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SPECIAL SUPPLEMENT .O. Bank P Examination Special-III MOCK TEST Quantitative Aptitude & Reasoning Based on “Latest” Pattern Quantitative Aptitude How much per cent of the total students do not get scholarships? 1. Which of these numbers is rational? (a) 68 (b) 75 (a) π (b) (0.04)−1 (c) 79.8 (d) 82.5 (e) 78.5 (c) 3 −1 (d) 3 0.8 7. If the diameter of a wire is increased by 10%, by how (e) 4 0.00016 much per cent approximately, will its length be decreased, if 2. For the equation px2 + px + q = 0, the value of the the volume remains the same? discriminant is zero. The roots of this equation are: (a) 15 (b) 16 (c) 17 (a) imaginary (d) 18 (e) 19 (b) irrational 8. There are two numbers R and S, related by the (c) rational and unequal equation R = S2. Now, if S is increased by 10%, what will (d) rational and equal happen to R? (e) real and equal (a) R increases by 10% 3. The sum of two times one natural number and three (b) R decreases by 10% times another natural number is less than 24. If the first natural (c) R increases by 21% number is less than or equal to eight, the highest value of the (d) R decreases by 21% second natural number is: (e) R remains unchanged (a) 5 (b) 6 (c) 7 9. Mr X gets a salary of Rs 1,44,000 p.a. Assuming the (d) 8 (e) 9 salary to be the same every month, what will happen to his 4. A shopkeeper bought 800 kg rice at Rs 3840. He had average income per day? to sell it at a loss of as much as he received for 16 kg. The (a) Maximum for (Jan, Feb, March) period selling price (per kg, in Rs) will be: (b) Maximum for (Feb, March, April) period (a) Rs 40 (b) Rs 100 (c) Rs 50 (c) Minimum for (July, Aug, Sep) period (d) Rs 80 (e) Rs 65 (d) All three above are true 9 8 5 7 (e) Both (b) and (c) above 5. The fractions , , and can be arranged in 10. The value of log10 16 – 3 log10 2 + log10 5 is: 14 13 7 9 1 1 the descending order as: (a) (b) 1 2 2 7 5 9 8 (a) , , , (c) 0 (d) 1 9 7 14 13 (e) 2 5 9 8 7 (b) , , , 11. A cistern is two-third full of water. Pipe A can fill 7 14 13 9 the remaining part in 12 minutes and pipe B in 8 minutes. 9 5 8 7 Once the cistern is emptied, how much time will they take to (c) , , , 14 7 13 9 fill it together completely? 7 9 5 8 (a) 12 minutes (d) , , , (b) 12 min, 12 sec 9 14 7 13 (c) 14 min, 24 sec 8 9 5 7 (d) 10 min, 12 sec (e) , , , 13 14 7 9 (e) 14 min, 40 sec 6. The boys and girls in a school are in the ratio 3 : 7. 12. Which inequations are represented by the shaded 25% of the boys and 20% of the girls are scholarship holders. area shown in the graph? 1139 s JULY 2002 s THE COMPETITION MASTER SPECIAL SUPPLEMENT 4 water must be evaporated from it so that the solution now 3 contains 25% salt? 2 (a) 54 (b) 45 (c) 36 1 (d) 27 (e) 18 20. Mr Mohit is 7 times as old as his son. 10 years hence 1 2 3 4 he will be 3 times as old as his son. What are their present ages (in years)? (a) 4, 28 (b) 5, 35 (c) 3, 21 (d) 6, 42 (e) 7, 49 Directions (Q. 21-25): Study the following bar-graph and (a) x > 0, y > 0 (b) x > 0, y ≥ 0 answer the questions (21-25) given below. (The diagram shows the (c) x > y, y > 0 (d) x = y, y < 0 sale of six garment companies in three successive financial years.) (e) x ≥ y, y ≥ 0 1998-99 1999-2000 2000-2001 100 13. There are 7 points in a plane, no three of them being 90 collinear. The number of triangles formed by using these points 80 80 is: Sales in Rs. (Crores) 70 66 68 63 60 (a) 7 (b) 21 (c) 10 60 52 57 57 50 (d) 4 (e) 35 44 46 40 43 46 40 40 14. In how many ways can we arrange 6 books on 33 34 30 30 different subjects, in a shelf? 