(Papers) SSC CGL (Tier – 2) Exam – 2017 “held on 20-Feb-2018 ” Morning Shift” (Quantitative Ability)Flame Institute

QID : 1 – Which of the following statement(s) is/are TRUE?

I. 33³> 3³³
II. 333 > (3³)³

Options:
1) Only I
2) Only II
3) Both I and II
4) Neither I nor II
Correct Answer: Neither I nor II

QID : 2 – If P = 2² + 6² + 10² + 14² + … 94² and Q = 1² + 5² + 9² + … 81², then what is the value of P – Q?

Options:
1) 24645
2) 26075
3) 29317
4) 31515
Correct Answer: 26075

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

Options:
1) 27272727.5
2) 25252525.5
3) 27777777.5
4) 25555555.5
Correct Answer: 27777777.5

QID : 4 – If M = 0.1 + (0.1)² + (0.01)² and N = 0.3 + (0.03)² + (0.003)², then what is the value of M + N?

Options:
1) 0.411009
2) 0.413131
3) 0.313131
4) 0.131313
Correct Answer: 0.411009

QID : 5 –

Options:
1) P < Q < R
2) R < Q < P
3) Q < P < R
4) R < P < Q
Correct Answer: R < Q < P

QID : 6 –

Options:
1) Only I
2) Only II
3) Only III
4) None is true.
Correct Answer: Only I

QID : 7 –

Options:
1) Only I
2) Only II
3) Both I and II
4) Neither I nor II
Correct Answer: Only I

QID : 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.

Options:
1) Only I and II
2) Only II and III
3) Only I and III
4) All are true.
Correct Answer: All are true.

QID : 9 – If M = (3/7) ÷ (6/5) × (2/3) + (1/5) × (3/2) and N = (2/5) × (5/6) ÷ (1/3) + (3/5) × (2/3) ÷ (3/5), then what is the value of M/N?

Options:
1) 207/560
2) 339/1120
3) 113/350
4) 69/175
Correct Answer: 113/350

QID : 10 – M is the largest 4 digit number, which when divided by 4, 5, 6 and 7 leaves remainder as 2, 3, 4, and 5 respectively. What will be the remainder when M is divided by 9?

Options:
1) 2
2) 1
3) 3
4) 6
Correct Answer: 1

QID : 11 – Which of the following statement(s) is/are TRUE?

I. √11 + √7 < √10 + √8.
II. √17 + √11 > √15 + √13

Options:
1) Only I
2) Only II
3) Both I and II
4) Neither I nor II
Correct Answer: Only I

QID : 12 –

Options:
1) Only I and II
2) Only I and III
3) Only I
4) All are true.
Correct Answer: Only I and II

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

Options:
1) 793
2) 681
3) 758
4) 715
Correct Answer: 758

QID : 14 – If (x + y)/z = 2, then what is the value of [y/(y – z)] + [x/(x – z)]?

Options:
1) 0
2) 1
3) 2
4) – 1
Correct Answer: 2

QID : 15 – If α and β are the roots of equation x² – 2x + 4 = 0, then what is the equation whose roots are α³/β² and β³/α²?

Options:
1) x2 – 4 x + 8 = 0
2) x2 – 32 x + 4 = 0
3) x2 – 2 x + 4 = 0
4) x2 – 16 x + 4 = 0
Correct Answer: x2 – 2 x + 4 = 0

QID : 16 – If one root of the equation Ax² +Bx + C = 0 is two and a half times the others, then which of the following is TRUE?

Options:
1) 7B2 = 3 CA
2) 7B2 = 4 CA
3) 7B2 = 36 CA
4) 10B2 = 49 CA
Correct Answer: 10B2 = 49 CA

QID : 17 – If x² – 12x + 33 = 0, then what is the value of (x – 4)² + [1/(x – 4)²]?

Options:
1) 16
2) 14
3) 18
4) 20
Correct Answer: 14

QID : 18 – If a⁴ + 1 = [a²/b²] (4b² – b⁴ – 1), then what is the value of a⁴ + b⁴?

