ExamBharo · SSC CGL 2017 Tier II — Quantitative Abilities — 18 February 2018 · exambharo.com/previous-year-papers/ssc-cgl-2017-tier-2-quant-18-feb/

Question paper · SSC CGL

SSC CGL 2017 Tier II — Quantitative Abilities — 18 February 2018

18 February 2018 · 10:30 AM–12:30 PM66 of the paper’s 100 questions1 per correct answer

Download PDFStart practice test

34 questions of the original paper are not included: those that need a figure or formatting we cannot show, that have no answer in the response sheet, or that we could not check against a second copy of the paper.

Questions from the Staff Selection Commission’s paper of 18 February 2018, 10:30 AM–12:30 PM. Each question’s answer is under it, hidden until you open it, and the full answer key is at the end. Take the paper as a timed practice test to be scored.

Quantitative Abilities

1. How many three digit numbers are there in which all the digits are odd?
- (a) 100
- (b) 125
- (c) 500
- (d) 250
Show answer
Answer: (b)
2. If the sum of ten different positive integers is 100, then what is the greatest possible number among these 10 numbers?
- (a) 45
- (b) 91
- (c) 55
- (d) 64
Show answer
Answer: (c)
6. If 56 × 75 × 60 × 84 × 210 = 2p × 3q × 5r × 7s, then what is the value of [(p + q)/s] + r?
- (a) 6
- (b) 8
- (c) 12
- (d) 10
Show answer
Answer: (b)
8. What is the sum of all natural numbers between 100 and 400 which are divisible by 13?
- (a) 5681
- (b) 5334
- (c) 5434
- (d) 5761
Show answer
Answer: (a)
10. If (333 + 333 + 333) (233 + 233) = 6x, then what is the value of x?
- (a) 34
- (b) 35
- (c) 33
- (d) 33.5
Show answer
Answer: (a)
11. Which of the following statement(s) is/are true? I. (65)1/6 > (17)1/4 > (12)1/3 II. (17)1/4 > (65)1/6 > (12)1/3 III. (12)1/3 > (17)1/4 > (65)1/6
- (a) Only I
- (b) Only III
- (c) Only II
- (d) None of these
Show answer
Answer: (b)
12. If P = 7 + 4√3 and PQ = 1, then what is the value of (1/P2) + (1/Q2)?
- (a) 148
- (b) 189
- (c) 194
- (d) 204
Show answer
Answer: (c)
13. If x = (√5) + 1 and y = (√5) – 1, then what is the value of (x2/y2) + (y2/x2) + 4[(x/y) + (y/x)] + 6?
- (a) 31
- (b) 23√5
- (c) 27√5
- (d) 25
Show answer
Answer: (d)
14. If x = 2 +√3, y = 2 – √3 and z = 1, then what is the value of (x/yz) + (y/xz) + (z/xy) + 2 [(1/x) + (1/y) + (1/z)]?
- (a) 25
- (b) 22
- (c) 17
- (d) 43
Show answer
Answer: (a)
15. A root of equation ax2 + bx + c = 0 (where a, b and c are rational numbers) is 5 + 3√3. What is the value of (a2 + b2 + c2 )/(a + b + c)?
- (a) 35/3
- (b) 37/3
- (c) – 105/11
- (d) – 105/13
Show answer
Answer: (c)
16. If x = (a/b) + (b/a), y = (b/c) + (c/b) and z = (c/a) + (a/c), then what is the value of xyz – x2 – y2 – z2?
- (a) – 4
- (b) 2
- (c) – 1
- (d) – 6
Show answer
Answer: (a)
17. If [a + (1/a)]2 – 2[a – (1/a)] = 12, then which of the following is a value of 'a'?
- (a) – 8 + √3
- (b) – 8 – √3
- (c) – 8 + √5
- (d) None of these
Show answer
Answer: (d)
19. If x + y = 3, then what is the value of x3 + y3 + 9xy?
- (a) 15
- (b) 81
- (c) 27
- (d) 9
Show answer
Answer: (c)
20. A = (x8 – 1)/(x4 + 1) and B = (y4 – 1)/(y2 + 1). If x = 2 and y = 9, then what is the value of A2 + 2AB + AB2?
- (a) 96475
- (b) 98625
- (c) 92425
- (d) 89125
Show answer
Answer: (b)
21. If x – 4y = 0 and x + 2y = 24, then what is the value of (2x + 3y)/(2x – 3y)?
- (a) 9/5
- (b) 11/5
- (c) 13/7
- (d) 9/7
Show answer
Answer: (b)
24. In a triangle PQR, ∠PQR = 90o, PQ = 10 cm and PR = 26 cm, then what is the value (in cm) of inradius of incircle?
- (a) 9
- (b) 4
- (c) 8
- (d) 6
Show answer
Answer: (b)
26. In a triangle PQR, PX, QY and RZ be altitudes intersecting at O. If PO = 6 cm, PX = 8 cm and QO = 4 cm, then what is the value (in cm) of QY?
- (a) 6.3
- (b) 5.8
