ExamBharo · SSC CGL 2017 Tier II — Quantitative Abilities — 19 February 2018 · exambharo.com/previous-year-papers/ssc-cgl-2017-tier-2-quant-19-feb/

Question paper · SSC CGL

SSC CGL 2017 Tier II — Quantitative Abilities — 19 February 2018

19 February 2018 · 10:30 AM–12:30 PM85 of the paper’s 100 questions1 per correct answer

Download PDFStart practice test

15 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 19 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. If N = 1 + 11 + 111 + 1111 + … +111111111, then what is the sum of the digit's of N?
- (a) 45
- (b) 18
- (c) 36
- (d) 5
Show answer
Answer: (a)
2. What is the sum of first 40 terms of 1 + 3 + 4 + 5 + 7 + 7 + 10 + 9 + ….?
- (a) 1010
- (b) 1115
- (c) 1030
- (d) 1031
Show answer
Answer: (c)
8. What is the unit digit of 15 + 25 + 35 + … + 205?
- (a) 0
- (b) 5
- (c) 2
- (d) 4
Show answer
Answer: (a)
9. x, y and z are prime numbers and x + y + z = 38. What is the maximum value of x?
- (a) 19
- (b) 23
- (c) 31
- (d) 29
Show answer
Answer: (c)
10. N is the smallest three digit prime number. When N is divided by 13, then what will be the remainder?
- (a) 8
- (b) 9
- (c) 7
- (d) 10
Show answer
Answer: (d)
11. How many natural numbers are there between √261 and √45109?
- (a) 144
- (b) 196
- (c) 168
- (d) 195
Show answer
Answer: (b)
12. What is the value of √121 + √12321 + √1234321 + √123454321?
- (a) 12345
- (b) 123456
- (c) 12344
- (d) 123454
Show answer
Answer: (c)
13. p3 + q3 + r3 – 3pqr = 4. If a = q + r, b = r + p and c = p + q, then what is the value of a3 + b3 + c3 – 3abc?
- (a) 4
- (b) 8
- (c) 2
- (d) 12
Show answer
Answer: (b)
14. If α and β are the roots of the equation x2 + x – 1 = 0, then what is the equation whose roots are α5 and β5?
- (a) x2 + 7x – 1 = 0
- (b) x2 – 7x – 1 = 0
- (c) x2 – 11x – 1 = 0
- (d) x2 + 11x – 1 = 0
Show answer
Answer: (d)
15. If x and y are natural numbers such that x + y = 2017, then what is the value of (– 1)x + (– 1)y?
- (a) 2
- (b) – 2
- (c) 0
- (d) 1
Show answer
Answer: (c)
16. If x + (1/x) = (√3 + 1)/2, then what is the value of x4 + (1/x4)?
- (a) (4√3 – 1)/4
- (b) (4√3 + 1)/2
- (c) (–4√3 – 1)/4
- (d) (–4√3 – 1)/2
Show answer
Answer: (c)
17. If a + a2 + a3 – 1 = 0, then what is the value of a3 + (1/a)?
- (a) 1
- (b) 4
- (c) 2
- (d) 3
Show answer
Answer: (c)
18. If a – (1/a) = b, b – (1/b) = c and c – (1/c) = a, then what is the value of (1/ab) + (1/bc) + (1/ca)?
- (a) – 3
- (b) – 6
- (c) – 1
- (d) – 9
Show answer
Answer: (a)
19. If the roots of the equation a(b – c)x2 +b(c – a)x + c(a – b) = 0 are equal, then which of the following is true?
- (a) b = ( a + c)/ ac
- (b) 2/ b = (1/ a) + (1/ c)
- (c) 2 b = (1/ a) + (1/ c)
- (d) abc = ab + bc + ca
Show answer
Answer: (b)
