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Question paper · SSC CGL

SSC CGL 2016 Tier II — Quantitative Abilities — 12 January 2017

12 January 2017 · 10:00 AM–12:00 PM77 of the paper’s 100 questions1 per correct answer

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23 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 12 January 2017, 10:00 AM–12:00 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. Twenty one times of a positive number is less than its square by 100. The value of the positive number is
- (a) 25
- (b) 26
- (c) 42
- (d) 41
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Answer: (a)
2. Two pipes of length 1.5 m and 1.2 m are to be cut into equal pieces without leaving any extra length of pipes. The greatest length of the pipe pieces of same size which can be cut from these two lengths will be
- (a) 0.13 m
- (b) 0.4 m
- (c) 0.3 m
- (d) 0.41 m
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Answer: (c)
3. A General of an Army wants to create a formation of square from 36562 army men. After arrangement, he found some army men remained unused. Then the number of such army men remained unused was
- (a) 36
- (b) 65
- (c) 81
- (d) 97
Show answer
Answer: (c)
4. The smallest number, which should be added to 756896 so as to obtain a multiple of 11, is
- (a) 1
- (b) 2
- (c) 3
- (d) 5
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Answer: (c)
5. A boy found the answer for the question "Subtract the sum of 1/4 and 1/5 from unity and express the answer in decimals" as 0.45. The percentage of error in his answer was
- (a) (100/11) %
- (b) 50%
- (c) 10%
- (d) (200/11)%
Show answer
Answer: (d)
6. The product of two numbers is 48. If one number equals "The number of wings of a bird plus 2 times the number of fingers on your hand divided by the number of wheels of a Tricycle". Then the other number is
- (a) 9
- (b) 10
- (c) 12
- (d) 18
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Answer: (c)
7. Natu and Buchku each have certain number of oranges. Natu says to Buchku,"If you give me 10 of your oranges, I will have twice the number of oranges left with you". Buchku replies,"If you give me 10 of your oranges, I will have the same number of oranges as left with you". What is the number of oranges with Natu and Buchku, respectively?
- (a) 50, 20
- (b) 70, 50
- (c) 20, 50
- (d) 50, 70
Show answer
Answer: (b)
9. Three electronic devices make a beep after every 48 sec, 72 sec and 108 sec respectively. They beeped together at 10 a.m. The time when they will next make a beep together at the earliest is
- (a) 10:07:12 hrs
- (b) 10:07:24 hrs
- (c) 10:07:36 hrs
- (d) 10:07:48 hrs
Show answer
Answer: (a)
10. Two baskets together have 640 oranges. If (1/5)th of the oranges in the first basket be taken to the second basket. The number of oranges in the first basket is
- (a) 800
- (b) 600
- (c) 400
- (d) 300
Show answer
Answer: (c)
11. P can do (1/4)th of work in 10 days, Q can do 40% of work in 40 days and R can do (1/3)rd of work in 13 days. Who will complete the work first?
- (a) P
- (b) Q
- (c) R
- (d) Both P and R
Show answer
Answer: (c)
12. Working 7 hours in a day, 4 men can do a piece of work in 8 days. Working 8 hours in a day, the required number of men to perform the same work in 4 days will be
- (a) 8
- (b) 4
- (c) 7
- (d) 9
Show answer
Answer: (c)
13. 35 persons are engaged to complete a work in 60 days. After 32 days it is observed that only (2/5)th part of the work has been done. The number of persons to be engaged to complete the remaining work in the said period is
- (a) 20
- (b) 35
- (c) 30
- (d) 25
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Answer: (d)
16. A and B together can complete a piece of work in 12 days. They worked together for 5 days and then A alone finished the rest work in 14 days. A alone can complete the work in _____.
- (a) 24 days
- (b) 22 days
- (c) 20 days
- (d) 18 days
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Answer: (a)
17. A shopkeeper offers 15% discount on all plastic toys. He offers a further discount of 4% on the reduced price to those customers who pay cash. What does a customer have to pay (in Rs) in case for a toy of Rs 200?
