QUANTITATIVE APTITUDE Directions (5 Questions): Refer to the graph and answer the given questions. Data related to number of books purchased for two libraries (A and B) during 6 years

31. What is the respective ratio between total number of books purchased for libraries A and B together in 2003 and total number of books purchased for the same libraries together in 2007?

a. 22 : 31 b. 24 : 31 c. 11 : 17 d. 11 : 19 e. 22 : 35

Ans: a Sol. Required ratio= (640 + 240) : (760 + 480)= 880 : 1240 = 22 : 31

32. What is the average number of books purchased for library A during 2004, 2005, 2007 and 2008?

a. 465 b. 455

c. 460 d. 445 e. 450

Ans: b Sol. Required average

160 + 380 + 760 + 5204

1820= = 4554

33. Out of the total number of books purchased by libraries A and B together in 2008, only 20% are graphic novels. What is the total number of graphic novels purchased for libraries A and B together in 2008?

a. 324 b. 312 c. 272 d. 336 e. 288

Ans: c Sol. Total number of books bought in 2008= 520 + 840 = 1360

Total number of graphic novels1360 20= 272

100

34. The number of books purchased for library B increased by what percent from 2003 to 2006?

a. 11753

b. 11723

c. 21963

d. 11833

e. 21943

Ans: d Sol.

Required percentage increase680 - 240 = 100

2404400 550 1= = = 183 %24 3 3

35. The number of books purchased for library B in 2003 is what percent of the number 0f books purchased for library A in 2006?

a. 30 b. 35 c. 55 d. 40 e. 45

Ans: a Sol. Required per cent

240= 100 = 30800

Directions (36 - 40): In these questions two equations numbered I and II are given. You have to solve both the equations and give answer (1) if < yx (2) if > yx (3) if yx (4) if yx (5) if = yx or relationship between x and y cannot be established 36.

2

2

I. 2 + 23 + 63 = 0II. 4y + 19y + 21 = 0

x x

a. < yx b. > yx c. yx d. yx e. = yx or relationship between x and y cannot be established

Ans: a Sol.

2

2

2

2

2 + 23 + 63 = 0 2 + 14 + 9 + 63 = 0 2 ( + 7) + 9 ( + 7) = 0 (2 + 9) ( + 7) = 0

9 = or, 92

4y + 19y + 21 = 0 4y + 12y + 7y + 21 = 0 4y (y + 3) + 7 (y + 3) = 0 (4y + 7) (y + 3)

x xx x xx x xx x

x

I.

II.

= 07 y = or, 3

2Clearly, < yx

37.

2

2

I. 3 + 29 + 56 = 0II. 2y + 15y + 25 = 0

x x

a. < yx b. > yx c. yx d. yx e. = yx or relationship between x and y cannot be established

Ans: a Sol.

2

2

2

2

3 + 29 + 56 = 0 3 + 21 + 8 + 56 = 0 3 ( + 7) + 8 ( + 7) = 0 (3 + 8) ( + 7) = 0

8 = or, 72

2y + 15y + 25 = 0 2y + 10y + 5y + 25 = 0 2y (y + 5) + 5 (y + 5) = 0 (2y + 5) (y + 5)

x xx x xx x xx x

x

I.

II.

= 05 y = or, 5

2Clearly, < yx

38.

2

2

I. 3 + 23 + 44 = 0II. 3y + 20y + 33 = 0

x x

a. < yx b. > yx c. yx d. yx e. = yx or relationship between x and y cannot be established

Ans: d Sol.

2

2

2

2

3 + 23 + 44 = 0 3 + 12 + 11 + 44 = 0 3 ( + 4) + 11 ( + 4) = 0 (3 + 11) ( + 4) = 0

11 = or, 44

3y + 20y + 33 = 0 3y + 9y + 11y + 33 = 0 3y (y + 3) + 11 (y + 3) = 0 (3y + 11) (

x xx x xx x xx x

x

I.

II.

y + 3) = 011 y = or, 33

Clearly, yx

39.

2

2

I. 4 29 + 45 = 0II. 3y 19y + 28 = 0

x x

a. < yx b. > yx c. yx d. yx e. = yx or relationship between x and y cannot be established

Ans: e Sol.

2

2

2

2

4 29 + 45 = 0 4 20 9 + 45 = 0 4 ( 5) 9 ( 5) = 0 (4 9) ( 5) = 0

9 = or, 54

3y 19y + 28 = 0 3y 12y 7y + 28 = 0 3y (y 4) 7 (y 4) = 0 (3y 7) (y 4) =

x xx x xx x xx x

x

I.