20. If [√(a2 + b2 + ab)] + [√(a2 + b2 – ab)] = 1, then what is the value of (1 – a2)(1 – b2)?
- (a) 1/4
- (b) 4/7
- (c) 5/4
- (d) 3/4
Show answer
Answer: (d)
21. If 3x + 4y – 11 = 18 and 8x – 6y + 12 = 6, then what is the value of 5x – 3y – 9?
- (a) 18
- (b) – 9
- (c) – 27
- (d) – 18
Show answer
Answer: (b)
22. If a + b + c = 7/12, 3a – 4b + 5c = 3/4 and 7a – 11b – 13c = – 7/12, then what is the value of a + c?
- (a) 1/2
- (b) 5/12
- (c) 3/4
- (d) 1/4
Show answer
Answer: (b)
24. In triangle PQR, C is the centroid. PQ = 30 cm, QR = 36 cm and PR = 50 cm. If D is the midpoint of QR, then what is the length (in cm) of CD?
- (a) (4√86)/3
- (b) (2√86)/3
- (c) (5√86)/3
- (d) (5√86)/2
Show answer
Answer: (a)
27. Two circles are having radii 9 cm and 12 cm. The distance between their centres is 15 cm. What is the length (in cm) of their common chord?
- (a) 6.8
- (b) 13.6
- (c) 7.2
- (d) 14.4
Show answer
Answer: (d)
28. Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?
- (a) 3.5
- (b) 3.75
- (c) 4.25
- (d) 4.45
Show answer
Answer: (b)
29. Two circles touch each other at point X. A common tangent touch them at two distinct points Y and Z. If another tangent passing through X cut YZ at A and XA= 16 cm, then what is the value (in cm) of YZ?
- (a) 18
- (b) 24
- (c) 16
- (d) 32
Show answer
Answer: (d)
30. There are 8 equidistant points A, B, C, D, E, F, G and H (in same order) on a circle. What is the value of ∠FDH (in degrees)?
- (a) 22.5
- (b) 45
- (c) 30
- (d) 42.5
Show answer
Answer: (b)
33. An equilateral triangle of area 300 cm2 is cut from its three vertices to form a regular hexagon. Area of hexagon is what percent of the area of triangle?
- (a) 66.66%
- (b) 33.33%
- (c) 83.33%
- (d) 56.41%
Show answer
Answer: (a)
39. The sum of radii of the two circles is 91 cm and the difference between their area is 2002 cm2. What is the radius (in cm) of the larger circle?
- (a) 56
- (b) 42
- (c) 63
- (d) 49
Show answer
Answer: (d)
40. A right triangular prism has equilateral triangle as its base. Side of the triangle is 15 cm. Height of the prism is 20√3 cm. What is the volume (in cm3) of the prism?
- (a) 1125
- (b) 6750
- (c) 4500
- (d) 3375
Show answer
Answer: (d)
41. The height of a cone is 45 cm. It is cut at a height of 15 cm from its base by a plane parallel to its base. If the volume of the smaller cone is 18480 cm3, then what is the volume (in cm3) of the original cone?
- (a) 34650
- (b) 61600
- (c) 36960
- (d) 62370
Show answer
Answer: (d)
42. The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm2, then what is the volume (in cm3) of the cylinder?
- (a) 4312√6
- (b) 3822√6
- (c) 4522√6
- (d) 4642√6
Show answer
Answer: (a)
43. The radius and height of a solid cylinder are increased by 2% each. What will be the approximate percentage increase in volume?
- (a) 6.76
- (b) 5.88
- (c) 6.12
- (d) 3.34
Show answer
Answer: (c)
44. A sphere of radius 21 cm is cut into 8 identical parts by 3 cuts (1 cut along each axis). What will be the total surface area (in cm2) of each part?
- (a) 844.5
- (b) 1732.5
- (c) 1039.5
- (d) 1115.6
Show answer
Answer: (b)
45. Two identical hemispheres of maximum possible size are cut from a solid cube of side 14 cm. The bases of the hemispheres are part of the two opposite faces of cube. What is the total volume (in cm3) of the remaining part of the cube?
- (a) 1556.33
- (b) 898.5
- (c) 1467.33
- (d) 1306.67
Show answer
Answer: (d)
46. Identical cubes of largest possible size are cut from a solid cuboid of size 65 cm × 26 cm × 3.9 cm. What is the total surface area (in cm2) of all the small cubes taken together?