- (a) 133.7
- (b) 129.8
- (c) 163.2
- (d) 153.3
Show answer
Answer: (c)
18. A photographer allows a discount of 10% on the advertised price of a camera. The price (in Rs) that must be marked on the camera, which cost him Rs 600, to make a profit of 20% would be
- (a) 650
- (b) 800
- (c) 700
- (d) 850
Show answer
Answer: (b)
19. A dinner set is quoted for Rs 1500. A customer pays Rs 1173 for it. If the customer got a series of two discounts and the rate of first discount is 15% then the rate of second discount was,
- (a) 15%
- (b) 7%
- (c) 9%
- (d) 8%
Show answer
Answer: (d)
21. In a college union, there are 48 students. The ratio of the number of boys to the number of girls is 5:3. The number of girls to be added in the union, so that the number of boys to girls in 6:5 is
- (a) 6
- (b) 7
- (c) 12
- (d) 17
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Answer: (b)
22. There are three bottles of mixture of syrup and water of ratios 2:3, 3:4 and 7:5. 10 Litres of first and 21 Litres of second bottles are taken. How much quantity from third bottle is to be taken so that final mixture from three bottles will be of ratios 1:1.
- (a) 25 Litres
- (b) 20 Litres
- (c) 35 Litres
- (d) 30 Litres
Show answer
Answer: (d)
23. In a colored picture of blue and yellow color, blue and yellow color is used in the ratio of 4:3 respectively. If in upper half, blue : yellow is 2:3, then in the lower half blue : yellow is
- (a) 1 : 1
- (b) 2 : 1
- (c) 26 : 9
- (d) 9 : 26
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Answer: (c)
24. A and B start an enterprise together, with A as active partner. A invests Rs 4000 and Rs 2000 more after 8 months. B invests Rs 5000 and withdraws Rs 2000 after 9 months. Being the active partner, A takes Rs 100 per month as allowance, from the profit. What is the share of B if the profit for the year is Rs 6700?
- (a) Rs 3350 3350
- (b) Rs 3250 3250
- (c) Rs 2700 2700
- (d) Rs 2800 2800
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Answer: (c)
25. A sum of Rs 15525 is divided among Sunil, Anil and Jamil such that if Rs 22, Rs 35 and Rs 48 be diminished from their shares respectively, their remaining sums shall be in the ratio 7:10:13. What would have been the ratio of their sums if Rs 16, Rs 77 and Rs 37 respectively were added to their original shares? 15525
- (a) 9:13:17
- (b) 18:26:35
- (c) 36:52:67
- (d) None of these
Show answer
Answer: (c)
26. A's income is Rs 140 more than B's income and C's income is Rs 80 more than D's. If the ratio of A's and C's income is 2:3 and the ratio of B's and D's income is 1:2, then the incomes of A, B, C and D are respectively
- (a) Rs 260, Rs 120, Rs 320 and Rs 240
- (b) Rs 300, Rs 160, Rs 600 and Rs 520
- (c) Rs 400, Rs 260, Rs 600 and Rs 520
- (d) Rs 320, Rs 180, Rs 480 and Rs 360 320 , 180 , 480
Show answer
Answer: (c)
27. A batsman has a certain average of runs for 12 innings. In the 13th inning he scores 96 runs thereby increasing his average by 5 runs. What will be his average after 13th inning?
- (a) 28
- (b) 32
- (c) 36
- (d) 42
Show answer
Answer: (c)
28. A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points the team scored was
- (a) 672
- (b) 665
- (c) 645
- (d) 588
Show answer
Answer: (b)
29. A librarian purchased 60 story books for his library. But he found that he could get 4 extra books by spending Rs 336 more and then the overall average price per book would be reduced by Re 1. The previous average price of each book was
- (a) Rs 84 84
- (b) Rs 83 83
- (c) Rs 68 68
- (d) Rs 100 100
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Answer: (d)
30. In an exam, the avarage marks obtained by John in English, Maths, Hindi and Drawing were 50. His average marks in Maths, Science, Social Studies and Craft were 70. If the average marks in all seven subjects is 58, his score in maths was
- (a) 50
- (b) 52
- (c) 60
- (d) 74
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Answer: (d)
31. The average weight of 3 men A, B and C is 84 Kg. Another man D joins the group and the average now becomes 80 Kg. If another man E whose weight is 3 Kg more than that of D, replaces A then the average weight of B, C, D and E becomes 79 Kg. What is the weight of A?