20 20 (a) 6 (b) 60 (c) infinite 10 (d) 720 (e) 120 0 Ramu & Co. Shyamu Champa Motu Bhai Lambu Dabbu Bhai 15. The recurring decimal 2. 345 can be expressed in the & Co. Garments & Brothers Tewari & & Sons Brothers rational form as: 21. Which of the following garment companies has a 2343 2345 fluctuating sales figure over the given period? (a) (b) 990 999 (a) Lambu Tewari and Brothers 2343 2345 (b) Dabbu Bhai and Sons (c) (d) (c) Motu Bhai and Brothers 999 99 (d) Champa Garments 2345 (e) (e) Shyamu and Company 1000 22. What is the total percentage increase in the sale of 16. If a = 4 6 3 9,b= 26 , c = 5 , then, which of these garments in 2000-2001 with respect of 1999-2000? statements is true? (a) 4% fall (b) 4% rise (a) 4 9 < 6 26 < 3 (c) No change (d) 7% increase 5 (e) 5% decrease (b) 4 6 3 9 > 26 > 5 23. For the total 3-year period under consideration, the (c) 6 26 > 3 5 > 4 9 nearest competitor of Ramu and Company is: 6 3 4 (a) Champa Garments (d) 26 < 5 < 9 (b) Motu Bhai and Brothers (e) None of these (c) Shyamu and Company x 2 + 7x + 10 (d) Dabbu Bhai and Sons 17. The value of the expression is: x 2 + 2x − 15 (e) None of these 24. For the years 1998-99 and 1999-2000, which company x+5 x+2 x−3 (a) (b) (c) has the minimum rate of change of sales? x−3 x−3 x+2 (a) Dabbu Bhai and Sons x+5 x+2 (b) Lambu Tewari and Brothers (d) (e) x+2 x+5 (c) Ramu and Company 1 1 (d) Champa Garments 18. If 3 x + 2 x = 64 – 2x, then x equals: (e) None of these 2 2 25. For the years 1999-2000 and 2000-2001, which (a) 8 (b) 7 (c) 6 company has the maximum rate of change of sales? (d) 5 (e) 4 (a) Dabbu Bhai and Sons (b) Ramu and Company 19. A 90 kg salt solution has 10% salt in it. How much (c) Shyamu and Company (d) Lambu Tewari and Sons 1140 s JULY 2002 s THE COMPETITION MASTER SPECIAL SUPPLEMENT (e) Champa Garments (a) 32 (b) 36 (c) 35 26. A train running at the speed of 90 km/hr crosses a (d) 30 (e) 38 platform of length 160 m in 10 seconds. What is the length of 35. How many girls are there in science stream of school the train (in metres)? D? (a) 60 (b) 90 (c) 150 (a) 264 (b) 704 (c) 88 (d) 140 (e) 40 (d) 264 (e) Data inadequate 27. The average of 4 consecutive even numbers is 9. 36. A square is inscribed inside a circle of radius 4 cm. Which of these is the first number? What is the area of the shaded region in the diagram? (a) 6 (b) 4 (c) 8 (d) 10 (e) 12 28. The distance between Charu’s and Mani’s places is 120 km. Charu travelled the whole distance from her place to Mani’s at 30 km/hr but returned at 40 km/hr. Her average speed for the whole journey is (approximately): (a) 36 km/hr (b) 37 km/hr (c) 33 km/hr (d) 34 km/hr (e) 35 km/hr 29. The average of the 1st 50 natural numbers is: 20 (a) 25 (b) 25.5 (c) 26.4 (a) 10 cm2 (b) 8 cm2 (c) cm2 3 (d) 50 (e) 50 (d) 16 cm2 (e) 8 cm 2 30. A certain sum of money doubles in 10 years at simple 37. A square is drawn inside a right-angled triangle with interest. What is the rate of interest? the two perpendicular sides as 12 cm and 8 cm. What is the (a) 20% (b) 30% (c) 10% side of the largest possible square that can be drawn? (d) 5% (e) 12% (a) 4 cm (b) 4.8 cm (c) 4.5 cm Directions (Q. 31-35): Study the pie-chart and table given (d) 4.4 cm (e) 5 cm below and