : 1
    • (c) 2 : 1
    • (d) 7 : 3
    उत्तर देखें

    उत्तर: (a)

23. 42. The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2 : 1. If the total surface area of cylinder is 23100 cm2, then what is the volume (in cm3) of cylinder?

    • (a) 247200
    • (b) 269500
    • (c) 312500
    • (d) 341800
    उत्तर देखें

    उत्तर: (b)

24. 44. 10 identical solid spherical balls of radius 3 cm are melted to form a single sphere. In this process 20% of solid is wasted. What is the radius (in cm) of the bigger sphere?

    • (a) 24
    • (b) 12
    • (c) 8
    • (d) 6
    उत्तर देखें

    उत्तर: (d)

25. 45. The radius of base of a solid cylinder is 7 cm and its height is 21 cm. It is melted and converted into small bullets. Each bullet is of same size. Each bullet consisted of two parts viz. a cylinder and a hemisphere on one of its base. The total height of bullet is 3.5 cm and radius of base is 2.1 cm. Approximately how many complete bullets can be obtained?

    • (a) 83
    • (b) 89
    • (c) 74
    • (d) 79
    उत्तर देखें

    उत्तर: (a)

26. 46. A cuboid of size 50 cm × 40 cm × 30 cm is cut into 8 identical parts by 3 cuts. What is the total surface area (in cm2) of all the 8 parts?

    • (a) 11750
    • (b) 14100
    • (c) 18800
    • (d) 23500
    उत्तर देखें

    उत्तर: (c)

27. 48. [(sin x + sin y) (sin x — sin y)]/[(cosx + cosy) (cosy - cosx)] का मान है?

    • (a) 0
    • (b) 1
    • (c) – 1
    • (d) 2
    उत्तर देखें

    उत्तर: (b)

28. 49. What is the value of [(tan 5θ + tan 3θ)/4 cos 4θ (tan 5θ – tan 3θ)]?

    • (a) sin 2θ
    • (b) cos 2θ
    • (c) tan 4θ
    • (d) cot 2θ
    उत्तर देखें

    उत्तर: (b)

29. 50. What is the value of (4/3) cot2 (p/6) + 3 cos2 (150o) – 4 cosec2 45o + 8 sin (p/2)?

    • (a) 25/4
    • (b) 1
    • (c) – 7/2
    • (d) 13/2
    उत्तर देखें

    उत्तर: (a)

30. 51. sin (B – C) cos (A – D) + sin (A – B) cos (C – D) + sin (C – A) cos (B – D) का मान है?

    • (a) 3/2
    • (b) – 3
    • (c) 1
    • (d) 0
    उत्तर देखें

    उत्तर: (d)

31. 53. What is the value of cos [(180 – θ)/2] cos [(180 – 9θ)/2] + sin [(180 – 3θ)/2] sin [(180 – 13θ)/2]?

    • (a) sin 2θ sin 4θ
    • (b) cos 2θ cos 6θ
    • (c) sin 2θ sin 6θ
    • (d) cos 2θ cos 4θ
    उत्तर देखें

    उत्तर: (b)

32. 54. What is the value of [tan2 (90 – θ) – sin2 (90 – θ)] cosec2 (90 – θ) cot2 (90 – θ)?

    • (a) 0
    • (b) 1
    • (c) – 1
    • (d) 2
    उत्तर देखें

    उत्तर: (b)

33. 56. The tops of two poles of height 60 metres and 35 metres are connected by a rope. If the rope makes an angle with the horizontal whose tangent is 5/9 metres, then what is the distance (in metres) between the two poles?

    • (a) 63
    • (b) 30
    • (c) 25
    • (d) 45
    उत्तर देखें

    उत्तर: (d)

34. 57. A Navy captain going away from a lighthouse at the speed of 4[(√3) – 1] m/s. He observes that it takes him 1 minute to change the angle of elevation of the top of the lighthouse from 60o to 45o. What is the height (in metres) of the lighthouse?

    • (a) 240√3
    • (b) 480[(√3) – 1]
    • (c) 360√3
    • (d) 280√2
    उत्तर देखें

    उत्तर: (a)

35. 58. If A equals to 15% of total applicants who are present at exam centre F and B equals to present applicants at exam centre K, then A is what percent of B?

