QUANTITATIVE APTITUDE

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Isabel Price
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1 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 1. What is the respective ratio between total number of books purchased for libraries A and B together in 00 and total number of books purchased for the same libraries together in 007? a. : 1 b. 4 : 1 c. 11 : 17 d. 11 : 19 e. : 5 Ans: a Required ratio = ( ) : ( ) = 880 : 140 = : 1. What is the average number of books purchased for library A during 004, 005, 007 and 008? a. 465 b. 455

2 c. 460 d. 445 e. 450 Ans: b Required average = = Out of the total number of books purchased by libraries A and B together in 008, only 0% are graphic novels. What is the total number of graphic novels purchased for libraries A and B together in 008? a. 4 b. 1 c. 7 d. 6 e. 88 Ans: c Total number of books bought in 008 = = 160 Total number of graphic novels = The number of books purchased for library B increased by what percent from 00 to 006? 1 a. 175 b. c. d. e Ans: d

3 Required percentage increase = = = = 18 % 4 5. The number of books purchased for library B in 00 is what percent of the number 0f books purchased for library A in 006? a. 0 b. 5 c. 55 d. 40 e. 45 Ans: a Required per cent 40 = 100 = Directions (6-40): In these questions two equations numbered I and II are given. You have to solve both the equations and give answer (1) if x < y () if x > y () if x y (4) if x y (5) if x = y or relationship between x and y cannot be established 6. I. x + x + 6 = 0 II. 4y + 19y + 1 = 0 Ans: a a. x < y b. x > y c. x y d. x y e. x = y or relationship between x and y cannot be established

4 I. x + x + 6 = 0 x + 14 x + 9 x + 6 = 0 x ( x + 7) + 9 ( x + 7) = 0 ( x + 9) ( x + 7) = 0 9 x = or, 9 II. 4y + 19y + 1 = 0 4y + 1y + 7y + 1 = 0 4y (y + ) + 7 (y + ) = 0 (4y + 7) (y + ) = 0 7 y = or, Clearly, x < y 7. I. x + 9 x + 56 = 0 II. y + 15y + 5 = 0 Ans: a a. x < y b. x > y c. x y d. x y e. x = y or relationship between x and y cannot be established

5 I. x + 9 x + 56 = 0 x + 1 x + 8 x + 56 = 0 x ( x + 7) + 8 ( x + 7) = 0 ( x + 8) ( x + 7) = 0 8 x = or, 7 II. y + 15y + 5 = 0 y + 10y + 5y + 5 = 0 y (y + 5) + 5 (y + 5) = 0 (y + 5) (y + 5) = 0 5 y = or, 5 Clearly, x < y 8. I. x + x + 44 = 0 II. y + 0y + = 0 Ans: d a. x < y b. x > y c. x y d. x y e. x = y or relationship between x and y cannot be established

6 I. x + x + 44 = 0 x + 1 x + 11 x + 44 = 0 x ( x + 4) + 11 ( x + 4) = 0 ( x + 11) ( x + 4) = 0 11 x = or, 4 4 II. y + 0y + = 0 y + 9y + 11y + = 0 y (y + ) + 11 (y + ) = 0 (y + 11) ( y + ) = 0 11 y = or, Clearly, x y 9. I. 4 x 9 x + 45 = 0 II. y 19y + 8 = 0 Ans: e a. x < y b. x > y c. x y d. x y e. x = y or relationship between x and y cannot be established

7 I. 4 x 9 x + 45 = 0 4 x 0 x 9 x + 45 = 0 4 x ( x 5) 9 ( x 5) = 0 (4 x 9) ( x 5) = 0 II. x 9 = or, 5 4 y 19y + 8 = 0 y 1y 7y + 8 = 0 y (y 4) 7 (y 4) = 0 (y 7) (y 4) = 0 7 y = or, I. x 1 x + 1 = 0 II. 5y y + 1 = 0 Ans: c a. x < y b. x > y c. x y d. x y e. x = y or relationship between x and y cannot be established

