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O B J E C T I V E -T Y P E Q U E S T I O N S QUANTITATIVE APTITUDE Questions asked in MIB Examination (A) 4% (B) 5% 1. If a + b + c = 0, then (a3 + b3 + c3) ÷ abc is equal to: 1 1 (A) 1 (B) 2 (C) 6 % (D) 8 % (C) 3 (D) 9 4 3 x 2 y 2 z2 9. A sum of money at simple interest rate amounts to 2. If x + y + z = 0, then + + is equal to: Rs 4,025 in 3 years and to Rs 4,550 in 6 years at the same yz xz xy rate of interest. Find the sum and the rate of interest per (A) 3 (B) 27 annum. (C) 1 (D) –3 (A) Rs 2,500, 6% (B) Rs 3,000, 5% 3. If ab + bc + ca = 0, then the value of (C) Rs 3,500, 5% (D) Rs 4,500, 4% 1 + 1 + 1 10. In how many years, will a sum of Rs 800 at 10% a2 – bc b2 – ca c2 – ab per annum compound interest semi-annually become Rs 926.10? is equal to: 1 1 (A) 3 (B) 3 abc (A) 2 (B) 1 2 2 (C) abc (D) 0 a c is equal to: 1 1 4. If a + b = 2c, then + (C) 2 (D) 1 a–c b–c 3 3 (A) 2 (B) 1 11. On a certain map of India the actual distance of (C) 0 (D) –2 1450 kms between two cities Delhi and Kolkata is shown as 5. If x = a2 – bc, y = b2 – ca, z = c2 – ab, then the value 5 cms. What scale is used to draw the map? (a + b + c)(x + y + z) (A) 1 : 15 × 106 (B) 1 : 20 × 106 of is: 6 ax + by + cz (C) 1 : 25 × 10 (D) 1 : 29 × 106 12. The ratio between the third proportional of 12 and (A) 3 (B) 2 30 and mean proportional of 9 and 25 is: (C) 1 (D) 0 (A) 2 : 1 (B) 5 : 1 6. The difference between compound interest and (C) 7 : 15 (D) 9 : 14 simple interest for 3 years at 5% per annum can be found 13. 5 mangoes and 4 oranges cost as much as 3 out by multiplying the principal by: mangoes and 7 oranges. What is the ratio of cost of one (A) 1.7625 (B) 0.7625 mango to the cost of one orange? (C) 0.07625 (D) 0.007625 (A) 4 : 3 (B) 1 : 3 1 (C) 3 : 2 (D) 5 : 2 7. The simple interest on a sum of money is th 9 14. Rs 1,050 are divided among P, Q and R. The share of the sum and the number of years and the rate per 2 of P is of the combined share of Q and R. P gets: cent per annum are equal. The rate per cent per annum 5 is: (A) Rs 320 (B) Rs 300 1 (C) Rs 200 (D) Rs 420 (A) 3 (B) 5 3 ma + nc 15. If a : b = c : d, then is equal to: 2 mb + nd (C) 6 (D) 10 3 (A) an : mb (B) m : n 8. A man invested Rs 5,000 at some rate of simple (C) a : b (D) dm : cn interest and Rs 4,000 at 1% higher rate of interest. If the 16. How many even numbers of four-digits can be interest in both the cases after 4 years is same the rate of formed with digits 1, 2, 3, 4, 5, 6 (repetition of the digit is interest in the former case is: allowed)? 