    • (a) 18.18
    • (b) 11.25
    • (c) 13.33
    • (d) 14.28
    उत्तर देखें

    उत्तर: (b)

36. 59. Total number of offline applicants from exam centre H, K and F are how much less than the total number of present applicants from exam centre G and J?

    • (a) 111420
    • (b) 100920
    • (c) 127370
    • (d) 109990
    उत्तर देखें

    उत्तर: (b)

37. 60. What are the total number of offline applicants from the exam centre F, H, J and G?

    • (a) 393720
    • (b) 963000
    • (c) 564720
    • (d) 428540
    उत्तर देखें

    उत्तर: (c)

38. 61. What is the ratio of total number of present applicants from exam centre K to total number of offline applicants from exam centre J?

    • (a) 40 : 41
    • (b) 80 : 81
    • (c) 10 : 9
    • (d) 7 : 11
    उत्तर देखें

    उत्तर: (b)

39. 62. What are the total number of present applicants from exam centre H and G together?

    • (a) 238200
    • (b) 151800
    • (c) 388200
    • (d) 442650
    उत्तर देखें

    उत्तर: (c)

40. 63. Solution A contains 10% acid and solution B contains 30% acid. In what ratio should solution A be mixed with Solution B to obtain a mixture with 25% acid?

    • (a) 1 : 2
    • (b) 3 : 1
    • (c) 1 : 3
    • (d) 2 : 1
    उत्तर देखें

    उत्तर: (c)

41. 64. In what ratio should coffee powder costing Rs 2500/kg be mixed with coffee powder costing Rs 1500/kg so that the cost of the mixture is Rs 2250/kg?

    • (a) 1 : 4
    • (b) 4 : 1
    • (c) 3 : 1
    • (d) 1 : 3
    उत्तर देखें

    उत्तर: (c)

42. 65. A and B started a partnership business investing in the ratio of 3 : 8. C joined them after 4 months with an amount equal to 3/4th of B. What was their profit (in Rs) at the end of the year if C got Rs 24,000 as his share?

    • (a) 120000
    • (b) 150000
    • (c) 90000
    • (d) 180000
    उत्तर देखें

    उत्तर: (c)

43. 66. A and B invest in a business in the ratio 4 : 5. After 10 months B leaves the business after withdrawing his investment. In the first year the business made a profit of Rs 49,000. What is B's share (in Rs) of this profit?

    • (a) 25000
    • (b) 20000
    • (c) 18000
    • (d) 22000
    उत्तर देखें

    उत्तर: (a)

44. 67. Working together A and B can do a job in 40 days, B and C in 36 days and all three together in 24 days. In how many days can B alone do the job?

    • (a) 60
    • (b) 90
    • (c) 72
    • (d) 120
    उत्तर देखें

    उत्तर: (b)

45. 68. A, B and C can do a job working alone in 50, 75 and 20 days respectively. They all work together for 4 days, then C quits. How many days will A and B take to finish the rest of the job?

    • (a) 20
    • (b) 30
    • (c) 18
    • (d) 24
    उत्तर देखें

    उत्तर: (a)

46. 69. A can do 50% of the job in 16 days, B can do 1/4th of the job in 24 days. In how many days can they do 3/4th of the job working together?

    • (a) 24
    • (b) 9
    • (c) 21
    • (d) 18
    उत्तर देखें

    उत्तर: (d)

47. 70. A and B can together complete a task in 18 hours. After 6 hours A leaves. B takes 36 hours to finish rest of the task. How many hours would A have taken to do the task if he worked alone?

    • (a) 54
    • (b) 45
    • (c) 21
    • (d) 27
    उत्तर देखें

    उत्तर: (d)

48. 71. 1 packet of biscuits costs Rs 16 but a pack of 4 of the same packet of biscuits costs Rs 56. What is the effective discount (in %) on the pack?

    • (a) 8
    • (b) 10
    • (c) 7.5
    • (d) 12.5
    उत्तर देखें

    उत्तर: (d)

49. 72. किसी वस्तु का लागत मूल्य रूपये है। इसे 200% से बढ़ाकर अंकित किया गया। 25% छूट देने के बाद इसे 540 रुपयों में बेचा गया। x का मान (रुपयों में) है?

    • (a) 360
    • (b) 250
    • (c) 300
    • (d) 240
    उत्तर देखें

    उत्तर: (d)

50. 73. A Rs 750 tin of cheese is offered at 8% discount and a Rs 1,250 tin of butter at 20% discount. If we buy 5 tins of cheese and 3 tins of butter, what is the effective discount we get (in %)?

