### 2015 SSC CGL Tier 2

Quantitative Aptitude

25 Oct

Question Paper with Answer Key

1.

(A) 305

(B) 355

(C) 300

(D) 330

The following graph shows production (in thousands) of two types (P and Q) of vehicles by a factory over the years 2009 to 2014. Study the graph and answer five questions:

2. The total production of Type P vehicles in the years 2009 and 2011 is what percent of total production of Type Q vehicles in 2010 and 2014?

(A) 80

(B) 69.25

(C) 81.25

(D) 75

The following graph shows production (in thousands) of two types (P and Q) of vehicles by a factory over the years 2009 to 2014. Study the graph and answer five questions:

3. The production of Type Q vehicles in 2010 was approximately what percent of Type p vehicles in 2014?

(A) 75

(B) 60

(C) 45.5

(D) 54.5

The following graph shows production (in thousands) of two types (P and Q) of vehicles by a factory over the years 2009 to 2014. Study the graph and answer five questions:

4. Approximate percentage decease in production of Type Q vehicles from 2010 to 2011 is

(A) 16.7

(B) 14.3

(C) 10.1

(D) 12.5

The following graph shows production (in thousands) of two types (P and Q) of vehicles by a factory over the years 2009 to 2014. Study the graph and answer five questions:

5. The ratio of total production of Type P vehicles to total production of Type Q vehicles over the years is

(A) 8 : 5

(B) 48 : 41

(C) 41 : 48

(D) 5 : 8

The following graph shows production (in thousands) of two types (P and Q) of vehicles by a factory over the years 2009 to 2014. Study the graph and answer five questions:

6. In how many of the given years. was the prediction of Type P vehicles of the company more than the average production of this type vehicles in the given years?

(A) 5

(B) 4

(C) 3

(D) 2

7. If 3(a2+b2+c2) = (a+ b+ c)2,then the relation between a, b and c is

(A) a ≠b = c

(B) a = b = c

(C) a ≠ b ≠ c

(D) a = b ≠ c

8. A car covers four successive 7 km distances at speeds of 10 km/hour. 20 km/hour, 60 km/hour respectively. Its average speed over this distance is

(A) 40 km/hour

(B) 20 km/hour

(C) 60 km/hour

(D) 30 km/hour

9. A cylinder with base radius 8 cm and height 2 cm is melted to form a cane of height 6 cm. The radius of the cone will be

(A) 6 cm

(B) 5 cm

(C) 4 cm

(D) 8 cm

10. A dealer fixed I tie price of an article 40% above the cost of production. While selling if the allows a discount of 20% and makes a profit of Rs. 4. 8The cost of production (in Rs.) of the article is

(A) 420

(B) 360

(C) 400

(D) 320

11. Average of n numbers is a. The first number is increased by 2, second one is increased by 4, the third one is increased by a and so on. The average of the new number is

12. It x= a sin Ө – b cos Ө, y = a cos Ө + b sin Ө, then which of the following is true’?

(A) x2 +y2 =a2 + b2

(B) x2/y2 +a2/b2 =1

(C) x2+y2= a2-b2

(D) x2/a2+y2/b2= 1

13.

(A) 1717

(B) 1771

(C) 1171

(D) 1177

14. 64 buckets of water are removed from a cubical shaped water tank completely filled with water, 1/3 of the tank remains filled with Water. The length of each side of the tank is 1.3 m. Assuming that all buckets are of the same measures then the volume (in litres) of water combined by each bucket is

(A) 16

(B) 18

(C) 12

(D) 15

15. In trapezium ABCD, AB || CD and AB = 2CD. its diagonals Intersect at O. If the area of ΔAOB = 84 cm2, then the area of ΔCOD is equal to

(A) 42cm2

(B) 21 cm2

(C) 72 cm2

(D) 26 cm2

16. Water tax is increased by 20% but its consumption is decreased by 20% Then the Increase or decrease In the expenditure of the money is

(A) 5% decrease

(B) 4% decrease

(C) No change

(D) 4% increase

17. A number when divided by 361 gives a remainder 47. If the same number Is divided by 19, the remainder obtained is

(A) 1

(B) 3

(C) 9

(D) 8

18.