Options:
1) 2
2) 16
3) 32
4) 64
Correct Answer: 2

QID : 19 –

Options:
1) 3/10, 7/10
2) 1/10, 9/10
3) 2/5, 3/5
4) 1/5, 4/5
Correct Answer: 1/10, 9/10

QID : 20 –

Options:
1) 450
2) 300
3) 600
4) 750
Correct Answer: 300

QID : 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?

Options:
1) – 28
2) – 14
3) – 31
4) – 45
Correct Answer: – 31

QID : 22 –

Options:
1) 414
2) 364
3) 384
4) 464
Correct Answer: 414

QID : 23 –

Options:
1) 1 : 1
2) 1 : 4
3) 2 : 3
4) 5 : 2
Correct Answer: [ No Correct Answer ]

QID : 24 –

Options:
1) 6
2) 4
3) 2
4) 3
Correct Answer: 2

QID : 25 –

Options:
1) 4√10
2) 2√10
3) 6√10
4) 3√5
Correct Answer: 4√10

QID : 26 – In a trapezium, one diagonal divides the other in the ratio 2 : 9. If the length of the larger of the two parallel sides is 45 cm, then what is the length (in cm) of the other parallel side?

Options:
1) 10
2) 5
3) 18
4) 14
Correct Answer: 10

QID : 27 –

Options:
1) [(5√3) – 3]
2) [(4√3) – 2]
3) [(2√5) – 1]
4) [(2√6) – 1]
Correct Answer: [(2√6) – 1]

QID : 28 –

Options:
1) 5√10
2) 4√10
3) 8√5
4) 16√2
Correct Answer: 5√10

QID : 29 –

Options:
1) 4.25
2) 3.75
3) 3.5
4) 4.55
Correct Answer: 3.75

QID : 30 –

Options:
1) 35.33
2) 37.33
3) 41.33
4) 43.33
Correct Answer: 37.33

QID : 31 –

Options:
1) 1 : 4
2) 2 : 5
3) 1 : 3
4) 2 : 7
Correct Answer: 1 : 3

QID : 32 – The distance between the centres of two circles is 61 cm and their radii are 35 cm and 24 cm. What is the length (in cm) of the direct common tangent to the circles?

Options:
1) 60
2) 54
3) 48
4) 72
Correct Answer: 60

QID : 33 –

Options:
1) (64√3)/3
2) (177√3)/2
3) (135√3)/2
4) (98√3)/3
Correct Answer: (135√3)/2

QID : 34 – PQR is a triangle, whose area is 180 cm². S is a point on side QR, such that PS is the angle bisector of ∠QPR. If PQ : PR = 2 : 3, then what is the area (in cm2) triangle PSR?

Options:
1) 90
2) 108
3) 144
4) 72
Correct Answer: 108

QID : 35 –

Options:
1) 98
2) 196
3) 122.5
4) 171.5
Correct Answer: 196

QID : 36 – ABCDEF is a regular hexagon of side 12 cm. What is the area (in cm²) of the triangle ECD?

Options:
1) 18√3
2) 24√3
3) 36√3
4) 42√3
Correct Answer: 36√3

QID : 37 – PQRS is a square whose side is 16 cm. What is the value of the side (in cm) of the largest regular octagon that can be cut from the given square?

Options:
1) 8 – 4√2
2) 16 + 8√2
3) 16√2 – √16
4) 16 – 8√2
Correct Answer: 16√2 – √16

QID : 38 –

Options:
1) 21 + 14√2
2) 21 – 14√2
3) Both 21 + 14√2 and 21 – 14√2
21 + 14√2 तथा 21 – 14√2 दोनों
4) None of these
Correct Answer: 21 – 14√2

QID : 39 –

Options:
1) 385 – 221√2
2) 308 – 154√2
3) 154 – 77√2
4) 462 – 308√2
Correct Answer: 462 – 308√2

QID : 40 – A prism has a regular hexagonal base with side 6 cm. If the total surface area of prism is 216√3 cm², then what is the height (in cm) of prism?