- (c) 6
- (d) 7
Show answer
Answer: (d)
27. A line cuts two concentric circles. The lengths of chords formed by that line on the two circles are 4 cm and 16 cm. What is the difference (in cm2) in squares of radii of two circles?
- (a) 240
- (b) 120
- (c) 60
- (d) 90
Show answer
Answer: (c)
38. A man is running at the speed of 20 km/hr. What is time (in seconds) taken by man to cover one round of a circular garden of radius 350 metres?
- (a) 412
- (b) 336
- (c) 396
- (d) 376
Show answer
Answer: (c)
40. A regular hexagonal base prism has height 8 cm and side of base is 4 cm. What is the total surface area (in cm2) of the prism?
- (a) 54(3 + √3)
- (b) 36(3 + √3)
- (c) 48(4 + √3)
- (d) 24(4 + √3)
Show answer
Answer: (c)
41. A cube is placed inside a cone of radius 20 cm and height 10 cm, one of its face being on the base of the cone and vertices of opposite face touching the cone. What is the length (in cm) of side of the cube?
- (a) 5
- (b) 6
- (c) 8
- (d) 9
Show answer
Answer: (c)
42. A cylinder of radius 4.5 cm and height 12 cm just fits in another cylinder completely with their axis perpendicular. What is the radius (in cm) of second cylinder?
- (a) 5
- (b) 6
- (c) 15
- (d) 7.5
Show answer
Answer: (d)
43. A right circular cylinder has height 28 cm and radius of base 14 cm. Two hemispheres of radius 7 cm each are cut from each of the two bases of the cylinder. What is the total surface area (in cm2) of the remaining part?
- (a) 3842
- (b) 4312
- (c) 3296
- (d) 4436
Show answer
Answer: (b)
44. Two spheres of equal radius are taken out by cutting from a solid cube of side (12 + 4√3) cm. What is the maximum volume (in cm3) of each sphere?
- (a) 1077.31
- (b) 905.14
- (c) 966.07
- (d) 1007.24
Show answer
Answer: (b)
45. Three toys are in a shape of cylinder, hemisphere and cone. The three toys have same base. Height of each toy is 2√2 cm. What is the ratio of the total surface areas of cylinder, hemisphere and cone respectively?
- (a) 4 : 3 : [(√2) + 1]
- (b) 4 : 3 : [2 + (√2)]
- (c) 4 : 3 : 2√2
- (d) 2 : 1 : (1 + √2)
Show answer
Answer: (a)
46. A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area?
- (a) 150
- (b) 200
- (c) 300
- (d) 250
Show answer
Answer: (b)
48. What is the value of [(sin 7x – sin 5x)÷(cos 7x + cos 5x)] – [(cos 6x – cos 4x)÷(sin 6x + sin 4x)]?
- (a) 1
- (b) 2 tan
- (c) tan 2
- (d) tan (3 /2) x
Show answer
Answer: (b)
49. What is the value of [(cos3 2θ + 3 cos 2θ)÷(cos6 θ – sin6 θ)]?
- (a) 0
- (b) 1
- (c) 4
- (d) 2
Show answer
Answer: (c)
52. What is the value of sin (630o + A) + cos A?
- (a) √3/2
- (b) 1/2
- (c) 0
- (d) 2/√3
Show answer
Answer: (c)
53. What is the value of [(sin 59o cos 31o + cos 59o sin 31o)÷(cos 20o cos 25o – sin 20o sin 25o)]?
- (a) 1/√2
- (b) 2√2
- (c) √3
- (d) √2
Show answer
Answer: (d)
54. What is the value of cos (90 – B) sin (C – A) + sin (90 + A) cos (B + C) – sin (90 – C) cos (A + B)?
- (a) 1
- (b) sin ( +
- (c) cos ( +
- (d) 0 A B – C) B C – A)
Show answer
Answer: (d)
55. Two trees are standing along the opposite sides of a road. Distance between the two trees is 400 metres. There is a point on the road between the trees. The angle of depressions of the point from the top of the trees are 45o and 60o. If the height of the tree which makes 45o angle is 200 metres, then what will be the height (in metres) of the other tree?
- (a) 200
- (b) 200√3
- (c) 100√3
- (d) 250
Show answer
Answer: (b)
56. A tower stands on the top of a building which is 40 metres high. The angle of depression of a point situated on the ground from the top and bottom of the tower are found to be 60o and 45o respectively. What is the height (in metres) of tower?
- (a) 20√3
- (b) 30(√3 + 1)
- (c) 40(√3 – 1)
- (d) 50(√3 – 1)