528 ◆ JANUARY 2005 ◆ THE COMPETITION MASTER O B J E C T I V E -T Y P E Q U E S T I O N S (A) 648 (B) 180 hand is Rs 2,380, what is his salary? (C) 1296 (D) 540 (A) Rs 5,000 (B) Rs 4,500 17. In how many ways 5 MBA students and 6 law (C) Rs 4,000 (D) Rs 3,500 students can be arranged together so that no two MBA students are side by side? Directions (Q. Nos. 25 to 28): Read the following and 7!6! answer the questions that follow: (A) (B) 6!.6! Two friends Shyam and Kailash own two versions of a 2! car. Shyam owns the diesel version while Kailash owns petrol 11 (C) 5!6! (D) P5 version. Kailash’s car gives an average that is 20% higher than Shyam’s (in terms of litres per kilometre). It is known 18. There is a number lock with four rings. How many that petrol costs 60% of its price higher than diesel. attempts at the maximum would have to be made before 25. The ratio of cost per kilometre of Kailash’s car to getting the right number? Shyam’s car is: (A) 104 (B) 255 (A) 3 : 1 (B) 1 : 3 (C) 104 – 1 (D) 256 (C) 1.92 : 1 (D) cannot be determined 19. There are four letters and four envelops addressed 26. Shyam’s car gives an average of 20 km per litre, to different persons. In how many ways can wrong choices then the difference in the cost of travel per kilometre between be made? the two cars is: (A) 64 (B) 23 (A) Rs 4.3 (B) Rs 3.5 (C) 16 (D) 255 (C) Rs 2.5 (D) cannot be determined 20. There are 10 points on a straight line AB and 8 27. For the above question (26), the ratio of the costs points on another AC, none of them being A. How many per kilometre of the Shyam’s travel to Kailash’s travel is: triangles can be formed with these points as vertices? (A) 3 : 1 (B) 1 : 3 (A) 720 (B) 640 (C) 1 : 1.92 (D) cannot be determined (C) 816 (D) 680 28. Diesel costs Rs 12.5 per litre, then the difference in 21. In a village consisting of p persons, x% can read the cost of travel per kilometre between Kailash’s and and write. Of the male alone y% and of the females alone 2% Shyam’s is (assume an average of 20 km per litre for Shyam’s can read and write. Find the number of males in the village car and also assume that petrol is 50% of its own price higher in terms of p, x, y and z, if z < y: p(x – z) p(x – z) than diesel): (A) (B) (A) Rs 1.75 (B) Rs 0.875 ( y + x – z) ( y + x – 2z) (C) Rs 1.25 (D) None of these p(y – x) p(x – z) 29. A shopkeeper gives 3 consecutive discounts of 10%, (C) (D) 15% and 15% after which he sells his goods at a percentage x–z y–z profit of 30.05% on the cost price. Find the value of the 22. The price of a commodity is first increased by x% percentage profit that the shopkeeper would have earned if K he had given discounts of 10% and 15% only: and then decreased by x%. If the new price is , find the 100 (A) 53% (B) 62.5% original price from the given below: (C) 72.5% (D) 68.6% (x – 100)100 2 2 30. A journey of 192 kms takes 2 hours less by a fast (A) (B) (x – 100 )100 K K train than by a slow train. If the average speed of the slow train is 16 kmph less than that of a fast train, what is the (x – 100)100 100 K (C) (D) average speed of the fast train? K (100 2 – x 2 ) (A) 30 kmph (B) 48 kmph 23. A fraction is such that if the double of the (C) 20 kmph (D) 25 kmph numerator and the triple of the denominator is changed by 31. Two planes move along a circle of circumference 16 1.2 kms with constant