- (a) 70 Kg
- (b) 72 Kg
- (c) 75 Kg
- (d) 80 Kg
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Answer: (c)
34. The ratio of cost price and selling price 25:26. The percent of profit will be
- (a) 26%
- (b) 25%
- (c) 1%
- (d) 4%
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Answer: (d)
36. Mr. Kapur purchased two toy cycles for Rs 750 each. He sold these cycles, gaining 6% on one and losing 4% on the other. The gain or loss percent in the whole transaction is
- (a) 1% loss
- (b) 1% gain
- (c) 1.5% loss
- (d) 1.5 gain
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Answer: (b)
37. The profit earned by a shopkeeper by selling a bucket at a gain of 8% is Rs 28 more than when he sells it at a loss of 8%. The cost price (in Rupees) of the bucket is
- (a) 170
- (b) 190
- (c) 175
- (d) 165
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Answer: (c)
38. A man bought 500 metres of electronic wire at 50 paise per metre. He sold 50% of it at a profit of 5%. At what percent should he sell the remainder so as to gain 10% on the whole transaction?
- (a) 13%
- (b) 12.5%
- (c) 15%
- (d) 20%
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Answer: (a)
40. A businessman imported Laptops, worth Rs 210000, Mobile phones worth Rs 100000 and Television sets worth Rs 150000. He had to pay 10% duty on laptops, 8% on Phones and 5% on Television sets as a special case. How much total duty (in Rupees) he had to pay on all items as per above details?
- (a) 36500
- (b) 37000
- (c) 37250
- (d) 37500
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Answer: (a)
42. On a certain date, Pakistan has a success rate of 60% against India in all the ODIs played between the two countries. They lost the next 30 ODIs in a row to India and their success rate comes down to 30%. The total number of ODIs played between the two countries is
- (a) 50
- (b) 45
- (c) 60
- (d) 30
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Answer: (c)
43. Two donkeys are standing 400 meters apart. First donkey can run at a speed of 3 m/sec and the second can run at 2 m/sec. If two donkeys run towards each other after how much time (in sec) will they bump into each other?
- (a) 60
- (b) 80
- (c) 400
- (d) 40
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Answer: (b)
44. Rubi goes to a multiplex at the speed of 3 km/hr to see a movie and reaches 5 minutes late. If she travels at the speed of 4 Km/hr she reaches 5 minutes early. Then the distance of the multiplex from her starting point is
- (a) 2 km
- (b) 5 km
- (c) 2 m
- (d) 5 m
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Answer: (a)
45. A man travels some distance at a speed of 12 km/hr and returns at a speed of 9 km/hr. If the total time taken by him is 2 hrs 20 min, the distance is
- (a) 35 Km
- (b) 21 Km
- (c) 9 Km
- (d) 12 Km
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Answer: (d)
46. A and B are 15 kms apart and when travelling towards each other meet after half an hour whereas they meet two and a half hours later if they travel in the same direction. The faster of the two travels at the speed of
- (a) 15 km/hr
- (b) 18 km/hr
- (c) 10 km/hr
- (d) 8 km/hr
Show answer
Answer: (b)
47. The sum for 2 years gives a compound interest of Rs 3225 at 15% rate. Then sum is
- (a) 10000
- (b) 20000
- (c) 15000
- (d) 32250
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Answer: (a)
49. A man borrowed some money and agreed to pay-off by paying Rs 3150 at the end of the 1st year and Rs 4410 at the end of the 2nd year. If the rate of compound interest is 5% per annum, then the sum is
- (a) Rs 5000 5000
- (b) Rs 6500 6500
- (c) Rs 7000 7000
- (d) Rs 9200 9200
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Answer: (c)
50. Rs 260200 is divided between Ram and Shyam so that the amount that Ram receives in 3 years is the same as that Shyam receives in 6 years. If the interest is compounded annually at the rate of 4% per annum then Ram's share is 260200
- (a) 125000
- (b) 135200
- (c) 152000
- (d) 108200
Show answer
Answer: (b)
51. The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. The ratio of their volumes is
- (a) 27:20
- (b) 20:27
- (c) 4:9
- (d) 9:4
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Answer: (b)
52. Three cubes of iron whose edges are 6cm, 8cm and 10cm respectively are melted and formed into a single cube. The edge of the new cube formed is
- (a) 12 cm
- (b) 14 cm
- (c) 16 cm
- (d) 18 cm
Show answer
Answer: (a)
53. The radii of two concentric circles are 68 cm and 22 cm. The area of the closed figure bounded by the boundaries of the circles is
- (a) 4140π sq.cm.
