SSC CGL 2017 Tier II — Quantitative Abilities — 20 February 2018

Quantitative Abilities

1. 1. Which of the following statement(s) is/are TRUE? 3 I. 33 > 3 33 3 3 II. 333 > (3 )

   • (a) Only I I
   • (b) Only II II
   • (c) Both I and II I II
   • (d) Neither I nor II
   उत्तर देखें

   उत्तर: (d)

2. 2. If P = 2 + 6 + 10 + 14 + … 94 and Q = 1 + 5 + 9 + … 81 , then what is the value of P – Q?

   • (a) 24645
   • (b) 26075
   • (c) 29317
   • (d) 31515
   उत्तर देखें

   उत्तर: (b)

3. 3. If A = (1/0.4) + (1/0.04) + (1/0.004) + … upto 8 terms, then what is the value of A?

   • (a) 27272727.5
   • (b) 25252525.5
   • (c) 27777777.5
   • (d) 25555555.5
   उत्तर देखें

   उत्तर: (c)

4. 4. If M = 0.1 + (0.1) + (0.01) and N = 0.3 + (0.03) + (0.003) , then what is the value of M + N?

   • (a) 0.411009
   • (b) 0.413131
   • (c) 0.313131
   • (d) 0.131313
   उत्तर देखें

   उत्तर: (a)

5. 8. Which of the following statement(s) is/are TRUE? I. The total number of positive factors of 72 is 12. II. The sum of first 20 odd numbers is 400. III. Largest two digit prime number is 97.

   • (a) Only I and II I II
   • (b) Only II and III
   • (c) Only I and III I III
   • (d) All are true.
   उत्तर देखें

   उत्तर: (d)

6. 11. Which of the following statement(s) is/are TRUE? I. √11 + √7 < √10 + √8. II. √17 + √11 > √15 + √13

   • (a) Only I
   • (b) Only II
   • (c) Both I and II I II
   • (d) Neither I nor II
   उत्तर देखें

   उत्तर: (a)

7. 13. If x + y + z = 22 and xy + yz + zx = 35, then what is the value of (x – y) + (y – z) + (z – x) ? 2

   • (a) 793
   • (b) 681
   • (c) 758
   • (d) 715
   उत्तर देखें

   उत्तर: (c)

8. 16. If one root of the equation Ax +Bx + C = 0 is two and a half times the others, then which of the following is TRUE?

   • (a) 7B = 3 CA 2
   • (b) 7B = 4 CA 2
   • (c) 7B = 36 CA 2
   • (d) 10B = 49 CA 2
   उत्तर देखें

   उत्तर: (d)

9. 21. If 3x + 4y – 2z + 9 = 17, 7x + 2y + 11z + 8 = 23 and 5x + 9y + 6z – 4 = 18, then what is the value of x + y + z – 34?

   • (a) – 28
   • (b) – 14
   • (c) – 31
   • (d) – 45
   उत्तर देखें

   उत्तर: (c)

10. 36. ABCDEF is a regular hexagon of side 12 cm. What is the area (in cm ) of the triangle ECD? ABCDEF 12 . .

    • (a) 18√3
    • (b) 24√3
    • (c) 36√3
    • (d) 42√3
    उत्तर देखें

    उत्तर: (c)

11. 41. The radius of base of solid cone is 9 cm and its height is 21 cm. It cut into 3 parts by two cuts, which are parallel to its base. The cuts are at height of 7 cm and 14 cm from the base respectively. What is the ratio of curved surface areas of top, middle and bottom parts respectively?

    • (a) 1 : 4 : 8
    • (b) 1 : 3 : 5
    • (c) 1 : 3 : 9
    • (d) 1 : 6 : 12
    उत्तर देखें

    उत्तर: (b)

12. 43. The ratio of curved surface area and volume of a cylinder is 1 : 7. The ratio of total surface area and volume is 187 : 770. What is the respective ratio of its base radius and height?

    • (a) 5 : 8
    • (b) 4 : 9
    • (c) 3 : 7
    • (d) 7 : 10
    उत्तर देखें

    उत्तर: (d)

13. 44. The ratio of total surface area and volume of a sphere is 1 : 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is 1/6 th 2 the radius of the large sphere. What is the sum (in cm ) of curved surface areas of all small spheres?

    • (a) 31276
    • (b) 36194
    • (c) 25182
    • (d) 33264
    उत्तर देखें

    उत्तर: (d)

14. 46. A solid cube has side 8 cm. It is cut along diagonals of top face to get 4 equal parts. What is the total surface area (in cm ) of each part?