- (a) 30420
- (b) 15210
- (c) 20280
- (d) 16440
Show answer
Answer: (a)
47. A regular triangular pyramid is cut by 2 planes which are parallel to its base. The planes trisects the altitude of the pyramid. Volume of top, middle and bottom part is V1, V2 and V3 respectively. What is the value of V1 :V2 : V3?
- (a) 1 : 8 : 27
- (b) 1 : 8 : 19
- (c) 2 : 9 : 27
- (d) 1 : 7 : 19
Show answer
Answer: (d)
48. What is the value of [(cos 7A + cos 5A)÷(sin 7A – sin 5A)]?
- (a) tan A
- (b) tan 4 A
- (c) cot 4 A
- (d) cot A
Show answer
Answer: (d)
49. What is the value of [1 – sin (90 – 2A)] / [1 + sin (90 + 2A)]?
- (a) sinA cosA
- (b) cot2A
- (c) tan2A
- (d) sin2A cosA
Show answer
Answer: (c)
50. What is the value of sin 75o + sin 15o?
- (a) √3
- (b) 2√3
- (c) √(3/2)
- (d) 3/√2
Show answer
Answer: (c)
51. What is the value of [(cos 3θ + 2cos 5θ + cos 7θ)÷(cos θ + 2cos 3θ + cos 5θ)] + sin 2θ tan 3θ?
- (a) cos 2θ
- (b) sin 2θ
- (c) tan 2θ
- (d) cot θ sin 2θ
Show answer
Answer: (a)
52. What is the value of [2 sin (45 + θ) sin (45 – θ)]/cos 2θ?
- (a) 0
- (b) tan 2θ
- (c) cot 2θ
- (d) 1
Show answer
Answer: (d)
53. What is the value of sin (90o + 2A)[4 – cos2 (90o – 2A)]?
- (a) 2(cos3 A – sin3 A)
- (b) 2(cos3 A + sin3 A)
- (c) 4(cos6 A+ sin6 A)
- (d) 4(cos6 A – sin6 A)
Show answer
Answer: (d)
54. What is the value of [cos (90 + A)÷sec (270 – A)] + [sin (270 + A)÷cosec (630 – A)]?
- (a) 3 sec A
- (b) tan A sec A
- (c) 0
- (d) 1
Show answer
Answer: (d)
55. On walking 100 metres towards a building in a horizontal line, the angle of elevation of its top changes from 45o to 60o. What will be the height (in metres) of the building?
- (a) 50(3 + √3)
- (b) 100(√3 + 1)
- (c) 150
- (d) 100√3
Show answer
Answer: (a)
56. The upper part of a tree broken over by the wind make an angle of 60o with the ground. The distance between the root and the point where top of the tree touches the ground is 25 metres. What was the height (in metres) of the tree?
- (a) 84.14
- (b) 93.3
- (c) 98.25
- (d) 120.24
Show answer
Answer: (b)
57. The height of a tower is 300 meters. When its top is seen from top of another tower,then the angle of depression is 60°. The horizontal distance between the bases of the two towers is 120 metres. What is the height (in metres) of the small tower?
- (a) 88.24
- (b) 106.71
- (c) 92.15
- (d) 112.64
Show answer
Answer: (c)
58. How many employees of department A and C together are living in city Z?
- (a) 9000
- (b) 9200
- (c) 8800
- (d) 8200
Show answer
Answer: (c)
59. Male employees of department E is what percent of the employees living in city Z from department A?
- (a) 1600
- (b) 2400
- (c) 3200
- (d) 4200
Show answer
Answer: (c)
60. What is the ratio of male employee working in department B and D together to female employee working in department A and E together?