II.

07 y = or, 43

40.

2

2

I. 2 13 + 21 = 0II. 5y 22y + 21 = 0

x x

a. < yx b. > yx c. yx d. yx e. = yx or relationship between x and y cannot be established

Ans: c Sol.

2

2

2

2

2 13 + 21 = 0 2 6 7 + 21 = 0 2 ( 3) 7 ( 3) = 0 (2 7) ( 3) = 0

7 = or, 32

5y 22y + 21 = 0 5y 15y 7y + 21 = 0 5y (y 3) 7 (y 3) = 0 (5y 7) (y 3) =

x xx x xx x xx x

x

I.

II.

07 y = or, 35

Clearly, yx

41.

A, B and C start a small busied ness. A contributes 1 th5

of the total capital invested in the

business. B contributes as much as A and C together. Total profit at the end of the year was Rs. 5,200. What was C's profit share? (in Rupees)

a. 1510 b. 2510 c. 1500 d. 2560 e. 1560

Ans: e Sol.

Total investment = Rs. (let)

A's investment = Rs. 5

(B + C)'s investment = 5

4= Rs. ........(i)5

B's investment

= + C's investment5

(B C)'s investment

= Rs. ..........(ii)5

On adding

xx

xx

x

x

x

both equations, 2 B's investment

4 = Rs. = Rs. 5 5

B's investment = Rs. 2

From equation (i) C's investment

4= Rs. 5 2

8 5 3= Rs. = Rs. 10 10

Ratio of profit sharing

=

x x x

x

x x

x x x

x

3 : : 5 2 10

= 2 : 5 : 33 C's share = 5200

10= Rs. 1560

x x

Directions (42 - 46): What will come in place of the question mark (?) in the given number series? 42. 17 19 25 37 ? 87

a. 63

b. 52 c. 55 d. 67 e. 57

Ans: e Sol. The pattern is :17 + 1 2 = 17 + 2 = 1919 + 2 3 = 19 + 6 = 2525 + 3 4 = 25 + 12 = 37

37 + 4 5 = 37 + 20 = 5757 + 5 6 = 57 + 30 = 87

43. 61 82 124 187 ? 376

a. 271 b. 263 c. 257 d. 287 e. 249

Ans: a Sol. The pattern is :61 + 1 21 = 61 + 21 = 8282 + 2 21 = 82 + 42 = 124124 + 3 21 = 124 + 63 = 187

187 + 4 21 = 187 + 84 = 127271 + 5 21 = 271 + 105 = 376

44. 23 30 46 80 141 ?

a. 244 b. 212 c. 226 d. 220 e. 238

Ans: e Sol.

The pattern is :23 + 7 = 3030 + 16 (= 9 + 7) = 4646 + 34 (=18 + 16) = 8080 + 61 (=27 + 34) = 141

141 + 97 (= 36 + 61) = 238

45. 179 180 172 199 135 ?

a. 236 b. 272 c. 240 d. 256 e. 260

Ans: e Sol.

3

3

3

3

3

The pattern is :179 + 1 = 179 + 1 = 180180 2 = 180 8 = 172172 + 3 = 172 + 27 = 199199 4 = 199 64 = 135

135 + 5 = 135 + 125 = 260

46. 14 6 5 6.5 12 ?

a. 29 b. 27 c. 23 d. 33 e. 35

Ans: a Sol. The pattern is :

114 1 = 7 - 1 = 62

6 1 1 = 6 1 = 535 1 = 7.5 1 = 6.52

46.5 1 = 13 1 = 122

512 1 = 30 1 = 292

47. A project manager hired 16 men to complete a project in 38 days. However, after 30 days, he

realized that only 5 th6

of the work is complete. How many more men does he need to hire to

complete the project on time? a. 48 b. 24 c. 32 d. 16 e. 36

Ans: c Sol.

1 1 2 2

1 2

2

2

2

Remaining work5 4= 1 = 9 9

M D M D = W W

M 816 30 = 5 49 9

M 8 5 = 16 30 416 30 4 M = = 48

8 5 Additional men = 48 16 = 32

48. A took a certain sum as loan from bank at a rate of 8% simple interest per annum. A lends the same amount to B at 12% simple interest per annum. If at the end of five years, A made profit of Rs. 800 from the deal, how much was the original sum?

a. Rs. 6,500 b. Rs. 4,000 c. Rs. 6,200 d. Rs. 6,000 e. Rs. 4,500

Ans: b Sol.