    • (a) 12
    • (b) 15
    • (c) 14
    • (d) 16
    उत्तर देखें

    उत्तर: (c)

51. 74. The selling price of an article is Rs 816 if the discount on it is 15%. What would be the selling price of the article (in Rs) if the discount on it is 25%?

    • (a) 750
    • (b) 720
    • (c) 800
    • (d) 700
    उत्तर देखें

    उत्तर: (b)

52. 75. The entry ticket at a fun park was increased in the ratio 7 : 9, due to which footfalls fell in the ratio 13 : 11. What is the new daily collection (in Rs), if the daily collection before the price hike was Rs 2,27,500?

    • (a) 237500
    • (b) 247500
    • (c) 232500
    • (d) 242500
    उत्तर देखें

    उत्तर: (b)

53. 76. If 6A = 4B = 9C; What is A : B : C?

    • (a) 6 : 4 : 9
    • (b) 9 : 4 : 6
    • (c) 4 : 9 : 6
    • (d) 6 : 9 : 4
    उत्तर देखें

    उत्तर: (d)

54. 77. If 50 less had applied and 25 less selected, the ratio of selected to unselected would have been 9 : 4. So how many candidates had applied if the ratio of selected to unselected was 2 : 1.

    • (a) 125
    • (b) 250
    • (c) 375
    • (d) 500
    उत्तर देखें

    उत्तर: (c)

55. 78. What is the fourth proportional to 189, 273 and 153?

    • (a) 117
    • (b) 299
    • (c) 221
    • (d) 187
    उत्तर देखें

    उत्तर: (c)

56. 79. Rs 11,550 has to be divided between X, Y & Z such that X gets 4/5 of what Y gets and Y gets 2/3 of what Z gets. How much more does Z get over X (in Rs)? 11,550

    • (a) 7200
    • (b) 1800
    • (c) =13*9
    • (d) 2450
    उत्तर देखें

    उत्तर: (d)

57. 80. Before a battle the ratio of tanks to planes in an army was 5 : 3. During the war 1000 tanks were destroyed and 800 planes were destroyed. The ratio of tanks to planes became 2 : 1. What is the number of tanks after the war.

    • (a) 2000
    • (b) 1000
    • (c) 3000
    • (d) 4000
    उत्तर देखें

    उत्तर: (a)

58. 81. 50 छात्रों के किसी परीक्षा में औसत अंक 65 थे। बाद में ऐसा पता चला की किसी छात्र के अंक 38 के बजाय 83 जोड़ दिए गए थे। सही औसत होगा?

    • (a) 63.9
    • (b) 64.5
    • (c) 64.7
    • (d) 64.1
    उत्तर देखें

    उत्तर: (d)

59. 82. 50 छात्रों की एक कक्षा में 22 लडकियाँ है जिन्होनें परीक्षा में औसत 35 अंक अर्जित किये। यदि कक्षा का औसत 42 अंक है तो लड़कों के औसत अंक कितने हैं?

    • (a) 50
    • (b) 52.5
    • (c) 47.5
    • (d) 55
    उत्तर देखें

    उत्तर: (c)

60. 83. The average of 41 consecutive odd numbers is 49. What is the largest number. 41

    • (a) 89
    • (b) 91
    • (c) 93
    • (d) 95
    उत्तर देखें

    उत्तर: (a)

61. 84. A batsman scores 87 runs in the 21st match of his career. His average runs per match increases by 2. What was his average before the 21st match.

    • (a) 45
    • (b) 46
    • (c) 44
    • (d) 43
    उत्तर देखें

    उत्तर: (a)

62. 85. Oil equal to 20% of the weight of ground nut is extracted in a mill. The matter left after extraction is sold as cattle feed at the rate of Rs 12.5/kg. The groundnuts are bought at Rs 20/kg. The processing cost is Rs 5/kg. At what price (Rs per kg) should the oil be sold to earn 20% profit on total costs (Total cost = Cost of groundnuts and Processing costs)?

    • (a) 250
    • (b) 150
    • (c) 200
    • (d) 100
    उत्तर देखें

    उत्तर: (d)

63. 86. If a vendor sells a coconut at Rs 14.4 he makes 10% loss. If he wants to make 25% profit, then at what price (in Rs) should he sell?