(A) 1

(B) 2

(C) 0

(D) -2/3

19. In triangle ABC, DE || BC where D is a point or AB and E is a point on AC. DE divides the area of ΔABC into two equal parts. Then DB: AB is equal to

(A) (√2+1):√2

(B) √2:(√2+1)

(C) √2:(√2-1)

(D) (√2-1):√2

20. A and B have their monthly incomes in the ratio 8: 5, While their monthly expenditures are in the ratio 5 : 3. If they have saved Rs. 12.000 and Rs. 10,000 monthly respectively, then the difference in their monthly income is

(A) Rs. 42,000

(B) Rs. 44,000

(C) Rs. 46,000

(D) Rs. 52,000

21. ABCD is a cyclic quadrilateral. AB and DC when produced meet at P, if PA= 8 cm, PB:: 6 cm. PC= 4 cm, then the length (in cm) of PD is

(A) 6

(B) 12

(C) 8

(D) 10

22. In a school there were 1554 students and the ratio of the number of the boys and girls was 4:3. After few days, 30 girls joined the school but few boys left: as a result the ratio of the boys and girls became 7 : 6. The number of boys who left the school is

(A) 84

(B) 76

(C) 86

(D) 74

23. If 7sin2Ө + 3cos2Ө = 4, then the value of tan Ө is (Ө is acute)

(A) 1/√3

(B) 1/√2

(C) 1

(D) √3

24.

(A) 25

(B) 1/5

(C) 1/25

(D) 5

25. If tan A = n tan B and sin A = m sin B. then the value of cos2 A is

(A) m2 +1/n2+1

(B) m2-1/n2-1

(C) m2+1/n2-1

(D) m2-1/n2+1

26. In an office, 40% of the staff is female 70% of the female staff and 50% of the male staff are married. The percentage of the unmarried staff in the office Is

(A) 42

(B) 60

(C) 54

(D) 64

27. In an examination average mark obtained by the girls of a class Is 85 and the average mark obtained by the boys of the same class is 87. If the girls and boys are in the ratio 4 : 5, average marks of the whole class (approx.) is closest to

(A) 86.4

(B) 86.1

(C) 85.9

(D) 86.5

28. Articles are marked at a price which gives a profit of 25%, Alter Allowing a certain discount the profit reduces to 12 1/2%. The discount percent is

(A) 121/2%

(B) 10%

(C) 12%

(D) 11.1%

29. If sin A + sin2 A =1, then the value of cos2 A + cos4 A is

(A) 1 2/3

(B) 2

(C) 1 ½

(D) 1

30. A manufacturer fixes his selling price at 33% over the cost of production. If cost of production goes up by 12% and manufacturer raises his selling price by 10%. his percentage profit is

(A) 35%

(B) 36 5/9%

(C) 28 3/8%

(D) 30 5/8%

31. A boat moves downstream at the rate of 1 km in 7 1/2 minutes and upstream at the rate of 5 km an hour. What is the speed (in km/hour})of the boat in the still water?

(A) 8

(B) 4

(C) 3 ½

(D) 6 ½

32. The greater number among 350, 440, 530, 620 is

(A) 440

(B) 530

(C) 620

(D) 350

33. Give that the ratio of altitudes of two triangles is 4: 5, ratio at their areas is 3:2. The ratio of their corresponding bases Is

(A) 8:15

(B) 5:8

(C) 15: 8

(D) 8: 5

34. If sec Ө – tan Ө = 1/√3 , the Value of sec Ө tan Ө is

(A) 2/3

(B) 2/√3

(C) 1/√3

(D) 4/√3

35. A man sells an article at 5% above its cost price. If he had bought It at 5% less than what he had paid for it and sold it at Rs.2 less, he would have gained 10%. The cost price of the article is

(A) Rs. 100

(B) Rs. 300

(C) Rs. 200

(D) Rs.400

36.