- (a) 13 : 8
- (b) 25 : 7
- (c) 23 : 9
- (d) 7 : 9
Show answer
Answer: (b)
61. On an average how many residents of city Y are working in each department?
- (a) 11360
- (b) 12420
- (c) 9130
- (d) 10940
Show answer
Answer: (a)
62. What are the total number of employee in department A and E together?
- (a) 29400
- (b) 17600
- (c) 46400
- (d) 36800
Show answer
Answer: (d)
63. If a dairy mixes cow's milk which contains 10% fat with buffalo's milk which contains 20% fat, then the resulting mixture has fat (120/7)% of fat. What ratio was the cow's milk mixed with buffalo's milk?
- (a) 2 : 5
- (b) 1 : 5
- (c) 2 : 3
- (d) 2 : 1
Show answer
Answer: (a)
64. In what ratio should tea costing Rs 300/kg be mixed with tea costing Rs 200/kg so that the cost of the mixture is Rs 225/kg?
- (a) 3 : 1
- (b) 1 : 3
- (c) 1 : 4
- (d) 4 : 1
Show answer
Answer: (b)
65. A and B started a partnership business investing some amount in the ratio of 5 : 6. C joined then after 6 months with an amount equal to 2/3rd of B. What was their profit (in Rs) at the end of the year if C got Rs 21,600 as his share?
- (a) 46800
- (b) 56160
- (c) 70200
- (d) 1,40,400
Show answer
Answer: (d)
66. A and B invest in a business in the ratio 2 : 5. If 50% of the total profit goes to charity and A's share is Rs 3.6 lakhs, the total profit is Rs __________ lakhs.
- (a) 12.6
- (b) 25.2
- (c) 37.8
- (d) 16.8
Show answer
Answer: (b)
67. A is thrice as productive as C. Together they can complete a job in 22.5 days. If B joins them after they have worked for 15 days then in how many days can they finish the rest of the job if B alone can do the job in 15 days?
- (a) 6
- (b) 3
- (c) 9
- (d) 2
Show answer
Answer: (b)
68. If A, B and C can do a job working alone in 12, 18 and 36 days respectively. They all work together for 2 day, then B quits. How many days will A and C take to finish rest of the job?
- (a) 9
- (b) 6
- (c) 3
- (d) 4
Show answer
Answer: (b)
69. If A, B and C together do a job in 4 days, A and C together do the job in 4.5 days and B and C together do the job in 12 days then in how many days can C alone do the job?
- (a) 36
- (b) 6
- (c) 18
- (d) 12
Show answer
Answer: (c)
70. If A alone can do a job in 40 days then, in how many days can B alone do the job if together they can do the job in 8 days?
- (a) 15
- (b) 10
- (c) 20
- (d) 25
Show answer
Answer: (b)
71. 1 bottle of honey costs Rs 240 but a pack of 4 of the same bottles costs Rs 768. What is the effective discount (in %) on the pack?
- (a) 16
- (b) 25
- (c) 10
- (d) 20
Show answer
Answer: (d)
72. If the cost price of an article is Rs x . It is marked up by 100%. It is sold at Rs 1,200 after giving 20% discount. What is value of x?
- (a) 750
- (b) 1500
- (c) 1000
- (d) 2000
Show answer
Answer: (a)
73. A Rs 1000 box of cookies is offered at 10% discount and a Rs 400 bar of chocolate at 8% discount. If we buy 2 boxes of cookies and 3 bars of chocolate, what is the effective discount we get (in %)?
- (a) 9
- (b) 9.25
- (c) 8.75
- (d) 8.5
Show answer
Answer: (b)
74. The price of a product after getting 20% discount is Rs 3,024 which includes 5% tax on selling price. What was the marked price (in Rs) of the product?
- (a) 3780
- (b) 2742
- (c) 3600
- (d) 2880
Show answer
Answer: (c)
75. and 2200 tickets were sold.
- (a) 44000
- (b) 440000
- (c) 39600
- (d) 396000
Show answer
Answer: (a)
76. If 2A = 3B = 8C; What is A : B : C?
- (a) 8 : 3 : 2
- (b) 8 : 4 : 3
- (c) 2 : 3 : 8
- (d) 12 : 8 : 3
Show answer
Answer: (d)
77. What is the Number of candidates who had applied if the ratio of selected to unselected was 14 : 25. If 35 less had applied and 10 less selected, the ratio of selected to unselected would have been 3 : 5?