Options:
1) 3√3
2) 6√3
3) 6
4) 3
Correct Answer: 3√3

QID : 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?

Options:
1) 1 : 4 : 8
2) 1 : 3 : 5
3) 1 : 3 : 9
4) 1 : 6 : 12
Correct Answer: 1 : 3 : 5

QID : 42 – A right circular cylinder has height as 18 cm and radius as 7 cm. The cylinder is cut in three equal parts (by 2 cuts parallel to base). What is the percentage increase in total surface area?

Options:
1) 62
2) 56
3) 48
4) 52
Correct Answer: 56

QID : 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?

Options:
1) 5 : 8
2) 4 : 9
3) 3 : 7
4) 7 : 10
Correct Answer: 7 : 10

QID : 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 1/6th the radius of the large sphere. What is the sum (in cm²) of curved surface areas of all small spheres?

Options:
1) 31276
2) 36194
3) 25182
4) 33264
Correct Answer: 33264

QID : 45 –

Options:
1) 3318.33
2) 3462.67
3) 3154.67
4) 3248.33
Correct Answer: 3462.67

QID : 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 cm²) of each part?

Options:
1) 96 + 64√2
2) 80 + 64√2
3) 96 + 48√2
4) 80 + 48√2
Correct Answer: 96 + 64√2

QID : 47 – A regular pyramid has a square base. The height of the pyramid is 22 cm and side of its base is 14 cm. Volume of pyramid is equal to the volume of a sphere. What is the radius (in cm) of the sphere?

Options:
1)

2) 7
3) 14
4)

Correct Answer: 7

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

Options:
1) cos x sin y
2) (sin y)/(sin x)
3) sin z
4) sin x tan y
Correct Answer: (sin y)/(sin x)

QID : 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)]?

Options:
1) 0
2) tan2 x
3) 1
4) 2 tan x
Correct Answer: tan2 x

QID : 50 – What is the value of [sin (90o – 10θ) – cos (p – 6θ)]/ [cos (p/2 – 10θ) – sin (p – 6θ)]?

Options:
1) tan 2θ
2) cot 2θ
3) cot θ
4) cot 3θ
Correct Answer: cot 2θ

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

Options:
1) 3√2
2) 3/√2
3) 1/√2
4) √2
Correct Answer: √2

QID : 52 –

Options:
1) tan2 θ sec2 θ
2) sec4 θ
3) tan4 θ
4) tan2 θ sin2 θ
Correct Answer: tan2 θ sec2 θ

QID : 53 – What is the value of [tan (90 – A) + cot (90 – A)]²/[2 sec² (90 – 2A)]?

Options:
1) 0
2) 1
3) 2
4) – 1
Correct Answer: 2

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

Options:
1) -cos y
2) -sin y
3) cos x
4) tan y
Correct Answer: -cos y

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

Options:
1) 50√3
2) 100√3
3) 200√3
4) 300√3
Correct Answer: 100√3

QID : 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 the ground is 30o. Assuming that there is no slack in the string, then what is the height (in metres) of the kite?

Options:
1) 210
2) 140√3
3) 210√3
4) 150
Correct Answer: 210

QID : 57 – A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450√3 metres from point P observes that angle of elevation of the balloon is 60o. Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon?

Options:
1) 4.25
2) 3.75
3) 4.5
4) 3.45
Correct Answer: 3.75

QID : 58 –

What is the total number of wooden bats of brand A manufactured by company T?

Options:
1) 23420
2) 22990
3) 68920
4) 72600
Correct Answer: 72600

QID : 59 –

N = Wooden bats of Brand B manufactured by U.
M = Total wooden bats manufactured by R and W together.
What is the value of N/M?