(A) 11

(B) 0.34

(C) 1.1

(D) 3.4

37. If a + b = 1 find the value of a3+b3 – ab (a2 –b2)2

(A) 0

(B) 1

(C) -1

(D) 2

38. AB and CD are two parallel chords of a circle of lengths 10 cm and 4 cm respectively. If the chords are on the same side of the centre and the distance between them is 3 cm, then the diameter of the circle is

(A) 2 √29 cm

(B) √21cm

(C) 2√21cm

(D) √29 cm

39. Let x be the least number, which when divided by 5,6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves, no remainder. The sum of digits of x is

(A) 22

(B) 21

(C) 18

(D) 24

40. Three science classes A, B and C take a Life Science test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. Then the average score of classes A, B and C is.

(A) 80.5

(B) 81.5

(C) 80

(D) 81

41. Two blends of a commodity costing Rs.35 and Rs.40 per kg respectively are mixed in the ratio 2:3 by weight If one-fifth of the mixture is sold at Rs.46 per kg and the remaking at the rate of Rs.55 per kg, the profit percent is

(A) 50

(B) 20

(C) 30

(D) 40

42.

(A) 1

(B) 2

(C) -1

(D) 0

43. Ram sold two horses at the same price. In one he gets a profit 10% and in the other he gets a loss of 10%. Then Ram gets

(A) no loss or profit

(B) 1% profit

(C) 2% loss

(D) 1 % loss

44. A and B can do a given piece of Work in 8 days, B and C can do the same work in 12 days and A, B, C complete it in 6 days. Number of days inquired to finish the work by A and C is

(A) 8

(B) 16

(C) 24

(D) 12

45. Pipe A can fill an empty tank in 6 hours and pipe B in 8 hours. If both the pipes are opened and after 2 hours pipe A Is closed, how much time B will take to fill the remaining tank?

(A) 2 2/5hours

(B) 7 ½ hours

(C) 2 1/3 hours

(D) 3 1/3 hours

46. There is a number consisting of two digits, the digit in the units place is twice that in the tens place and if 2 be subtracted from the sum of the digits, the difference is equal to 1/6thof the number. The number is

(A) 26

(B) 23

(C) 25

(D) 24

47. The value of cot41°. cot42°. cot43°. cot44°. cot45°. cot46°. cot47°. cot48°. cot49°

(A) 0

(B) 1

(C) √3/2

(D) 1/√2

48. A man purchases some oranges at the rate of 3 for Rs.40 and the same quantity at 5 for Rs.60. if he sells all the oranges at the rate of 3 for Rs. 50. Find his gain or loss percent (to the nearest integer).

(A) 32% profit

(B) 34% loss

(C) 31% profit

(D) 31% loss

49. The perimeter of a rhombus is 60 cm and one of its diagonal is 24cm. The area (in sq.cm) of the rhombus is

(A) 206

(B) 432

(C) 108

(D) 216

50. A sum of money is paid back in two annual instalments of Rs. 17,640 each, allowing 5% compound interest compounded annually The sum borrowed was

(A) Rs. 32,400

(B) Rs. 32,800

(C) Rs.32,000

(D) Rs. 32,200

51. A man starts from a place P and reaches the place Q in 7 hours. He travels 1/4th of the distance at 10 km/hour and the remaining distance al 12Km/hour. The distance, in kilometre, between P and Q is

(A) 72

(B) 80

(C) 90

(D) 70

52. If O is the circum centre of a triangle ABC lying inside the triangle, then ∠OBC + ∠BAC is equal to

(A) 110°

(B) 90°

(C) 120°

(D) 60°

53. The simple interest on a sum of money is 8/25 of the sum. If the number of years is numerically half the rate percent per annum, then the rate percent per Annam is