answer the questions that follow—(The data shows 38. Three terrorists are employed to shoot a reknowned statistics about 4 schools (A, B, C and D) as in the year 2001.) person Mr X. Only one bullet is sufficient to kill him if it Students’ Ratio strikes in the head. The probabilities of the terrorists striking School Science : Boys : Mr X’s head by their bullets are 0.2, 0.3 and 0.4. What is the Commerce : Girls probability that Mr X is shot dead? Arts (a) 0.336 (b) 0.9 (c) 0.1 A 1:4:1 5:4 B 4:1:1 5:1 (d) 0.760 (e) 0.664 C 2:5:2 2:7 39. Which of the following numbers is a perfect square? D 3:5:1 1:8 (a) 10201 (b) 12222 (c) 11112 (d) 55555 (e) 10101 31. Which school has the maximum number of girl 40. The following two figures have the same perimeter. students? (a) A (b) B (c) both C and D (d) C (e) D 32. If the number of students of school A increase by 12.5% and that of school B decrease by 10%, what is the ratio of the number of students in the two schools? Square Circle (a) 2 : 3 (b) 3 : 2 (c) 1 : 1 (d) 4 : 3 (e) 3 : 4 Which of the following statements is true? 33. In school B, 10% students failed in science, 20% failed (a) The square and the circle have equal areas. in commerce and 30% failed in arts. What is the percentage of (b) The area of square is greater than that of the circle. failures in school B? (c) The area of the circle is greater. (a) 15 (b) 25 (c) 12 (d) Area of circle is π times that of the square. 1 (e) None of these. (d) 12 (e) 17 2 41. Prasoon’s bike needs a fresh paint. He wants 2 shades 34. The total number of arts students expressed as a on his bike. The painter shows all the available 5 shades. In percentage of total number of commerce students is how many ways can Prasoon paint his bike? (approximately): (a) 7 (b) 10 (c) 25 2 (d) 20 (e) 5 1141 s JULY 2002 s THE COMPETITION MASTER SPECIAL SUPPLEMENT 42. A bag contains 4 white and 3 black balls. 2 balls are and answer the incomplete series (B), in the following questions. drawn out one at a time, randomly in succession. What is the Assume that series B follows the same rule as series A. probability that both the balls drawn out are white in colour, 48. Series A: 12 24 48 96 192 if the first ball is replaced before the second draw is made. Series B: 0.5 x y z t 9 4 12 What should come in place of t? (a) (b) (c) 49 12 49 (a) Both (d) and (e) (b) 4 (c) 84.5 4 16 (d) 8 (e) 180.5 (d) (e) 49. Series A: 2 5 17 71 ... 7 49 Series B: 1 a b c 43. What is the maximum value of the function What will replace the symbol b? f(x) = x2 + 5x + 16 (a) 47 (b) 11 (c) 3 16 4 (a) (b) (c) 16 (d) 17 (e) 12 5 3 50. Series A: 2 11 47 128 ... 39 25 Series B: 5 m n o ... (d) (e) 4 16 The value of n is ... 44. On giving a reduction of 20% on clothes, a cloth- (a) 27 (b) 50 (c) 25 merchant’s sale increased by 30% to become Rs 26,000 in the (d) 21 (e) 62 month of June 2002. What was the previous sale? (a) Rs 25,000 (b) Rs 30,000 Answers (with Hints and Solutions) (c) Rs 13,000 (d) Rs 24,500 (e) Rs 20,000 1. (b) (0.04)−1 = 100 = ± 10 FG IJ 45. The difference between the product of two numbers 4 2 H K and their sum is 24. What is the difference between the two 2. (e) If D = 0 → the roots are real and equal numbers? (a) 24 3. (c) We can write: 2x + 3y < 24 (b) 25 The highest value of second can take place when the first is having lowest value. (c) Data inadequate (d) Several solutions Lowest value of 1st = 1 (Q smallest