- (a) 195
- (b) 205
- (c) 185
- (d) 175
Show answer
Answer: (a)
78. What is the fourth proportional to 6, 24 and 83?
- (a) 249
- (b) 332
- (c) 166
- (d) 498
Show answer
Answer: (b)
79. Rs 10,200 has to be divided between A,B & C so that A gets 2/3 of what B gets and B gets 1/4 of what C gets. How much more does C get over A (in Rs)? 10,200
- (a) 6000
- (b) 7200
- (c) 1800
- (d) 1200
Show answer
Answer: (a)
80. Before a battle there were the ratio of captains to soldiers was 2 : 7. During the war 25 captains and 100 soldiers were martyred. The new ratio of captains to soldiers became 3 : 10. What is the number of soldiers after the war?
- (a) 250
- (b) 200
- (c) 150
- (d) 100
Show answer
Answer: (a)
81. The average marks of 18 students in an examination was 60. It was later found that the marks of one student had been wrongly entered as 63 instead of 36. The correct average is:
- (a) 59
- (b) 59.5
- (c) 58
- (d) 58.5
Show answer
Answer: (d)
82. In a class of 60 students there are 20 girls who scored an average of 40 marks in the test, what is the average marks of the boys if the class average is 60 marks?
- (a) 60
- (b) 70
- (c) 50
- (d) 80
Show answer
Answer: (b)
83. The average of 44 consecutive odd numbers is 144.What is the largest number? 44
- (a) 189
- (b) 191
- (c) 187
- (d) 193
Show answer
Answer: (c)
84. A batsman makes 100 runs in the 25th match of his career. His average runs per match increases by 1.4. Find his average before the 25th match.
- (a) 65
- (b) 55
- (c) 75
- (d) 45
Show answer
Answer: (a)
85. An oil refinery buys oil at Rs 3600 per barrel. There is 10% wastage. If the refinery wants to earn 5% profit then at what price should it sell including 8% tax on selling price? (in Rs per barrel)
- (a) 3674
- (b) 3711
- (c) 4219
- (d) 4536
Show answer
Answer: (d)
86. A vendor sells a coconut at Rs 24 and suffers 24% loss. If he wants to make 14% profit, then at what price (in Rs) should he sell?
- (a) 32
- (b) 30
- (c) 36
- (d) 28
Show answer
Answer: (c)
87. A villager buys a goat and a sheep together for Rs 14,250. He sold the sheep at a profit of 10% and the goat at a loss of 20%. If he sold both the animals at the same price , then what was the cost price of the cheaper animal?
- (a) 8250
- (b) 6600
- (c) 7500
- (d) 6000
Show answer
Answer: (d)
88. On a certain item profit is 120%. If the cost price increases by 10% then what will be the new profit margin (in %) if selling price remains the same?
- (a) 50
- (b) 60
- (c) 100
- (d) 90
Show answer
Answer: (c)
89. If 35% are the passing marks. A student gets 200 marks yet fails by 24 marks. What is the maximum marks?
- (a) 820
- (b) 550
- (c) 640
- (d) 680
Show answer
Answer: (c)
90. A student gets 22 marks more in French than what she got in German. Her German marks are 28% of the sum of her French and German marks. What are her French marks?
- (a) 14
- (b) 36
- (c) 18
- (d) 42
Show answer
Answer: (b)
91. 2% of a = b, then b% of 10 is the same as:
- (a) 200% of a
- (b) 20% of a/100
- (c) 20% of a/10
- (d) 200% of a/10
Show answer
Answer: (b)
92. A man's annual income has increased by Rs 1.2 lakhs but the tax on income that he has to pay has reduced from 12% to 10%. He now pays the same amount of tax as before. What is his increased income (in Rs lakhs)?
- (a) 8.4
- (b) 7.2
- (c) 9.6
- (d) 6
Show answer
Answer: (b)
93. A car travelling at an average speed of 72 km/hr takes 9 minutes to travel a certain distance. By how much should it increase its speed (in km/hr) to travel the same distance in 8 minutes?