8 I. x 1 x + 1 = 0 x 6 x 7 x + 1 = 0 x ( x ) 7 ( x ) = 0 ( x 7) ( x ) = 0 II. x 7 = or, 5y y + 1 = 0 5y 15y 7y + 1 = 0 5y (y ) 7 (y ) = 0 (5y 7) (y ) = 0 7 y = or, 5 Clearly, x y 41. A, B and C start a small busied ness. A contributes 1 th of the total capital invested in the 5 business. B contributes as much as A and C together. Total profit at the end of the year was Rs. 5,00. What was C's profit share? (in Rupees) a b. 510 c d. 560 e Ans: e

9 Total investment = Rs. x (let) x A's investment = Rs. 5 (B + C)'s investment = x 4x = Rs....(i) 5 B's investment x = + C's investment 5 (B C)'s investment x = Rs....(ii) 5 On adding both equations, B's investment 4 x x = Rs. = Rs. x 5 5 x B's investment = Rs. x 5 From equation (i) C's investment 4x x = Rs. 5 8 x 5x x = Rs. = Rs Ratio of profit sharing x x x = : : 5 10 = : 5 : C's share = = Rs Directions (4-46): What will come in place of the question mark (?) in the given number series? ? 87 a. 6

10 b. 5 c. 55 d. 67 e. 57 Ans: e The pattern is : = 17 + = = = = = = = = = ? 76 a. 71 b. 6 c. 57 d. 87 e. 49 Ans: a The pattern is : = = = = = = = = = = ? a. 44 b. 1 c. 6 d. 0 e. 8 Ans: e

11 The pattern is : + 7 = (= 9 + 7) = (= ) = (=7 + 4) = (= ) = ? a. 6 b. 7 c. 40 d. 56 e. 60 Ans: e The pattern is : = = = = = = = = = = ? a. 9 b. 7 c. d. e. 5 Ans: a The pattern is : = 7-1 = = 6 1 = = = = 1 1 = = 0 1 = 9

12 47. A project manager hired 16 men to complete a project in 8 days. However, after 0 days, he realized that only 5 th of the work is complete. How many more men does he need to hire to 6 complete the project on time? a. 48 b. 4 c. d. 16 e. 6 Ans: c Remaining work 5 4 = 1 = 9 9 M D M D = W W M 8 = M 8 5 = M = = Additional men = = 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 1% 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. 6,00 d. Rs. 6,000 e. Rs. 4,500 Ans: b

13 Let the principal be Rs. x. Prtncipal Time Rate S.I. = 100 According to the question, x 1 5 x 8 5 = x = x = =Rs 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 :. If he sold the mixed variety at Rs. 100 per kilogram, how much was his profit percentage? a. 4 7 b. c. d. e Ans: d Cost of 9 kg of mixture = Rs. ( ) = Rs. ( ) = Rs. 60 S.P. of 9 kg of mixture = = Rs. 900 Profit percent = = = = 4 % Joe's present age is th of his father's present age. Joe's brother is years older than Joe. 7 The respective ratio between present ages of Joe's father and Joe's brother is 14 : 5. What is Joe's present age?

14 a. 6 years b. 15 years c. 1 years d. 18 years e. 0 years Ans: c Joe's present age = x years (let) 7x His father's present age = years Joe's borther's age = ( x + ) years According to the question, 7x 14 = 5 x 7x 14 = x x = 8 x x = 84 x 84 = = 1 years In a 90 Iitres mixture of milk and water, percentage of water is only 0%. 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. 5 d. 68 e. 56 Ans: e

15 Remaining mixture = = 7 lttres 7 70 Milk = = itres 100 Water = = 1.6 1itres On adding 18 litres of water, Required percentage of milk 50.4 = = = 56% 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? 0 a. 91 b. c. d. e. Ans: c

16 Total number of balls = = 15 Total possible outcomes = selection of balls out of 15 balls = 15C = = 455 l Total favourable outcomes = selection of balls out of 6 green balls and selection of 1 ball out of 5 blue balls = 6 C C = 5 = 75 1 Required probability = = 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 1911 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