Show answer
Answer: (c)
57. From a point P, the angle of elevation of a tower is such that its tangent is 3/4. On walking 560 metres towards the tower the tangent of the angle of elevation of the tower becomes 4/3. What is the height (in metres) of the tower?
- (a) 720
- (b) 960
- (c) 840
- (d) 1030
Show answer
Answer: (b)
63. A beaker contains acid and water in the ratio 1 : x. When 300 ml of the mixture and 50 ml of water are mixed, the ratio of acid and water becomes 2 : 5. What is the value of x?
- (a) 2
- (b) 1
- (c) 3
- (d) 4
Show answer
Answer: (a)
64. A mixture is composed of 11 parts of pure milk and 2 parts of water. If 35 litres of water were added to the mixture then the new mixture will contain twice as much pure milk as water, then how many litres of pure milk does the original mixture contain?
- (a) 110
- (b) 55
- (c) 220
- (d) 70
Show answer
Answer: (a)
66. A, B and C invest in a business in the ratio 4 : 5 : 7. C is a sleeping partner, so his share of profits will be half of what it would have been if he were a working partner. If they make Rs 36,000 profit of which 25% is reinvested in the business, how much does B get (in Rs)?
- (a) 7560
- (b) 10800
- (c) 8640
- (d) 9200
Show answer
Answer: (b)
67. A can do a work in 36 days and B in 12 days. If they work on it together for 3 days, then what fraction of work is left?
- (a) 2/3
- (b) 1/3
- (c) 1/4
- (d) 1/5
Show answer
Answer: (a)
69. A,B and C together can finish a task in 7.5 days. C is thrice as productive as A and B alone can do the task in 15 days. In how many days can A and C do the job if B goes on leave?
- (a) 30
- (b) 10
- (c) 20
- (d) 15
Show answer
Answer: (d)
70. A, B and C can do job in 9, 12 and 36 days respectively if they worked alone. A leaves after they have worked together for 3 days. In how many days can B and C do the rest of the job?
- (a) 3
- (b) 4
- (c) 5
- (d) 6
Show answer
Answer: (a)
72. If a website is selling smartphone at Rs 18,000 which is marked at Rs 25,000, then what is the discount (in %) at which the smartphone is being sold?
- (a) 25
- (b) 22
- (c) 28
- (d) 20
Show answer
Answer: (c)
73. If on an item there is 12% discount on the marked price of Rs 10,000 but the item is sold at Rs 8,360 only then what additional discount (in %) did the customer get? 10,000
- (a) 6
- (b) 7
- (c) 5
- (d) 8
Show answer
Answer: (c)
74. A shopkeeper marks up his wares by 125% and offers 25% discount. What will be the selling price if the cost price (in Rs) is Rs 640?
- (a) 1080
- (b) 1000
- (c) 920
- (d) 860
Show answer
Answer: (a)
75. Priya's marks in History and Geography are in the ratio 5 : 7. If she got 14 marks more in Geography than in History, what are her History marks?
- (a) 49
- (b) 42
- (c) 56
- (d) 35
Show answer
Answer: (d)
76. The ratio of present ages of Rahul and his sister is 3 : 4. Before 10 years the ratio of their ages was 13:19. What is Rahul's present age (in years)?
- (a) 36
- (b) 48
- (c) 42
- (d) 54
Show answer
Answer: (a)
77. What is the third proportional to 9 and 15?
- (a) 30
- (b) 27
- (c) 36
- (d) 25
Show answer
Answer: (d)
79. If Rs 7,800 is to be divided between A, B and C in the ratio 1/2 : 1/3 : 1/4, then how much share will B get (in Rs)?
- (a) 3600
- (b) 1800
- (c) 2400
- (d) 1200
Show answer
Answer: (c)
80. Bunty had candies and chewing gums in his sweet box in the ratio 7 : 13. After he has eaten 8 candies and 11 chewing gums the ratio became 1 : 2. How many candies does he have now?
- (a) 65
- (b) 35
- (c) 54
- (d) 27
Show answer
Answer: (d)
81. The average weight of P, Q and R is 71 kg. If the average weight of P and Q be 66 kg and that of Q and R be 76.5 kg, then the weight (in kg) of Q is.
- (a) 60
- (b) 72
- (c) 81