speeds. When they move in different + 10% and – 30% respectively, then we get 11% of . Find 21 directions, they meet every 15 seconds and when they move in the same direction one plane overtakes the other every 60 fraction: 4 2 seconds. Find the speed of the slower plane: (A) (B) (A) 0.04 km/s (B) 0.03 km/s 25 25 (C) 0.05 km/s (D) 0.02 km/s 3 32. The distance between two towns is x km. A car (C) (D) None of these 25 travelling between the towns covers the first ‘k’ km at an 24. A credits 15% of his salary in his fixed account and average speed of y kmph and the remaining distance at z spends 30% of the remaining on groceries. If the cash in kmph. The time taken for the journey is: 529 ◆ JANUARY 2005 ◆ THE COMPETITION MASTER O B J E C T I V E -T Y P E Q U E S T I O N S k (x – k ) 38. 2/3 of a consignment was sold at a profit of 6% (A) + y z and the rest at a loss of 3%. If, however, there was an overall (k – x) profit of Rs 540.00, the value of consignment was: (B) ky + (A) Rs 1,620 (B) Rs 4,860 z (C) Rs 5,400 (D) Rs 18,000 k k–x 1 (C) + 39. A cistern is filled by a tap in 3 hours. Due to a y z 2 (D) ky + z (x – k) 1 leak in its bottom, it takes hour longer to fill. If cistern is 33. The metro service has a train going from Mumbai 2 to Pune and Pune to Mumbai every hour. The first one at 6 1 full, how long will it take to leak to empty it? a.m. The trip from one city to another takes 4 hours, and (A) 7 hours (B) 8 hours 2 (C) 14 hours (D) 28 hours all trains travel at the same speed. How many trains will 40. A can do a piece of work in 7 days of 9 hours each pass while going from Mumbai to Pune, if you start at 12 whereas B can do the same work in 6 days of 7 hours each. noon? How long will it take to complete the work together working (A) 8 (B) 10 2 8 hours a day? (C) 9 (D) 13 5 (A) 2 days (B) 3 days Directions (Q. Nos. 34 to 38): Read the following and 1 2 answer the questions that follow: (C) 3 days (D) 4 days A train journey from P to D by an X-express has 4 classes 7 5 of fares: 41. If 12 men and 16 boys can do a piece of work in 5 (i) 3 tier Rs 300 72 berths per Train has days and 13 men and 24 boys can do it in 4 days, the ratio bogie 8 bogies of daily work done by a man to that done by a boy is: (ii) AC-3 tier Rs 898 64 berths per Train has (A) 1 : 3 (B) 1 : 2 bogie 2 bogies (C) 2 : 1 (D) 3 : 1 (iii) AC-2 tier 45 berths per Train has 42. A bus left Delhi for Ambala at 50 km/hr and turned Rs 1,388 bogie 2 bogies over the same route at 40 km/hr. Thus it took 1 hour more (iv) AC-first class 26 berths per Train has on the return trip. The distance between Delhi and Ambala Rs 2,691 bogie one bogie is: The distance between P to D is 1100 km. Assume the (A) 200 kms train does not stop at any station unless otherwise indicated. (B) 180 kms The running cost per kilometre : AC-bogie—Rs 25, non-AC- (C) 400 kms bogie—Rs 10. (D) None of these 34. Assuming full occupancy, a bogie of which class 43. A train running at 72 kms