17 Let the width of cross-road be x metre. Area of cross road = 55 x + 45 x x = (100 x x ) sq. metre Area oflawn = 1911 sq. metre (100 x x ) = = 100 x x = 100 x x 100 x x = 564 x (100 x) = (100 6) x = 6 metre 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 6 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. 1 : 0 pm d. 1 : 0 pm e. None of these Ans: a Let trains meet after thours since 5 a.m. Distance = Speed Time 6 t + 59(t ) = 850 6t + 59t 118 = 850 1l t = = t = = 8 hours 11 i.e. at 1 pm. 55. Abhay gave 0% of his money to Vijay. Vijay gave rd of what he received to his mother. Vijay's mother gave 5 th of the money she received from Vijay, to the grocer. Vijay's mother is 8 now left with Rs How much money did Abhay have initially?

18 a. Rs. 6,00 b. Rs. 8,000 c. Rs. 6,000 d. Rs. 8,00 e. Rs. 10,00 Ans: b Original amount with Abhay = Rs. x (let) Amount received by : x 0x x Vljay = Rs x Vljay's mother 10 x = Rs. 5 5 x x Grocer = Rs According to the question, x x = x 5x = x = x = = Rs 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 007, 008, 009, 010 in the country XYZ Year Civil Services Engineering Services Total number of candidates appeared Total number of candidates appeared Graduates out of the total candidates appeared (in percentage) Graduates out of the total candidates appeared (in percentage)

19 56. Total number of candidates who appeared for CS and.es together in 011 was 5% more than the total number of candidates who appeared for the same together in 010. How many female candidates appeared for both the exams together in 0 II if they formed th of the total number 5 of candidates appearing for both CS and ES exam that year? a. 5,000 b. 58,000 c. 60,000 d. 6,000 e. 64,000 Ans: b Number of students who appeared in CS and ES in the year 010 = = 116 thousand Number of students who appeared in CS and ES in the year = = 145 thousand 100 Required number of females = 145 = 58 thousand 5 = What is the respective ratio between the number of graduates who had appeared for ES in 010 and the number of graduates who appeared for CS in 010? a. 1 : 1 b. 1 : 17 c. 1 : 19 d. 11 : 17 e. 11 : 19 Ans: c

20 Number of graduate students who appeared in CS in the year = = 8 thousand 100 Number of graduate students who appeared in ES in = 4 thousand 100 Required ratio = 4 : 8 = 1 : Total number of graduates who appeared for ES in 008 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 Graduates who appeared in the year 008 : 1 E.S. 6 = 18 thousand C.S. = 6 thousand 100 Required percentage 18 = 100 = 50% What is the difference between the average number of candidates who appeared for CS in the year 007 and 008 together and average number of candidates who appeared for ES in the same years together? a. 8,400 b. 4,400 c. 6,000 d. 6,400 e. 4,000 Ans: c

21 Required difference 1 = [( ) (6 + 0)] thousand 1 = (118 66) thousand 5 = thousand = What is the total number of graduates who appeared for both CS and ES together in the year 009? a. 66,00 b. 64,00 c. 60,800 d. 6,800 e. 66,800 Ans: a Number of graduates who appeared in both the exams in the year = + thousand = ( ) thousand = 66. thousand = 66,00 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) l =? a. 115 b. 165 c. 115 d e. 165 Ans: b 1440? =

22 =?.85 a. 15 b. c. 4 d. 5 e. 1 Ans: d ? ? ? ? 5? (19.97% of 781) +? + (0% of 87) = 5 a. 40 b. 50 c. 5 d. 70 e. 80 Ans: d ? ? ? 5? = Required answer = ? = 40 a. 105 b. 17 c. 11 d. 4 e. 14 Ans: c

23 80 1 +? ? ? 40? = = ? = 4.0 a. 85 b. 6 c. 5 d. 150 e. 185 Ans: b ? ? ? 576?

IBPS CLERKS Numerical Ability

IBPS CLERKS Numerical Ability Directions (Q.1-4): What should come in place of question mark (?) in the following questions? 1. 240% of 42? = 44% of 160 1) 43.7 2) 30.4 3) 53.7 4) 14.37 5) None of these