- (b) 4110π sq.cm.
- (c) 4080π sq.cm.
- (d) 4050π sq.cm.
Show answer
Answer: (a)
54. The radius of a sphere is 6 cm. It is melted and drawn into a wire of radius 0.2 cm. The length of the wire is
- (a) 81 m
- (b) 80 m
- (c) 75 m
- (d) 72 m
Show answer
Answer: (d)
55. The radius of a wire is decreased to one-third. If volume remains the same, length will increase by
- (a) 1.5 times
- (b) 3 times
- (c) 6 times
- (d) 9 times
Show answer
Answer: (d)
56. In a trapezium ABCD, AB and DC are parallel sides and ∠ ADC = 90°. If AB = 15 cm, CD = 40 cm and diagonal AC = 41 cm. Then the area of the trapezium ABCD is
- (a) 245 cm2
- (b) 240 cm2
- (c) 247.5 cm2
- (d) 250 cm2
Show answer
Answer: (c)
57. The area of a rhombus having one side 10 cm and one diagonal 12 cm is
- (a) 48 cm2
- (b) 96 cm2
- (c) 144 cm2
- (d) 192 cm2
Show answer
Answer: (b)
58. The cost of levelling a circular field at 50 Paise per square metre is Rs 7700. The cost (in Rs) of putting up a fence all round it at Rs 1.20 per meter is ( Use π = 22/7)
- (a) Rs 132 132
- (b) Rs 264 264
- (c) Rs 528 528
- (d) Rs 1056 1056
Show answer
Answer: (c)
60. The height and the total surface area of a right circular cylinder are 4 cm and 8π sq.cm. respectively. The radius of the base of cylinder is
- (a) (2√2 - 2) cm
- (b) (2 - √2) cm
- (c) 2 cm
- (d) √2 cm
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Answer: (a)
61. The radius of a cylindrical milk container is half its height and surface area of the inner part is 616 sq.cm. The amount of milk that the container can hold, approximately, is [ Use : √5 = 2.23 and π = 22/7 ]
- (a) 1.42 litres
- (b) 1.53 litres
- (c) 1.71 litres
- (d) 1.82 litres
Show answer
Answer: (b)
62. A solid brass sphere of radius 2.1 dm is converted into a right circular cylindrical rod of length 7cm. The ratio of total surface areas of the rod to the sphere is
- (a) 3:1
- (b) 1:3
- (c) 7:3
- (d) 3:7
Show answer
Answer: (c)
65. A solid sphere of radius 3 cm is melted to form a hollow right circular cylindrical tube of length 4 cm and external radius 5 cm. The thickness of the tube is
- (a) 1 cm
- (b) 9 cm
- (c) 0.6 cm
- (d) 1.5 cm
Show answer
Answer: (a)
68. If x = y + 2 then x3- y3- z3 is
- (a) 0
- (b) 3xyz
- (c) -3xyz
- (d) 1
Show answer
Answer: (b)
71. If x = 11, the value of x5 - 12x4 + 12x3 - 12x2 + 12x - 1 is
- (a) 11
- (b) 10
- (c) 12
- (d) -10
Show answer
Answer: (b)
75. If x, y, z are the three factors of a3-7a - 6, then value of x+y+z will be
- (a) 3a
- (b) 3
- (c) 6
- (d) a
Show answer
Answer: (a)
76. ABCD is a cyclic quadrilateral of which AB is the diameter. Diagonals AC and BD intersect at E. If ∠DBC = 35°, Then ∠AED measures
- (a) 35°
- (b) 45°
- (c) 55°
- (d) 90°
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Answer: (c)
77. In a triangle ABC, ∠A = 70°, ∠B = 80° and D is the incentre of ΔABC. ∠ACB = 2x° and ∠BDC = y°. The values of x and y, respectively are
- (a) 15, 130
- (b) 15, 125