(A) 8

(B) 5

(C) 6 1/4

(D) 4

54. In ΔABC, ∠BAC – 90° and AD⊥ EC. If BD =3 cm and CD = 4 cm, then the length (in cm) of AD is

(A) 2 √3

(B) 6

(C) 3.5

(D) 5

55. Three glasses of equal volume contains and mixed with water. The ratio of acid and water are 2:3, 3:4 and 4:5 respectively. Contents of these glasses are poured in a large vessel. The ratio of acid and water In the large vessel is

(A) 407 : 560

(B) 417 : 564

(C) 411: 540

(D) 401 : 544

56. If A: B = 2 : 3 and B : C = 3 :7 then A + B: B+C: C+A is

(A) 4:8:9

(B) 5 : 5:9

(C) 4: 10 :9

(D) 5 : 10 : 9

57. The numerical values of the volume and the area of the lateral surface of a right circular cone are equal If the height of the cone be h and radius, be r, the value of 1/h2 + 1/r2 is

(A) 3/1

(B) 9/1

(C) 1/9

(D) 1/3

58. Two places P and Q are 162 km apart A train leaves P for Q and simultaneously another train leaves Q for P. They meet at the end of 6 hours. If the former train travels 8km/hour faster then the other, then speed of train from Q is

(A) 9 ½ km/hour

(B) 10 5/6 cm/hour

(C) 12 5/6 km/hour

(D) 8 ½ km/hour

59. If tan Ө – cot Ө= 0 and Ө is positive acute angle. then the value of tan(Ө+15°)/tan(Ө-15°) is

(A) 1/3

(B) √3

(C) 1/√3

(D) 3

60. The portion of a ditch 48 m long, 16.5 m wide and 4 m deep that can be filled with stones and earth available during excavation of a tunnel, cylindrical in shape, of a diameter 4 m and length 56 m is [Take π =22/7]
(A) 1/9 part

(B) 2/9 part

(C) ½ part

(D) ¼ part

61. If (x3 – y3) : (x2 + xy + y2) = 5: 1 and (x2-y2) :(x-y) = 7:1, then the ratio 2x : 3y equals

(A) 2:3

(B) 4:1

(C) 4 : 3

(D) 3 : 2

62. If x = a1/2 +,a-1/2, y = a1/2 – a-1/2, then value of (x4-x2y2-1)+(y4-x2y2+1)

(A) 16

(B) 14

(C) 12

(D) 13

63. The marked price of a tape recorder is Rs. 12,600. A festival discount of 5% is allowed on it. Further for cash payment, a second discount of 2% is given. The cash payment, In rupees, that Is to be made for buying it is

(A) 11,730,60

(B) 11,073,60

(C) 11,703,60

(D) 11,370,60

64. If a man walks at the rate of 5 km/hour, he misses a train by 7 minutes. However, if he walks at the rate of 6 km/hour, he reaches the station 5 minutes before the arrival of the train. The distance covered by him to reach the station is

(A) 6 km

(B) 7 km

(C) 4 km

(D) 6.25 km

65. If x – √3 -√2 = 0 and y – √3 +√2 = 0 then value of (x3 – 20√2) – (y3 + 2 √2 )

(A) 3

(B) 2

(C) 0

(D) 1

66. The rad of two solid Iron spheres are 1 cm and 6 cm respectively. A hollow sphere Is made by melting the two spheres, it the external radius of the hollow sphere is 9 cm, then its thickness (in cm) is

(A) 0.5

(B) 2

(C) 1.5

(D) 1

67. There is a wooden sphere of radius 6√3 cm, The surface area of the largest possible cube cut out from the sphere will be

(A) 464√3 cm2

(B) 646√ 3cm2

(C) 462 cm2

(D) 864 cm2

68. If 60% of A = 30 % of B , B = 40 % of C and C =x% of A, then value of x is

(A) 200

(B) 500

(C) 300

(D) 800

69. A and B can do a piece of work in 30 and 36 days respectively They began the work together but A leaves after some days and B finished the remaining work In 25 days. After how many days did A leave?