- (a) 8
- (b) 9
- (c) 7
- (d) 6
Show answer
Answer: (b)
94. Train A takes 1 hour more than train B to travel a distance of 720 km. Due to engine trouble speed of train B falls by a third, so it takes 3 hours more than Train A to complete the same journey? What is the speed of Train A (in km/hr)?
- (a) 80
- (b) 90
- (c) 60
- (d) 70
Show answer
Answer: (a)
95. Two cars A and B travel from one city to another city, at speeds of 60 km/hr and 108 km/hr respectively. If car B takes 2 hours lesser time than car A for the journey, then what is the distance (in km) between the two cities?
- (a) 240
- (b) 270
- (c) 300
- (d) 330
Show answer
Answer: (b)
96. B starts 4.5 minutes after A from the same point, for a place at a distance of 3.5 miles from the starting point. A on reaching the destination turns back and walk a mile where he meets B. If A's speed is a mile in 6 minutes then B's speed is a mile in ____ minutes?
- (a) 8
- (b) 10
- (c) 12
- (d) 9
Show answer
Answer: (d)
97. If compound interest received on a certain amount in the 3rd year is Rs. 12,100, what will be the compound interest (in Rs) for the 4th year on the same amount if rate of interest is 9%?
- (a) 17080
- (b) 15669
- (c) 13189
- (d) 14376
Show answer
Answer: (c)
98. The amount received at 10% per annum compound interest after 3 yrs is Rs 10,648. What was the principal (in Rs)?
- (a) 8000
- (b) 9000
- (c) 8500
- (d) 7500
Show answer
Answer: (a)
99. In how many years will Rs 25,000 yield Rs 8,275 as compound interest at 10% per annum compounded annually?
- (a) 2
- (b) 4
- (c) 3
- (d) 5
Show answer
Answer: (c)
100. What is the rate of interest if simple interest earned on a certain sum for the 3rd year is Rs 1,750 and compound interest earned for 2 years is Rs 3622.5?
- (a) 8
- (b) 9
- (c) 10
- (d) 7
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: (a)
Q 2: (c)
Q 8: (a)
Q 9: (c)
Q 10: (d)
Q 11: (b)
Q 12: (c)
Q 13: (b)
Q 14: (d)
Q 15: (c)
Q 16: (c)
Q 17: (c)
Q 18: (a)
Q 19: (b)
Q 20: (d)
Q 21: (b)
Q 22: (b)
Q 24: (a)
Q 27: (d)
Q 28: (b)
Q 29: (d)
Q 30: (b)
Q 33: (a)
Q 39: (d)
Q 40: (d)
Q 41: (d)
Q 42: (a)
Q 43: (c)
Q 44: (b)
Q 45: (d)
Q 46: (a)
Q 47: (d)
Q 48: (d)
Q 49: (c)
Q 50: (c)
Q 51: (a)
Q 52: (d)
Q 53: (d)
Q 54: (d)
Q 55: (a)
Q 56: (b)
Q 57: (c)
Q 58: (c)
Q 59: (c)
Q 60: (b)
Q 61: (a)
Q 62: (d)
Q 63: (a)
Q 64: (b)
Q 65: (d)
Q 66: (b)
Q 67: (b)
Q 68: (b)
Q 69: (c)
Q 70: (b)
Q 71: (d)
Q 72: (a)
Q 73: (b)
Q 74: (c)
Q 75: (a)
Q 76: (d)
Q 77: (a)
Q 78: (b)
Q 79: (a)
Q 80: (a)
Q 81: (d)
Q 82: (b)
Q 83: (c)
Q 84: (a)
Q 85: (d)
Q 86: (c)
Q 87: (d)
Q 88: (c)
Q 89: (c)
Q 90: (b)
Q 91: (b)
Q 92: (b)
Q 93: (b)
Q 94: (a)
Q 95: (b)
Q 96: (d)
Q 97: (c)
Q 98: (a)
Q 99: (c)
Q 100: (d)