per hour crosses a exhibits the highest profit margin? coconut tree standing by the side of the track in 7 seconds. (A) AC-3 tier (B) AC-2 tier The length of the train is: (C) AC-first class (D) 3 tier (A) 104 metres 35. Assuming full occupancy in all the classes, for a (B) 140 metres journey between P and D to Delhi, the profit margin (as a (C) 504 metres percentage of running costs) of the class showing the lowest (D) 540 metres profit is approximately: 44. A man purchased a bag of rice containing 70 kgs (A) 116% (B) 127% for Rs 175. He sold it at the rate of Rs 2.75 per kg. Find the (C) 109% (D) None of these profit and loss per cent. 36. For the above question, the percentage of the total (A) 10% profit (B) 10% loss profit that comes out of AC bogie is (approximately): (C) 12.5% profit (D) 12.5% loss (A) 50% (B) 60% 45. If 16% of 140% of a number is 28, the number is: (C) 70% (D) 80% (A) 200 (B) 225 37. The highest revenue for a journey from P to D will (C) 125 (D) 320 always be generated by: 46. A person marks his goods 20% higher than the (A) 3 tier cost price and allows a discount of 5%. The percentage of (B) AC-3 tier profit is: (C) AC-2 tier (A) 15% (B) 20% (D) cannot be determined (C) 5% (D) 14% 530 ◆ JANUARY 2005 ◆ THE COMPETITION MASTER O B J E C T I V E -T Y P E Q U E S T I O N S ANSWERS AND EXPLANATIONS 1. (C) Q a + b + c = 0 ∴ a3 + b3 + c3 = 3 abc A=P+I or (a3 + b3 + c3) ÷ abc = 3 ∴ P = 4025 – 525 = Rs 3500 x2 y2 z2 x 3 + y 3 + z 3 3xyz 525 × 100 2. (A) + + = = =3 R= =5 yz xz xy xyz xyz 3 × 3500 10 (Q x + y + z = 0) 1 10. (B) 926.10 = 800 (1 + 2 )n ⇒ n = 3 half years = 1 years 3. (D) ab + bc + ca = 0 ⇒ bc = – (ab + ca) 100 2 ca = – (ab + bc) 11. (D) ab = – (bc + ca) 302 Given exp 12. (B) Third proportional of 12 and 30 = = 75 1 1 1 12 = + + a 2 – bc b 2 – ca c 2 – ab Mean proportional of 9 and 25 = 9 × 25 = 15 1 1 1 75 5 = + + Reqd ratio = = =5:1 a + ca + ab 2 b + ab + bc c + bc + ca 2 2 15 1 1 1 1 13. (C) Let the cost of 1 mango be Rs x and that of 1 orange = + + be Rs y a ( a + c + b) b ( b + a + c ) c ( c + b + a) x 3 bc + ca + ab 0 ATS 5x + 4y = 3x + 7y ⇒ = = = =0 y 2 abc(a + b + c) abc(a + b + c) 14. (B) Let the combined share of Q and R be Rs x 4. (B) a + b = 2c or a – c = c – b = – (b – c) 2x a c a c ∴ + x = Rs 1050 ⇒ x = 750 + = + 5 a – c b – c –( b – c) b – c 2 –a + c –(a – c) b – c ∴ Share of P = × 750 = Rs 300 = = = =1 5 b–c b–c b–c a c (a + b + c)(x + y + z) 15. (C) = = k ⇒ a = bk, c = dk 5. (C) b d a(a2 – bc) + b(b2 – ca) + c(c2 – ab) ma + nc mbk + ndk = =k=a:b (a + b + c)(x + y + z) mb + nd nb + nd = a 3 – abc + b 3 – abc + c 3 – abc 16. (A) Unit’s place be filled in 3 ways (i.e. by 2 or 4 or 6) (a + b + c)(x + y + z) Each of three remaining places (i.e. ten’s hundred’s = a 3 + b 3 + c 3 – 3abc and thousand’s) can be filled in 6 ways (Q repetition is allowed) (a + b + c)(a 2 – bc + b 2 – ca + c 2 – ab) ∴ Reqd. no. of nos. = 6 × 6 × 6 × 3 = 648 = a 3 + b 3 + c 3 – 3abc 17. (A) 6 law students can be arranged in 6! ways a3 + b3 + c3 – 3abc = 1 Now in 7 places, 5 MBA students can be arranged = in 7P5 ways .