(A) 6 days

(B) 5 days

(C) 11 days

(D) 10 days

70. A sum of money placed at compound interest doubles itself in 5 years. It will amount to eight times Itself at the same rate of interest In

(A) 10 years

(B) 20 years

(C) 12 years

(D) 15 years.

71. Quadrilateral ABCD is circumscribed about a circle. If the lengths of AB, BC, CD are 7 cm, 8.5 cm and 9.2 cm respectively, then the length (in cm) of DA is

(A) 16.2

(B) 7.2

(C) 7.7

(D) 10.7

72. A right prism has a triangular base whose sides are 13 cm, 20 cm and 21 cm. If the altitude of the prism is B cm, then its volume is

(A) 1134 cm3

(B) 1314 cm3

(C) 1413 cm3

(D) 1143 cm3

73. 300 grams of sugar solution has 40% of sugar in it How much sugar should be added to make it 50 % in the solution?

(A) 60 gms

(B) 10 gms

(C) 80 gms

(D) 40 gms

74. The area of isosceles trapezium is 176cm2 and the height is 2/11th of the sum of its parallel sides .If the ratio of the length of the parallel sides Is 4 : 7, then the length of a diagonal (in cm) is

(A) 2√137

(B) √137

(C) 24

(D) 28ss

75. A and B are centres of two circles of radii 11 cm and 6 cm, respectively PQ is a direct common tangent to the circles If AB = 13 cm, then length of PQ will be

(A) 8.5 cm

(B) 12 cm

(C) 13 cm

(D) 17 cm

76. A, B and C can do work separately in 16, 32 and 48 days respectively .They started the work together but B leaving off 8 days and C six days before the completion of the work. In what time is the Work finished?

(A) 12 days

(B) 10 days

(C) 14 days

(D) 9 days

77. AD is perpendicular to the internal bisector of ∠ABC of ΔABC. DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm) is

(A) 3

(B) 6

(C) 8

(D) 4

78. The average of five consecutive positive Integers is n. If the next two integers are also included, the average of all these integers will

(A) increase by 1

(B) remains the same

(C) increase by 2

(D) Increase by 1.5

79. If a-1/a-3 = 5, then the value of(a – 3)3-1/(a-3)3 is

(A) 14

(B) 5

(C) 2

(D) 7

80. A plane divides a right circular cone into two parts of equal volume. If the plane is parallel to the base, then the ratio, in which the height of the cone Is divided. Is

(A) 1: 3√2

(B) 1:√2

(C) 1:3√2-1

(D) 1:3√2+1

81. Let x be the smallest number, which when added to 2000 makes the resulting number divisible by 12, 16, 18 and 21. The sum of the digits of x is

(A) 4

(B) 7

(C) 6

(D) 5

82. The diameter of each wheel of a car is 70 cm if each wheel rotates 400 times per minute, then the speed of the car (in Km/hr) is (Take π = 22/7]
(A) 52.8

(B) 0.528

(C) 528

(D) 5.28

83. The average age of 30.students of a class is 14 years 4 months. After admission of 5 new students in the class the average becomes 13 years 9 months. The youngest one of the five new students is 9 years 11 months old. The average age of the remaining 4 new students is

(A) 13 years 6 months

(B) 10 years 4 months

(C) 11 years 2 months

(D) 12 years 4 months

84. P and Q together can do a job in 6 days Q and R can finish the same job m 60/7 days. P sorted the work and worked for 3 days. Q and R continued for 6 days. Then the difference of days in which R and P can complete the job is

(A) 8

(B) 12

(C) 10

(D) 15

85. A telegraph post is bent at a point above the ground due to storm. Its top just touches the ground at a distance of 10√3 m from its foot and makes an angle of 30° with the horizontal Then height (in metres) of the telegraph post is