- (d) 75
Show answer
Answer: (b)
82. Rita buys 5 sarees at an average cost of Rs 2250. If she buys three more sarees at an average cost of Rs 2750, what will be the average (in Rs) of all the sarees she buys?
- (a) 2437.5
- (b) 2500
- (c) 2450
- (d) 2332.5
Show answer
Answer: (a)
83. In a one day match of 50 overs in an innings the team A had a run rate of 5.3 runs per over. Team B is playing and 5 overs are left and the required run rate to tie the match is 7.2 per over to match the score of Team A. What is team B's score?
- (a) 265
- (b) 238
- (c) 254
- (d) 229
Show answer
Answer: (d)
84. Average of all even numbers between 104 and 148 is __________.
- (a) 128
- (b) 130
- (c) 124
- (d) 126
Show answer
Answer: (d)
85. A vendor buys bananas at 4 for Rs 3 and sells at 3 for Rs 4. What will be the result?
- (a) 43.75% profit
- (b) 77.7% loss
- (c) 77.7% profit
- (d) 43.75% loss
Show answer
Answer: (c)
86. A wholesaler sells a watch to a retailer at a profit of 8% and the retailer sells it to a customer at a profit of 12%. If the customer pays Rs. 8,448 what had it cost (approximately) to the wholesaler (in Rs)?
- (a) 6984
- (b) 6082
- (c) 7120
- (d) 7022
Show answer
Answer: (a)
87. A trader had 2000 kgs of rice. He sold a part of it at 10% profit and the rest at 16% profit, so that he made a total profit of 14.2%. How much rice (in kg) did he sell at 10% profit?
- (a) 1400
- (b) 600
- (c) 800
- (d) 1000
Show answer
Answer: (b)
88. A used car dealer sells a car for Rs 7.6 lakhs and makes some loss. If he had sold it for Rs 9.2 lakhs his profit would have been thrice his loss. What was the cost price of the car (in Rs lakhs)?
- (a) 8.5
- (b) 8.75
- (c) 8.25
- (d) 8
Show answer
Answer: (d)
89. 0.09% of 25% of 1200 is equal to____________.
- (a) 0.27
- (b) 2.7
- (c) 27
- (d) 270
Show answer
Answer: (a)
90. When a number is increased by 20, it becomes 116% of itself. What is the number?
- (a) 100
- (b) 250
- (c) 125
- (d) 400
Show answer
Answer: (c)
91. Two numbers are 50% and 75% lesser than a third number. By how much percent is the second number to be enhanced to make it equal to the first number?
- (a) 50
- (b) 25
- (c) 75
- (d) 100
Show answer
Answer: (d)
92. Price of petrol increased from Rs 60/liter to Rs 75/liter. How much should the consumption of petrol be reduced (in %) so as to increase expenditure by only 10%?
- (a) 12
- (b) 20
- (c) 15
- (d) 18
Show answer
Answer: (a)
93. A train has to cover a distance of 900 km in 25 hours. What should be its average speed in meters/second?
- (a) 20
- (b) 10
- (c) 18
- (d) 36
Show answer
Answer: (b)
95. Two cyclists A and B start cycling at 21 km/hr and 24 km/hr towards each other. They meet after 1 hour and 12 minutes. How far (in km) were they from each other when they started?
- (a) 48
- (b) 42
- (c) 54
- (d) 36
Show answer
Answer: (c)
96. Excluding stoppages, the speed of a bus is 60 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
- (a) 12
- (b) 9
- (c) 15
- (d) 10
Show answer
Answer: (c)
98. If the amount received at the end of 2nd and 3rd year at compound Interest on a certain Principal is Rs 9,600 and Rs 10,272 respectively, what is the rate of interest (in %)?
- (a) 7
- (b) 8
- (c) 6
- (d) 5
Show answer
Answer: (a)
99. A invested an amount of x rupees in a bank for 2 years which gave 5% interest in year 1 and 6% interest in year 2. The amount received after 2 years is Rs 24,486. What is the value of x?
- (a) 23000
- (b) 22500
- (c) 22000
- (d) 21500
Show answer
Answer: (c)
100. What is the difference (in Rs) in Compound interest earned in 1 year on a sum of Rs 10,000 at 40% per annum compounded quarterly and annually?
- (a) 461
- (b) 346
- (c) 463
- (d) 641
Show answer
Answer: (d)