    • (a) 96 + 64√2
    • (b) 80 + 64√2
    • (c) 96 + 48√2
    • (d) 80 + 48√2
    उत्तर देखें

    उत्तर: (a)

15. 48. What is the value of [sin (y – z) + sin (y + z) + 2 sin y]/[sin (x – z) + sin (x + z) + 2 sin x]? [sin (y – z) + sin (y + z) + 2 sin y]/[sin (x – z) + sin (x + z) + 2 sin x]

    • (a) cos sin
    • (b) (sin )/(sin )
    • (c) sin
    • (d) sin tan
    उत्तर देखें

    उत्तर: (b)

16. 49. What is the value of {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]? {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]

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

    उत्तर: (b)

17. 51. If sec θ (cos θ + sin θ) = √2, then what is the value of (2 sin θ)/(cos θ – sin θ)?

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

    उत्तर: (d)

18. 54. What is the value of {sin (90 – x) cos [π – (x – y)]} + {cos (90 – x) sin [π – (y – x)]}? {sin (90 – x) cos [π – (x – y)]} + {cos (90 – x) sin [π – (y – x)]}

    • (a) -cos
    • (b) -sin
    • (c) cos x
    • (d) tan
    उत्तर देखें

    उत्तर: (a)

19. 55. The angle of elevation of an aeroplane from a point on the ground is 60 . After flying for 30 seconds, the angle of elevation o changes to 30 . If the aeroplane is flying at a height of 4500 m, then what is the speed (in m/s) of aeroplane?

    • (a) 50√3
    • (b) 100√3
    • (c) 200√3
    • (d) 300√3
    उत्तर देखें

    उत्तर: (b)

20. 56. A kite is flying in the sky. The length of string between a point on the ground and kite is 420 m. The angle of elevation of string with o the ground is 30 . Assuming that there is no slack in the string, then what is the height (in metres) of the kite?

    • (a) 210
    • (b) 140√3
    • (c) 210√3
    • (d) 150
    उत्तर देखें

    उत्तर: (a)

21. 60. An alloy is made by mixing metal A costing Rs 2000/kg and metal B costing Rs 400/kg in the ratio A:B = 3:1. What is the cost (in Rs) of 8 kilograms of this alloy?

    • (a) 1600
    • (b) 9800
    • (c) 6400
    • (d) 12800
    उत्तर देखें

    उत्तर: (d)

22. 61. A, B and C invest to start a restaurant. The total investment was Rs 3 lakhs. B invested Rs 50,000 more than A and C invested Rs 25,000 less than B. If the profit at the end of the year was Rs 14,400 then what is C's share of the profit (in Rs)? A, B

    • (a) 3600
    • (b) 4800
    • (c) 6000
    • (d) 7200
    उत्तर देखें

    उत्तर: (b)

23. 62. Two businessmen A and B invest in a business in the ratio 5 : 8. They decided to reinvest 30% of the profit they earned back into the business. The remaining profit they distributed amongst themselves. If A's share of the profit was Rs 87,500 then how much profit (in Rs) did the business make?

    • (a) 227000
    • (b) 250000
    • (c) 375000
    • (d) 325000
    उत्तर देखें

    उत्तर: (d)

24. 63. Working alone A can do the task in 27 hours and B can do it in 54 hours. Find C's share (in Rs) if A, B and C get paid Rs 4,320 for completing a task in 12 hours on which they worked together.

    • (a) 1440
    • (b) 960
    • (c) 1920
    • (d) 1280
    उत्तर देखें

    उत्तर: (a)

25. 64. If A had worked alone he would have taken 63 hours to do the task. What is B's share, if A and B work together on a task finishing it in 36 hours and they get paid Rs 5,950 for it?

    • (a) 3400
    • (b) 3600
    • (c) 2550
    • (d) 2750
    उत्तर देखें

    उत्तर: (c)

26. 68. A retailer marks up his goods by 150% and offers 40% discount. What will be the selling price (in Rs) if the cost price is Rs 800?

    • (a) 1200
    • (b) 1500
    • (c) 1000
    • (d) 2000
    उत्तर देखें

    उत्तर: (a)

27. 69. On a television of brand A the discount is 25% and on television of brand B the discount is 40%. The price of B after discount Rs 2,250 greater than the price of A after discount. What is the marked price of A (in Rs) if marked price of B is Rs 35,000?