Options:
1) 0.043
2) 0.061
3) 0.125
4) 0.087
Correct Answer: 0.061

QID : 60 –

P = Sum of wooden bats of Brand B manufactured by S and wooden bats of Brand A manufactured by W.
Q = Difference of Brand B wooden bats and Brand A wooden bats manufactured by U.

What is the value P – Q?

Options:
1) 67500
2) 177700
3) 159500
4) 123500
Correct Answer: 159500

QID : 61 –

Taking all 6 companies together, how many wooden bats of Brand A have been produced?

Options:
1) 691000
2) 724000
3) 683000
4) 716000
Correct Answer: 691000

QID : 62 –

X = Average of plastic bats manufactured by V, U and T.
Y = Wooden bats of Brand A manufactured by V.
What is the value X – Y?

Options:
1) 197600
2) 432890
3) 260000
4) 293300
Correct Answer: 260000

QID : 63 – A drum contains 80 litres of ethanol. 20 litres of this liquid is removed and replaced with water. 20 litres of this mixture is again removed and replaced with water. How much water (in litres) is present in this drum now?

Options:
1) 45
2) 40
3) 35
4) 44
Correct Answer: 35

QID : 64 – 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?

Options:
1) 1600
2) 9800
3) 6400
4) 12800
Correct Answer: 12800

QID : 65 – 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)?

Options:
1) 3600
2) 4800
3) 6000
4) 7200
Correct Answer: 4800

QID : 66 – 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?

Options:
1) 227000
2) 250000
3) 375000
4) 325000
Correct Answer: 325000

QID : 67 – 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.

Options:
1) 1440
2) 960
3) 1920
4) 1280
Correct Answer: 1440

QID : 68 – 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?

Options:
1) 3400
2) 3600
3) 2550
4) 2750
Correct Answer: 2550

QID : 69 – Working together A, B and C can complete a task in 12 days. A and B can do the task in 55 days and 66 days respectively if they worked alone. In how many days can C do the task if he worked alone?

Options:
1) 22
2) 44
3) 20
4) 40
Correct Answer: 20

QID : 70 – B would have taken 10 hours more than what A would have taken to complete a task if each of them worked alone. Working together they can complete the task in 12 hours. How many hours would B take to do 50% of the task?

Options:
1) 30
2) 15
3) 20
4) 10
Correct Answer: 15

QID : 71 – Giving two successive discounts of 20% is same as giving one discount of ________ %.

Options:
1) 36
2) 40
3) 44
4) 50
Correct Answer: 36

QID : 72 – 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?

Options:
1) 1200
2) 1500
3) 1000
4) 2000
Correct Answer: 1200

QID : 73 – 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?

Options:
1) 18750
2) 21000
3) 25000
4) 17850
Correct Answer: 25000

QID : 74 – If 60% discount is offered on the marked price and selling price becomes equal to cost price then what was the % mark up?

Options:
1) 100
2) 250
3) 150
4) 40
Correct Answer: 150

QID : 75 – If 3A = 6B = 9C; What is A : B : C

Options:
1) 6 : 3 : 1
2) 6 : 3 : 2
3) 9 : 3 : 6
4) 9 : 3 : 1
Correct Answer: 6 : 3 : 2

QID : 76 – 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.

Options:
1) 6000
2) 7200
3) 8400
4) 4800
Correct Answer: 7200

QID : 77 – What is the third proportional to 10 and 20?

Options:
1) 30
2) 25
3) 50
4) 40
Correct Answer: 40

QID : 78 – 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?

Options:
1) 72000
2) 60000
3) 50000
4) 86400
Correct Answer: 60000

QID : 79 – 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 (in Rs) in revenue if revenue before increase in price of ticket was Rs 36,800?

Options:
1) 21250
2) 9400
3) 7850
4) 12850
Correct Answer: 9400

QID : 80 – 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?

Options:
1) 15 : 14
2) 14 : 13
3) 16 : 15
4) 17 : 16
Correct Answer: 15 : 14

QID : 81 – Of the 3 numbers whose average is 22, the first is 3/8th the sum of other 2. What is the first number?