Let the principal be Rs. .Prtncipal Time RateS.I. =

100According to the question,

12 5 8 5 = 800100 100

20 = 8000080000 = =Rs. 4000

20

x

x x

x

x

49. A wholesaler blends two varieties of tea, one costing Rs. 60 per kilogram and another costing Rs. 105 per kilogram. The respective ratio of quantities they were mixed in was 7 : 2. If he sold the mixed variety at Rs. 100 per kilogram, how much was his profit percentage?

a. 2347

b. 2385

c. 2325

d. 6427

e. 6487

Ans: d Sol. Cost of 9 kg of mixture= Rs. (60 7 + 105 2)= Rs. (420 + 210) = Rs. 630S.P. of 9 kg of mixture= 9 100 = Rs. 900

Profit percent900 630= 100

6302700 300 6= = = 42 %

63 7 7

50.

Joe's present age is 2 th7

of his father's present age. Joe's brother is 3 years older than Joe.

The respective ratio between present ages of Joe's father and Joe's brother is 14 : 5. What is Joe's present age?

a. 6 years b. 15 years c. 12 years d. 18 years e. 20 years

Ans: c Sol.

Joe's present age = years (let)

7 His father's present age = years2

Joe's borther's age = ( + 3) yearsAccording to the question,

7 14 = 2 53

7 14 = 2 + 6 5

35 = 28 + 84 7 = 84

84 = = 17

xx

x

x

xx

xx x

x

x

2 years

51. In a 90 Iitres mixture of milk and water, percentage of water is only 30%. The milkman gave 18 Iitres of this mixture to a customer and then added 18 lttres of water to the remaining mixture. What is the percentage of milk in the final mixture?

a. 64 b. 48 c. 52 d. 68 e. 56

Ans: e Sol.

Remaining mixture= 90 18 = 72 lttres

72 70Milk = = 50.4 1itres100

Water = 72 - 50.4 = 21.6 1itresOn adding 18 litres of water,Required percentage of milk

50.4= 10090

504= = 56%90

52. A bag contains 4 red balls. 6 green balls and 5 blue balls. If three balls are picked at random, what is the probability that two of them are green and one of them is blue in colour?

a. 2091

b. 1091

c. 1591

d. 591

e. 2591

Ans: c Sol.

3

Total number of balls= 4 + 6 + 5 = 15Total possible outcomes= selection of 3 balls out of 15 balls

15 14 13= 15C = = 455l 2 3

Total favourable outcomes= selection of 2 balls out of 6green ba

2

5C 2

lls and selection of 1ball out of 5 blue balls

6 5= 6 C = 5 = 751 2

Required probability75 15= = 455 91

53. A rectangular plot 55 m long and 45 m broad, has two concrete crossroads (of equal width) running in the middle of it - one parallel to the length and the other parallel to the breadth. The rest of the plot is used as a lawn. If the area of the lawn is 21911 m , what is the width of each of the crossroads? (in m)

a. 5 b. 5.5 c. 6 d. 4 e. 4.5

Ans: c Sol.

2

2

2

2

Let the width of cross-road be metre.

Area of cross road= 55 + 45 = (100 ) sq. metreArea oflawn = 1911 sq. metre

55 45 (100 ) = 1911 55 45 1911 = 100 2475 1911

x

x x xx x

x xx x

2

2

= 100 100 = 564 (100 ) = 6 94 6(100 6) = 6 metre

x xx x

x x

x

54. Two stations, A and B are 850 km apart from each other. One train starts from station A at 5 am and travels towards station B at 62 kmph. Another train starts from station B at 7 am and travels towards station A at 59 kmph. At what time win they meet?

a. 1 pm b. 11 : 45 am c. 12 : 30 pm d. 1 : 30 pm e. None of these

Ans: a Sol. Let trains meet after thourssince 5 a.m.Distance = Speed Time

62 t + 59(t 2) = 850 62t + 59t 118 = 850 12l t = 850 + 118 = 968

968 t = = 8 hours121

i.e. at 1 pm.

55.

Abhay gave 30% of his money to Vijay. Vijay gave 2 rd3

of what he received to his mother.