(A) 24

(B) 20

(C) 25

(D) 30

86. It 5cosӨ +12sin Ө = 13, 0° < Ө <90°, then the Value of sin Ө is

(A) -12/13

(B) 5/13

(C) 12/13

(D) 6/13

87. If a+1/b= b+1/c = c+1/a, where a ≠ b ≠ c ≠ 0 then the value of a2b2c2 is

(A) -1

(B) 1

(C) abc

(D) 0

88. The H.C F and L.C.M of two numbers are 21 and 84 respectively If the ratio of the two numbers is 1:4, then the larger of the two numbers Is

(A) 48

(B) 108

(C) 12

(D) 84

89. If 90 men can do a certain job in 16 days, working 12 hours/day, then the part of that work which can be completed by 70 men in 24 days, working 8 hours/day is

(A) 2/3

(B) 7/9

(C) 1/3

(D) 5/8

90. A sum of Rs.7,930 is divided into 3 parts and given on loan at 5% simple interest to A, B and C for 2,3 and 4 years respectively. If the amounts of all three are equal after their respective periods of loan, then the A received a loan of

(A) Rs. 2,750

(B) Rs. 2,800

(C) Rs. 2,760

(D) Rs. 3,050

91. The Value of (coseca – sina) (seca – cosa) (tana + cota)

(A) 4

(B) 2

(C) 1

(D) 6

92. There would be a 10% loss, if rice is sold at Rs.54 per kg. To earn a profit of 20%, the price of rice per kg Will be

(A) Rs.65

(B) Rs.63

(C) Rs.70

(D) Rs.72

93. If a hemisphere is melted and four spheres of equal volume are made the radius of each sphere will be equal to

(A) radius at the hemisphere

(B) 1/6th of the radius of the hemisphere

(C) 1/2 of the radius of the hemisphere

(D) 1/4th of the radius of the hemisphere

94. 60 kg of an alloy A is mixed with 100 kg of alloy B If alloy A has lead and tin in the ratio 3 : 2 and alloy B has tin and copper in the ratio 1 : 4, the amount of tin in the new alloy is

(A) 53 kg

(B) 80 kg

(C) 44 kg

(D) 24 kg

95. Base of a right pyramid Is a square of side 10cm If the height of the pyramid Is 12cm, then its total surface area is

(A) 260 cm2

(B) 460 cm2

(C) 400 cm2

(D) 300 cm2

96. If a shopkeeper wants to give 20% discount on a toy, he has to sell It for Rs.300. If he sells it at Rs.405, then his gain percent is

(A) 6%

(B) 4%

(C) 8%

(D) 5%

97. The unit digit In the product (2467)153 X (341)72 is

(A) 1

(B) 3

(C) 7

(D) 9

98. The interior angle of a regular polygon exceeds its exterior angle by 108°. The number of sides of the polygon is

(A) 10

(B) 16

(C) 14

(D) 12

99.

(A) 1/8

(B) 1/64

(C) 1/16

(D) 1/32

100. The centroid of a ΔABC is G. The area of Δ abc is 50 cm2. The area of ΔGBC is

(A) 40 cm2

(B) 30 cm2

(C) 20 cm2

(D) 10 cm2

1. D

2. A

3. D

4. A

5. B

6. C

7. B

8. B

9. D

10. C

11. A

12. A

13. A

14. B

15. B

16. B

17. C

18. D

19. D

20. A

21. B

22. B

23. A

24. A

25. B

26. A

27. B

28. B

29. D

30. D

31. D

32. A

33. C

34. A

35. D

36. B

37. A

38. A

39. C

40. B

41. D

42. A

43. D

44. A

45. D

46. D

47. B

48. A

49. D

50. B

51. B

52. B

53. A

54. A

55. D

56. D

57. C

58. A

59. D

60. B

61. B

62. A

63. A

64. A

65. C

66. D

67. D

68. B

69. B

70. D

71. C

72. A

73. A

74. A

75. B

76. A

77. B

78. A

79. A

80. C

81. B

82. A

83. B

84. C

85. D

86. C

87. B

88. D

89. B

90. C

91. C

92. D

93. C

94. C

95. D

96. C

97. C

98. A

99. A

100. C