× . × . × . × . × . × . a3 + b3 + c3 – 3abc 6! × 7 ! ∴ Total no. of ways = 6! × P5 = 7 6. (D) P LMFG1 + R IJ n – 1OP – P × R × T 2! NMH 100K QP 100 18. (C) 19. (D) 44 – 1 = 255 LMRF 5 I | 3 U | 5×3 OP 20. (B) 8C2 × 10 + 10C2 × 8 = 640 =P MNSGH1 + 100 JK | T –1 – V | W 100 = P × .007625 PQ [No. of bases on AC = 8C2 No. of vertices on AB = 10 s ∴ No. of ∆ with bases on AC and vertices P P× R× R 10 1 7. (A) = ⇒ R= =3 8 on AB = C2 × 10 9 100 3 3 s No. of ∆ with bases on AB and vertices 4 4 8. (A) 5000 × x × = 4000 (x + 1) × ⇒ x=4 on AC = 10C2 × 8] 100 100 px 9. (C) I for 3 years = Rs 4550 – 4025 = Rs 525 21. (D) Total persons who can read and write = 100 531 ◆ JANUARY 2005 ◆ THE COMPETITION MASTER O B J E C T I V E -T Y P E Q U E S T I O N S Let the no. of males be M 34. (D) 3 tier y z px 35. (D) A.T.S. M× + (p – M) = 100 100 100 36. (B) 60% p(x – z) 37. (A) 3 tier ⇒ M = y–z 38. (D) Let total value of consignment be Rs x 2 106 x 97 A.T.S. x × + × – x = 540 22. (D) Let the original price be Rs y 3 100 3 100 y FG 100 + x IJ FG 100 – x IJ = k ⇒ y = 100k ⇒ x = Rs 18000 H 100 K H 100 K 100 100 – x 2 2 2 x 39. (D) Tap’s 1 hour’s work = 23. (B) Let the fraction be 7 y Let the reqd time be x hrs 110 2 1 1 2x × ATS – = ⇒ x = 28 A.T.S. 100 = 11 × 16 ⇒ x = 2 7 x 4 70 100 21 y 25 1 3y × 100 40. (B) A’s one day’s work = (by working 1 hour a day) 63 24. (C) Let his salary be Rs x 1 1 5 85x 70 (A + B)’s one day’s work = + = A.T.S. × = 2380 ⇒ x = Rs 4000 63 42 126 100 100 42 25. (C) (A + B)’s work by working hours a day 5 26. (D) 5 42 1 27. (C) = × = 28. (D) 126 5 3 29. (A) Let CP = Rs 100, P = 30.05% Reqd time = 3 days ∴ S.P. = Rs 130.05 41. (C) Work done by 12 M + 16B in 5 days Discounts = 10%, 15%, 15% = work done by 13 M + 24 B in 4 days 100 100 100 ∴ M.P. = 130.05 × × × = Rs 200 ⇒ 60M + 80B = 52 M + 96 B ⇒ 1M = 2B 90 85 85 M 2 If discounts are 10% and 15% only = 2 : 1 = Reqd ratio B 1 ∴ S.P. = M.P. × FG 100 – d IJ × FG 100 – d IJ 1 2 D D H 100 K H 100 K 42. (A) – 40 50 = 1 ⇒ D = 200 km 90 85 = 200 × × = Rs 153 43. (B) Let the length of train be x 100 100 x ∴ = 7 ⇒ x = 140 m ∴ Profit = 53% 5 72 × 192 192 18 30. (B) – = 2 ⇒ x = Speed of fast train = 48 x – 16 x 44. (A) C.P. of 70 kg rice = Rs 175 31. (C) Let the speeds of fast plane and slow planes be x 385 S.P. = 2.75 × 70 = and y m/sec respectively D=s×t 2 If they move in opposite direction 385 35 15 (x + y) = 1200 ⇒ x + y = 80 m/sec ... (i) P= – 175 = 2 2 If they move in same direction, relative speed = x – y m/sec 35 1 ∴ P% = × × 100 = 10 Time = 60 i.e. 4 times 2 175 1 16 140 ∴ Speed is 4 th x – y = 20 m/sec ... (ii) 45. (C) × × x = 28 ⇒ x = 125 100 100 Solving (i) and (ii), 46. (D) Let CP = Rs 100 y = 50 m/sec = 0.05 km/sec ∴ MP = Rs 120 k x–k 95 32. (A) Reqd time = + S.P. = 120 × = Rs 114 y z 100 33. (D) 13 trains ∴ P% = 14 532 ◆ JANUARY 2005 ◆ THE COMPETITION MASTER