- (c) 35, 40
- (d) 30, 150
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Answer: (b)
78. In a right angled triangle ΔDEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is
- (a) 3 cm
- (b) 4 cm
- (c) 6 cm
- (d) 12 cm
Show answer
Answer: (c)
80. PQRA is a rectangle, AP = 22 cm, PQ = 8 cm. ΔABC is a triangle whose vertices lie on the sides of PQRA such that BQ = 2 cm and QC = 16 cm .Then the length of the line joining the mid points of the sides AB and BC is
- (a) 4√2 cm
- (b) 5 cm
- (c) 6 cm
- (d) 10 cm
Show answer
Answer: (b)
81. ΔABC is an isosceles right angled triangle having ∠C = 90°. If D is any point on AB, then AD2+ BD2 is equal to
- (a) CD2
- (b) 2CD2
- (c) 3CD2
- (d) 4CD2
Show answer
Answer: (b)
82. D and E are points on the sides AB and AC respectively of ΔABC such that DE is parallel to BC and AD:DB = 4:5, CD and BE intersect each other at F. Then the ratio of the areas of ΔDEF and ΔCBF
- (a) 16:25
- (b) 16:81
- (c) 81:16
- (d) 4:9
Show answer
Answer: (b)
83. Diagonals of a Trapezium ABCD with AB CD intersect each other at the point O. If AB = 2CD, then the ratio of the areas of ΔAOB and ΔCOD is
- (a) 4:1
- (b) 1:16
- (c) 1:4
- (d) 16:1
Show answer
Answer: (a)
84. If O is the orthocentre of a triangle ABC and ∠BOC = 100°, the measure of ∠BAC is
- (a) 100°
- (b) 180°
- (c) 80°
- (d) 200°
Show answer
Answer: (c)
85. PQ and RS are common tangents to two circles intersecting at A and B. AB, when produced both sides, meet the tangents PQ and RS at X and Y, respectively. If AB = 3 cm, XY = 5 cm, then PQ (in cm) will be
- (a) 3 cm
- (b) 4 cm
- (c) 5 cm
- (d) 2 cm
Show answer
Answer: (b)
87. If sin P + cosec P = 2, then the value of sin7 P + cosec7P is
- (a) 1
- (b) 2
- (c) 3
- (d) 0
Show answer
Answer: (b)
88. If cosx.cosy + sinx.siny = -1 then cosx + cosy is
- (a) -2
- (b) 1
- (c) 0
- (d) 2
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Answer: (c)
89. The value of the expression 2(sin6θ+cos6θ)-3(sin4θ+cos4θ)+1 is
- (a) -1
- (b) 0
- (c) 1
- (d) 2
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Answer: (b)
91. The distance between two pillars is 120 metres. The height of one pillar is thrice the other. The angles of elevation of their tops from the midpoint of the line connecting their feet are complementary to each other. The height (in metres) of the taller pillar is (Use : √3 = 1.732)
- (a) 34.64
- (b) 51.96
- (c) 69.28
- (d) 103.92
Show answer
Answer: (d)
92. If x = cosecθ - sinθ and y = secθ - cosθ, then the relation between x and y is
- (a) x2+ y2+ 3 =1
- (b) x2y2(x2+ y2+3)=1
- (c) x2(x2+ y2- 5)=1
- (d) y2(x2+ y2- 5)=1
Show answer
Answer: (b)
93. A hydrogen filled balloon ascending at the rate of 18 kmph was drifted by wind. Its angle of elevation at 10th and 15th minutes were found to be 60° and 45° respectively. The wind speed (in whole numbers) during the last five minutes, approximately, is equal to
- (a) 7 km/hr
- (b) 11 km/ hr
- (c) 26 km/hr.