natural number = 1) (e) None of these 46. Mr Sanjay Sharma, Mr Pravesh Khare and Mr Mitra Thus, 2(1) + 3y < 24 are partners in a business. Mr Mitra started the business with 3y < 22 Rs 40,000. After 3 months, Mr Sanjay and Mr Pravesh joined 22 y< ~ 7 him with Rs 60,000 each. If the total profits at the end of the 3 year amount to Rs 31,200, what would be Mr Khare’s share in 4. (a) Let SP per kg be Rs x it? → Total SP = 80 x and loss = 16 x (a) Rs 15600 (b) Rs 9600 Now, loss = CP – SP (c) Rs 10800 (d) Rs 21600 → 16x = 3840 – 80x (e) None of these 47. Mr Rajiv and Mr Jogesh can complete a piece of work i.e. x = 40 in 6 days and 8 days respectively. They started together but 5. (a) By cross-multiplication (or otherwise), compare the 4 7 5 9 8 Rajiv left the work after 2 days. In how many days will Mr fractions. Thus, > > > Jogesh complete the remaining work now? 9 7 14 13 3 25(3x) 20 (a) 4 days 6. (e) Scholarship holders = + (7x) 4 100 100 2 3x 1 43x (b) 2 days = + .7x = 3 4 5 20 1 Total = 3x + 7x = 10 x (c) 4 days 2 F 43x I % of scholarship holders = GG 20 JJ × 100 = 21.5 (d) 4 days GH 10x JK 1 (e) 3 days 3 ∴ % of those without scholarships = 78.5 Directions (Q. 48-50): Study the given series (A) carefully 7. (c) V1 = V2 → π × 100 × 100 × l1 = π × 110 × 110 × l2 1142 s JULY 2002 s THE COMPETITION MASTER SPECIAL SUPPLEMENT l2 100 x = 5 and father’s age = 7 × 5 = 35 years → l = 21. (e) Shyamu and Company—It first registered a growth 1 121 and then a fall in the sales. 21 ∴ % decrease = × 100 ≅ 17 22. (c) Sum of sales figures in both the years are the same i.e. 121 328 crore each 8. (c) R = S2 23. (c) The total sales of Ramu and Company is Rs 200 crore S 11 which is closest to Rs 166 crore of Shyamu and S increases by 10% and becomes S + i.e. S 10 10 Company. 11 2 121 2 24. (a) For Dabbu Bhai and Sons, the rate of change is only Since R = S2 → R becomes ( S) = S 46 − 40 6 10 100 i.e. 46 46 → % increase in R = 21% 25. (a) For Dabbu Bhai and Sons, the rate of change is 9. (e) February has 28 days while July and August have 31 40 − 30 1 days. Find average using number of days. = 40 4 16 × 5 10. (d) Given expression = log10 ( ) = log10 10 = 1 For others it is less than this. 8 26. (b) Refer June issue for direct formula on TRAIN problems 1 11. (c) Pipes A and B fill 3 tank in 12 and 8 minutes 10 = FG IJ 18 x H K 5 90 → They fill the whole tank in 36 and 24 minutes x = 250 → length = 250 – 160 = 90 m 1 1 5 1 minute’s work = + = 27. (a) Let the first number be x 36 24 72 x + (x + 2) + (x + 4) + (x + 6) 72 Then, =9 4 → Time taken = minutes = 14.4 minutes 5 → 4x = 36 – 12 = 14 minutes, 24 seconds 24 12. (e) Refer special P.O. Exam issues of THE COMPETITION → x= =6 4 MASTER (May and June 2002) 13. (e) 7C3 = 35 (Refer May and June issues of CM) 2 × 30 × 40 2400 28. (d) Average speed = = = 34.33 km/hr 14. (d) 6P6 or ∠6 = 720 (Refer May and June issues of CM) 30 + 40 70 15. (c) n 16. (b) LCM of 4, 6, 3 is 12 29. (b) Sum of 1st n natural numbers is [a + l] 1 12 2 Thus, 4 9 = 9 bge j14 bg = 9 3 12 = 93 = 12 729 Where n = number of terms, a= 1st term, l = last term n 16 2 12 2 1 12 [a + l ] a + l 1 + 50 6 26 = b 26g = b 26g = e 26 j = 12 676 Thus, average = 2 = = = 25.5 n 2 2 13 4 12 4 1 12 and 5 = b 5g = b 5g 3 = e5 j = 12 625 30. (c) S.I. = Amount – Principal → S.I. = 2P – P = P ∴ 12 729 > 12 676 > 12 625 PTR P × 10 × R 17. (b) Factorise by splitting the middle term Now, S.I. = → P= (x + 2)(x + 5) (x + 2) 100 100 Thus, we have: = (x + 5) (x − 3) (x − 3) → R = 10% 18. (a) Solve as simple linear equations. 