    • (a) 18
    • (b) 20
    • (c) 16
    • (d) 22
    उत्तर देखें

    उत्तर: (b)

64. 87. At a village trade fair a man buys a horse and a camel together for Rs 51,250. He sold the horse at a profit of 25 % and the camel at a loss of 20 %. If he sold both the animals at the same price, then the cost price of the cheaper animal was Rs ____________.

    • (a) 6600
    • (b) 7500
    • (c) 25000
    • (d) 20000
    उत्तर देखें

    उत्तर: (d)

65. 88. On a certain item profit is 150%. If the cost price increases by 25% what will be the new profit margin (in %)?

    • (a) 25
    • (b) 50
    • (c) 100
    • (d) 75
    उत्तर देखें

    उत्तर: (c)

66. 89. 40% are the passing marks. A student gets 250 marks yet fails by 38 marks. What is the maximum marks?

    • (a) 720
    • (b) 750
    • (c) 800
    • (d) 840
    उत्तर देखें

    उत्तर: (a)

67. 90. Ravi is 12 years younger than Surya. Ravi's age is 40% of the sum of his and Surya's age. What will be Surya's age 9 years hence?

    • (a) 36
    • (b) 24
    • (c) 33
    • (d) 45
    उत्तर देखें

    उत्तर: (d)

68. 91. 5% of a = b, then b% of 20 is the same as __________.

    • (a) 20% of a/2
    • (b) 50% of a/20
    • (c) 50% of a/2
    • (d) 20% of a/20
    उत्तर देखें

    उत्तर: (d)

69. 92. A man's annual income has increased by Rs 5 lakhs but the tax on income that he has to pay has reduced from 12% to 10%. He now pays Rs 10,000 more income tax. What is his increased income (in Rs lakhs)?

    • (a) 20
    • (b) 25
    • (c) 15
    • (d) 10
    उत्तर देखें

    उत्तर: (b)

70. 93. A racing car going at an average speed of 108 km/hr takes 15 minutes to complete a lap on a racing track. By how much should it increase its speed (in km/hr) to complete the lap in 12 minutes?

    • (a) 24
    • (b) 21
    • (c) 27
    • (d) 30
    उत्तर देखें

    उत्तर: (c)

71. 94. Train A takes 45 minutes more than train B to travel a distance of 450 km. Due to engine trouble speed of train B falls by a quarter, so it takes 30 minutes more than Train A to complete the same journey. What is the speed of Train A (in km/hr)?

    • (a) 90
    • (b) 120
    • (c) 100
    • (d) 110
    उत्तर देखें

    उत्तर: (c)

72. 95. Two cars A and B travel from one city to another, at speeds of 72 km/hr and 90 km/hr respectively. If car B takes 1 hour lesser than car A for the journey, then what is the distance (in km) between the two cities?

    • (a) 270
    • (b) 360
    • (c) 240
    • (d) 400
    उत्तर देखें

    उत्तर: (b)

73. 96. B starts 4 minutes after A from the same point, for a place at a distance of 7 miles from the starting point. A on reaching the destination turns back and walks a mile where he meets B. If A's speed is a mile in 8 minutes then B's speed is a mile in ____ minutes.

    • (a) 9
    • (b) 12
    • (c) 10
    • (d) 8
    उत्तर देखें

    उत्तर: (c)

74. 97. If the amount on a certain principal in 3 years at 12% rate of interest compounded annually is Rs 12,000, what will be the amount (in Rs) after the 4th year?

    • (a) 14330
    • (b) 15440
    • (c) 13440
    • (d) 14550
    उत्तर देखें

    उत्तर: (c)

75. 98. The amount (in Rs) received at 10% per annum compound interest after 3 yrs is Rs 1,19,790. What was the principal?

    • (a) 90000
    • (b) 1,00,000
    • (c) 80000
    • (d) 75000
    उत्तर देखें

    उत्तर: (a)

76. 99. In how many months will Rs 8,000 yield Rs 2,648 as compound interest at 20% per annum compounded semi-annually?

    • (a) 18
    • (b) 24
    • (c) 12
    • (d) 30
    उत्तर देखें

    उत्तर: (a)

77. 100. What is the rate of interest (in %) if simple interest earned on a certain sum for the 3rd year is Rs 2,000 and compound interest earned in 2 years is Rs 4,160?

    • (a) 8
    • (b) 10
    • (c) 12
    • (d) 6
    उत्तर देखें

    उत्तर: (a)