    • (a) 18750
    • (b) 21000
    • (c) 25000
    • (d) 17850
    उत्तर देखें

    उत्तर: (c)

28. 70. If 60% discount is offered on the marked price and selling price becomes equal to cost price then what was the % mark up?

    • (a) 100
    • (b) 250
    • (c) 150
    • (d) 40
    उत्तर देखें

    उत्तर: (c)

29. 72. How many job applicants had applied if the ratio of selected to unselected was 19:17. If 1,200 less had applied and 800 less selected, then the ratio of selected to unselected would have been 1:1.

    • (a) 6000
    • (b) 7200
    • (c) 8400
    • (d) 4800
    उत्तर देखें

    उत्तर: (b)

30. 74. The ratio of the sum of the salaries of A and B to the difference of their salaries is 11:1 and the ratio of the sum of the salaries of B and C to the difference of their salaries is also 11:1. If A's salary is the highest and C's is the lowest then what is B's salary (in Rs) given the total of all their salaries is Rs 1,82,000? A

    • (a) 72000
    • (b) 60000
    • (c) 50000
    • (d) 86400
    उत्तर देखें

    उत्तर: (b)

31. 75. If by increasing the price of a ticket in the ratio 8:11 the number of tickets sold fall in the ratio 23:21 then what is the increase

    • (a) 21250
    • (b) 9400
    • (c) 7850
    • (d) 12850
    उत्तर देखें

    उत्तर: (b)

32. 76. The ratio of ages of the father and mother was 11:10 when their son was born. The ratio of ages of the father and mother will be 19:18 when the son will be twice his present age. What is the ratio of present ages of father and mother?

    • (a) 15 : 14
    • (b) 14 : 13
    • (c) 16 : 15
    • (d) 17 : 16
    उत्तर देखें

    उत्तर: (a)

33. 80. What is the average of all numbers between 100 and 200 which are divisible by 13? 100

    • (a) 147.5
    • (b) 145.5
    • (c) 143.5
    • (d) 149.5
    उत्तर देखें

    उत्तर: (d)

34. 81. A vendor buys bananas at 9 for Rs 8 and sells at 8 for Rs 9. What will be the profit or loss (in %)?

    • (a) 13.28% profit
    • (b) 26.56% loss
    • (c) 26.56% profit 26.56%
    • (d) 13.28% loss
    उत्तर देखें

    उत्तर: (c)

35. 82. If a stall sells a pizza at Rs 200 he makes 20% loss if he wants to make 10% profit then at what price (in Rs) should he sell?

    • (a) 250
    • (b) 300
    • (c) 275
    • (d) 325
    उत्तर देखें

    उत्तर: (c)

36. 86. Two numbers are 90% and 75% lesser than a third number. By what % should the first number be increased so that it becomes equal to the second number?

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

    उत्तर: (c)

37. 87. When a number is increased by 216, it becomes 140% of itself. What is the number?

    • (a) 540
    • (b) 756
    • (c) 450
    • (d) 675
    उत्तर देखें

    उत्तर: (a)

38. 88. A man donates 30% of his wealth to charity. 30% and 25% of the remaining wealth to his wife and son respectively. The rest he divides equally between his three daughters. One of his daughter gets Rs 42 lakh as her share. What was the man's wealth (in Rs lakhs)?

    • (a) 280
    • (b) 400
    • (c) 500
    • (d) 350
    उत्तर देखें

    उत्तर: (b)

39. 92. Flight A usually takes 1 hour more than Flight B to travel a distance of 7200 km. Due to engine trouble speed of flight B falls by a th factor of 1/6 , so it takes 36 minutes more than Flight A to complete the same journey? What is the speed of Flight A (in km/hr)?

    • (a) 800
    • (b) 900
    • (c) 750
    • (d) 720
    उत्तर देखें

    उत्तर: (a)

40. 94. What is the compound interest earned on Rs 80,000 at 40% per annum in 1 year compounded quarterly?

    • (a) 28317
    • (b) 37128
    • (c) 18732
    • (d) 21387
    उत्तर देखें

    उत्तर: (b)

41. 95. An investor invested his saving in the stock market. The value of his investments increased by 12% and 9% in the first year and the second year respectively. If the value of his investments after two years became Rs 97,664 then how much had he invested (in Rs)?

    • (a) 81000
    • (b) 75000
    • (c) 80000
    • (d) 72000
    उत्तर देखें

    उत्तर: (c)