31. (d) First put all the data in a relevant form 10 From the pie-chart, we get, 19. (a) Quantity of salt = 90 × = 9 kg 20 3600 100 A= × 3600 = = 720 100 5 If ‘x’ kg water is evaporated, FG 9 IJ × 100 = 25 25 3600 H 90 − x K B= 100 × 3600 = 4 = 900 Thus, x = 54 33 20. (b) Let the son be x years old and father be 7x years old C= × 3600 = 1188 100 Their ages after 10 years are (x + 10) and (7x + 10) Thus, according to the question, we have 22 D= × 3600 = 792 (7x + 10) = 3(x + 10) 100 1143 s JULY 2002 s THE COMPETITION MASTER SPECIAL SUPPLEMENT Now, dividing the students as per the table, we have: = π FG 2xIJ =FG 4 IJ x 2 2 School Science : Comm. : Arts A(720) 120 / 480 / 120 Boys : Girls 400 / 320 H π K H πK B(900) 600 / 150 / 150 750 / 150 4 C(1188) 264 / 660 / 264 264 / 924 Since > 1 → Area of circle > Area of square D(792) 264 / 440 / 88 88 / 704 π 32. (c) 12.5% increase in A = 720 + 90 = 810 41. (d) (Refer April 2002 issue of CM for more details on the 10% decrease in B = 900 – 90 = 810 topic of permutations and combinations). 810 Using arrangements or permutations, we have Ratio = =1:1=1 5 5! 5 × 4 × 3 ! 810 P2 = = = 20 3! 3! 33. (a) Number of failures 10 20 30 42. (e) (Refer May 2002 issue of CM for more details on = × 600 + × 150 + × 150 probability). 100 100 100 Required probability = p (1st white) × p (2nd white) = 60 + 30 + 45 = 135 4 4 16 135 = × = % failures = × 100 = 15 4+3 4 + 3 49 900 b2 ( 5 )2 25 39 34. (b) Required percentage 43. (d) Maximum value = c = 16 − = 16 − = 4a 4 4 4 120 + 150 + 264 + 88 = × 100 (of ax2 + bx + c) 480 + 150 + 660 + 440 100 100 622 44. (a) Required figure = 26,000 × × = Rs 25,000 = × 100 = 36 (approx.) 80 130 1730 45. (c) Let the two numbers be x and y 35. (e) The given data only provides the number of students It is only given that xy – (x + y) = 24 in the 3 streams and the ratio of boys to girls in a We need at least two equations to solve for the two particular school. unknown variables 1 2 1 36. (b) Area = × r = × 4 2 = 8 cm2 46. (c) Money will be divided according to the time and 2 2 investment ratios (Solve using Pythagoras’ theorem) Thus, required ratio 37. (b) A = 40,000 × 12 : 60,000 × 9 : 60,000 × 9 8-x = 48 : 54 : 54 = 8 : 9 : 9 X Y 9 8 x Mr Khare’s share = × 31200 = Rs 10800 8+9+9 x x 1 1 7 B x C 47. (e) Their 1-day work = + = Z 12-x 6 8 24 12 The triangles AXY and YZC are similar 7 ∴ They do 2 24 FG IJ work in 2 days Thus, we have: x = 12 x H K 8−x x 14 5 Remaining work = 1 – = i.e., x2 = 96 – 20x + x2 24 12 i.e., x = 4.8 cm 5 10 38. (e) (Refer May issue of CM for a more systematic approach Days taken by Jogesh = ×8= 12 3 to this topic) Required Probability = 1– q1 q2 q3 (Where q = proba- 48. (a) We can have two possibilities × 2, × 2, × 2 ... = 1– 0.8×0.7×0.6 bility of fail- + 12, + 24, + 48 ... = 1– 0.336 ing to strike) Thus, both (d) and (e) = 0.664 49. (b) The series A is: ×2 + 1, × 3 + 2, × 4 + 3 ... 39. (a) (101)2 = 10201 Thus, 1 × 2 + 1 = 3, 3 × 3 + 2 40. (c) Let side of square be ‘x’ cm, i.e. perimeter = 4x cm = 11, 11 × 4 + 3 = 47 etc 2x 50. (b) The given series A is: +32, +62, +92, etc Since perimeters are same → 4x = 2 π r i.e. r = π Thus, series B is: m = 5 + 32 = 14, Now, Area of square = x2 and area of circle n = 14 + 62 = 50, etc 1144 s JULY 2002 s THE COMPETITION MASTER