- (d) 33 km/hr
Show answer
Answer: (d)
94. The angle of elevation of an aeroplane as observed from a point 30 m above the transparent water-surface of a lake is 30° and the angle of depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water-surface of the lake is
- (a) 60 m
- (b) 45 m
- (c) 50 m
- (d) 75 m
Show answer
Answer: (a)
95. The angles of depression of two ships from the top of a light house are 60° and 45° towards east. If the ships are 300 m apart, the height of the light house is
- (a) 200(3+√3) meter
- (b) 250(3+√3) meter
- (c) 150(3+√3) meter
- (d) 160(3+√3) meter
Show answer
Answer: (c)
96. What is the difference between the total number of females and the total number of males from all the organisations together?
- (a) 2005
- (b) 2050
- (c) 2500
- (d) 2055
Show answer
Answer: (c)
97. By how much percentage is the average number of females from all the organisations together is more than the number of males in organization 'D'?
- (a) 30%
- (b) 38%
- (c) 40%
- (d) 45%
Show answer
Answer: (c)
98. What is the ratio of the number of females from the organisations B and C to the number of males from the organisations D and E?
- (a) 12 : 11
- (b) 12 : 15
- (c) 11 : 15
- (d) 15 : 11
Show answer
Answer: (d)
99. Males from organisations A and B together form what percent of total number of males from organisations C, D and E together?
- (a) 78.04%
- (b) 87.44%
- (c) 47.08%
- (d) 74.08%
Show answer
Answer: (a)
100. What is the ratio of average number of females from the organisations A, B and C to the average number of males from the organisations C, D and E?
- (a) 42 : 41
- (b) 41 : 42
- (c) 40 : 41
- (d) 41 : 40
Show answer
Answer: (a)

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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 3: (c)
Q 4: (c)
Q 5: (d)
Q 6: (c)
Q 7: (b)
Q 9: (a)
Q 10: (c)
Q 11: (c)
Q 12: (c)
Q 13: (d)
Q 16: (a)
Q 17: (c)
Q 18: (b)
Q 19: (d)
Q 21: (b)
Q 22: (d)
Q 23: (c)
Q 24: (c)
Q 25: (c)
Q 26: (c)
Q 27: (c)
Q 28: (b)
Q 29: (d)
Q 30: (d)
Q 31: (c)
Q 34: (d)
Q 36: (b)
Q 37: (c)
Q 38: (a)
Q 40: (a)
Q 42: (c)
Q 43: (b)
Q 44: (a)
Q 45: (d)
Q 46: (b)
Q 47: (a)
Q 49: (c)
Q 50: (b)
Q 51: (b)
Q 52: (a)
Q 53: (a)
Q 54: (d)
Q 55: (d)
Q 56: (c)
Q 57: (b)
Q 58: (c)
Q 60: (a)
Q 61: (b)
Q 62: (c)
Q 65: (a)
Q 68: (b)
Q 71: (b)
Q 75: (a)
Q 76: (c)
Q 77: (b)
Q 78: (c)
Q 80: (b)
Q 81: (b)
Q 82: (b)
Q 83: (a)
Q 84: (c)
Q 85: (b)
Q 87: (b)
Q 88: (c)
Q 89: (b)
Q 91: (d)
Q 92: (b)
Q 93: (d)
Q 94: (a)
Q 95: (c)
Q 96: (c)
Q 97: (c)
Q 98: (d)
Q 99: (a)
Q 100: (a)