Vijay's mother gave 5 th8

of the money she received from Vijay, to the grocer. Vijay's mother is

now left with Rs. 600. How much money did Abhay have initially?

a. Rs. 6,200 b. Rs. 8,000 c. Rs. 6,000 d. Rs. 8,200 e. Rs. 10,200

Ans: b Sol. Original amount with Abhay= Rs. (let)Amount received by : 3x

30 3Vljay = Rs. 100 10

2 3Vljay's mother 3 10

= Rs. 5

5Grocer = Rs. 8 5 8

According to the question,

= 6005 8

8x 5x = 40

x

x x

x

x

x x

x x

600

3 = 600 40600 40 = = Rs. 8000

3

x

x

Directions (56 - 60): Study the following table carefully to answer the given questions. Data regarding number of candidates appearing for Civil Services (CS) and Engineering Services (ES) Examination in the years 2007, 2008, 2009, 2010 in the country XYZ Year Civil Services Engineering Services Total number of

candidates appeared

Graduates out of the total candidates appeared (in percentage)

Total number of candidates appeared

Graduates out of the total candidates appeared (in percentage)

2207 58 75 30 52 2008 60 60 36 50 2009 70 65 52 40 2010 76 50 40 60

56. Total number of candidates who appeared for CS and .ES together in 2011 was 25% more than the total number of candidates who appeared for the same together in 2010. How many female

candidates appeared for both the exams together in 20 II if they formed 2 th5

of the total number

of candidates appearing for both CS and ES exam that year? a. 52,000 b. 58,000 c. 60,000 d. 62,000 e. 64,000

Ans: b Sol. Number of students whoappeared in CS and ES in theyear 2010= 76 + 40 = 116 thousandNumber of students whoappeared in CS and ES in theyear 2011

116 125= = 145 thousand100

Required number of female

s2= 145 = 58 thousand5

= 58000

57. What is the respective ratio between the number of graduates who had appeared for ES in 2010 and the number of graduates who appeared for CS in 2010?

a. 13 : 21 b. 12 : 17 c. 12 : 19 d. 11 : 17 e. 11 : 19

Ans: c Sol.

Number of graduate studentswho appeared in CS inthe year 2010

76 50= = 38 thousand100

Number of graduate studentswho appeared in ES in 201040 60 = 24 thousand

100 Required ratio = 24 : 38

= 12 : 19

58. Total number of graduates who appeared for ES in 2008 is what percent of the total number of graduates who appeared for CS in the same year?

a. 75 b. 40 c. 55 d. 60 e. 50

Ans: e Sol. Graduates who appeared inthe year 2008 :

1E.S. 36 = 18 thousand2

60 60C.S. = 36 thousand100

Required percentage18 = 100 = 50%36

59. What is the difference between the average number of candidates who appeared for CS in the year 2007 and 2008 together and average number of candidates who appeared for ES in the same years together?

a. 38,400 b. 24,400 c. 26,000 d. 26,400 e. 24,000

Ans: c Sol.

Required difference1= [(58 + 60) (36 + 30)] thousand21= (118 66) thousand252= thousand = 260002

60. What is the total number of graduates who appeared for both CS and ES together in the year 2009?

a. 66,300 b. 64,200 c. 60,800 d. 62,800 e. 66,800

Ans: a Sol. Number of graduates whoappeared in both the examsin the year 2009

70 65 52 40= + thousand100 100

= (45.5 + 20.8) thousand= 66.3 thousand= 66,300

Directions (61 - 65): What approximate value will come in place of the question mark (1) in the given questions? (You are not expected to calculate the exact value) 61.

1439 l6 14.99 + 228 = ? a. 1315 b. 1365 c. 1215 d. 1465 e. 1265

Ans: b Sol.

1440? = 15 + 22516

90 15 + 15 1350 15 1365

62.

2 2 2 211.92 + 16.01 = ? 3.85 a. 15 b. 2 c. 4 d. 5 e. 12

Ans: d Sol.

2 2 2 2

2

2

2

12 + 16 ? 4 144 + 256 ? 16 400 ? 16

400 ? 2516

? 25 5

63. (19.97% of 781) + ? + (30% of 87) = 252

a. 40 b. 50 c. 25 d. 70 e. 80

Ans: d Sol. 780 20 90 30 + ? +

100 100 252 156 + ? + 27 252 183 + ? 252 ? = 252 183 69

Required answer = 70

64. 820.01 21 32.99 + ? = 240

a. 105 b. 173 c. 113 d. 234 e. 143

Ans: c Sol.

820 21 33 + ? 240 820 693 + ? 240 127 + ? 240 ? = 240 127 = 113

65.

2299 12 13.95 + ? = 24.02 a. 285 b. 226 c. 325 d. 150 e. 185

Ans: b Sol.

2300 12 14 + ? 24300 7 14 + ? 57612

350 + ? 576 ? 576 350 226