Show answers

Answer key

Answer key as marked in the Staff Selection Commission’s response sheet. “—” means the sheet did not show it clearly.

Quantitative Abilities

Q 1: (b)
Q 2: (c)
Q 6: (b)
Q 8: (a)
Q 10: (a)
Q 11: (b)
Q 12: (c)
Q 13: (d)
Q 14: (a)
Q 15: (c)
Q 16: (a)
Q 17: (d)
Q 19: (c)
Q 20: (b)
Q 21: (b)
Q 24: (b)
Q 26: (d)
Q 27: (c)
Q 38: (c)
Q 40: (c)
Q 41: (c)
Q 42: (d)
Q 43: (b)
Q 44: (b)
Q 45: (a)
Q 46: (b)
Q 48: (b)
Q 49: (c)
Q 52: (c)
Q 53: (d)
Q 54: (d)
Q 55: (b)
Q 56: (c)
Q 57: (b)
Q 63: (a)
Q 64: (a)
Q 66: (b)
Q 67: (a)
Q 69: (d)
Q 70: (a)
Q 72: (c)
Q 73: (c)
Q 74: (a)
Q 75: (d)
Q 76: (a)
Q 77: (d)
Q 79: (c)
Q 80: (d)
Q 81: (b)
Q 82: (a)
Q 83: (d)
Q 84: (d)
Q 85: (c)
Q 86: (a)
Q 87: (b)
Q 88: (d)
Q 89: (a)
Q 90: (c)
Q 91: (d)
Q 92: (a)
Q 93: (b)
Q 95: (c)
Q 96: (c)
Q 98: (a)
Q 99: (c)
Q 100: (d)