Options:
1) 16
2) 20
3) 22
4) 18
Correct Answer: 18

QID : 82 – The average of three consecutive odd numbers is 52 more than 1/3rd of the largest of these numbers. What is the smallest of these numbers?

Options:
1) 79
2) 75
3) 81
4) 77
Correct Answer: 77

QID : 83 – A batsman scores 98 runs in the 17th match of his career. His average runs per match increased by 2.5. What is his average before the 17th match?

Options:
1) 58
2) 60.5
3) 63
4) 55.5
Correct Answer: 55.5

QID : 84 – What is the average of all numbers between 100 and 200 which are divisible by 13?

Options:
1) 147.5
2) 145.5
3) 143.5
4) 149.5
Correct Answer: 149.5

QID : 85 – A vendor buys bananas at 9 for Rs 8 and sells at 8 for Rs 9. What will be the profit or loss (in %)?

Options:
1) 13.28% profit
2) 26.56% loss
3) 26.56% profit
4) 13.28% loss
Correct Answer: 26.56% profit

QID : 86 – 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?

Options:
1) 250
2) 300
3) 275
4) 325
Correct Answer: 275

QID : 87 – A wholesaler had 200 dozens of mangoes. He sold some of these mangoes at 20% profit and the rest at 10% profit, so that he made 13% profit on selling all the mangoes. How many mangoes (in dozens) did he sell at 20% profit?

Options:
1) 140
2) 60
3) 80
4) 120
Correct Answer: 60

QID : 88 – If the selling price is tripled and cost price doubled the profit would become 65%. What is the present profit (in %)?

Options:
1) 20
2) 15
3) 25
4) 10
Correct Answer: 10

QID : 89 – 0.06% of 250% of 1600 is _________.

Options:
1) 24
2) 0.24
3) 0.024
4) 2.4
Correct Answer: 2.4

QID : 90 – 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?

Options:
1) 250
2) 200
3) 150
4) 100
Correct Answer: 150

QID : 91 – When a number is increased by 216, it becomes 140% of itself. What is the number?

Options:
1) 540
2) 756
3) 450
4) 675
Correct Answer: 540

QID : 92 – 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)?

Options:
1) 280
2) 400
3) 500
4) 350
Correct Answer: 400

QID : 93 – A bus travels 720 km in 20 hours. Calculate its average speed in meters/second.

Options:
1) 12
2) 15
3) 18
4) 10
Correct Answer: 10

QID : 94 – If a boat goes upstream at a speed of 21 km/h and comes back the same distance at 28 km/h. What is the average speed (in km/hr) for the total journey?

Options:
1) 24.5
2) 24
3) 25
4) 25.4
Correct Answer: 24

QID : 95 – Two runners A and B start running at 12 km/hr and 16 km/hr towards each other. They meet after 1 hour and 30 minutes. How far (in km) were they from each other when they started?

Options:
1) 42
2) 36
3) 40
4) 45
Correct Answer: 42

QID : 96 – 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 factor of 1/6th, so it takes 36 minutes more than Flight A to complete the same journey? What is the speed of Flight A (in km/hr)?

Options:
1) 800
2) 900
3) 750
4) 720
Correct Answer: 800

QID : 97 – In how many years will Rs 2,000 yield Rs 662 as compound interest at 10% per annum compounded annually?

Options:
1) 3
2) 2
3) 4
4) 5
Correct Answer: 3

QID : 98 – What is the compound interest earned on Rs 80,000 at 40% per annum in 1 year compounded quarterly?

Options:
1) 28317
2) 37128
3) 18732
4) 21387
Correct Answer: 37128

QID : 99 – 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)?

Options:
1) 81000
2) 75000
3) 80000
4) 72000
Correct Answer: 80000

QID : 100 – What is the rate of interest (in %) if simple interest earned on a certain sum for the 3 years is Rs 6,000 and compound interest earned for 2 years is Rs 4,160?