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Q0304 B 1.Which of the following ratios is greatest? a) 7:15 b) 15:23 c) 17:25 d) 21 : 29. 2.The ratio of males to females in a committee of 48 members is 3:1. How many more ladies be added to the committee so that the ratio of males to females may be 9:5? a)5 b)8 c)4d) 3. 3.If A: B = 2:3, B:C = 4:5 and C:D = 5:7, find A:B:C:D. a)8:12:18:21 b)4:21:35:42 c)8:12:15:21 d) 8:12:21:15. 4.In 50 litres mixture of milk and water, the ratio of milk and water is 3:2. Find the quantity of water to be added in the mixture in order to make this ratio 2:3. a)20 litres b) 10 litres c) 25 litres d) 5 litres. 5.The sum of two numbers is 20 , their difference is 5. What is the ratio of the two numbers? a) 5:3 b)2:3 c)4:1 d)1:2 6.In covering a distance of 30 km, A takes 2 hours more than B. If A doubles his speed, then he would take 1 hour less than B. A’s speed is a)5kmph b)6kmph c)6.25 kmph d) 7.5 kmph. 7.In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is a)1 hr b)2 hrs c)3 hrs d)4 hrs 8.It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the car is a) 2:3 b) 3:2 c)3:4 d)4:3 9.The jogging track in a sports complex is 726 metres in circumference. Deepak and his wife started from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in a) 4.9 min b) 5.28 min c)5.5 min d) 6 min. 10. Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/ hr and 40 km/hr respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is a) 500 km b) 630 km c) 660 km d) 900 km. R0304 B Directions: In each question below are given two statements followed by two conclusions numbered I and II. Give your answer as (A) Only I follow (B) Only II follows (C) Both I and II follows (D) Neither I or II follows. No Statements Conclusions 11. Some books are magazines. I. Some books are novels. Some magazines are novels. II.Some novels are books. 12. All beautiful girls are foolish I. No girl is smart. No foolish girls are smart. II.No beautiful persons are smart. 13. Some cows are deer. I. Some cows are fish. Some deer are fish. II.Some fish are cows. 14. Some shirts are socks. I. Some socks are shirts. No sock is red. II.No shirt is red. 15. All bulbs are birds. I. All butterflies are bulbs. Some birds are butterflies. II.Some bulbs are butterflies. In the following questions a statement is followed by two arguments – one from the positive side and the other from negative side. Mark A if only argument I is forceful , B if only argument II is forceful, C if both I and II are forceful and D if neither I nor II is forceful. No Statement Arguments 16. Should LOC in Jammu & I. Yes, because this is the only possible solution to this Kashmir be accepted as the problem. border between India and II. No, because the whole of Jammu & Kashmir belongs Pakistan? to India. 17. Should Samjhauta express III. Yes, it helps in improving relations between the continue to run between India two countries. and Pakistan? IV. No, it is used by militants and smugglers from Pakistan. 18. Should child labour be totally V. Yes, because many countries have refused to buy banned? Indian goods because of child labour working in Indian industries. VI. No, because a good number of families are able to get square meal because their children work. 19. Should power generation and VII. Yes, because it will bring down Transfer and distribution be privatised in distribution losses due to theft and pilferage. India? VIII. No, because the experiment has failed to click in many states. 20. Should there be a screening test IX. Yes, because other countries like U.K. and the for foreign educated doctors if U.S.A. conduct such tests. they want to practice in India? X. No, because such a step would discourage foreign qualified doctors from settling in India. Mathematical Aptitude Development Programme Aptitude Test No: QR0304B Venue: Time taken: minutes Name: Course: Date: Registration Number No Answers No Answers No Answers 1 6 11 16 2 7 12 17 If no choice given is 3 8 13 18 appropriate then 4 9 14 19 choose choice 5. 5 10 15 20 Q0304 B 7 15 21 1. = 0.466, = 0.652, = 0.724 . Therefore 21:29 is greatest. 15 23 29 Another method. Out of 7:15(= 21: 45) and 21:29 , 21:29 is greatest. out of 15:23 and 21:29, the lcm between 15 and 21 is 105. Between 105:161 and 105: 145, 105:145 is greatest. 48(3 x5 − 1x9 ) 2.Using theorem 2, =8. 9(3 + 1) A A B C A 2 4 5 8 3. = × × . Therefore, = × × = . Hence the ratio is 8:12:15:21. D B C D D 3 5 7 21 50(9 − 4) ) 4.Use theorem 2. =25 litres. 2(3 + 2 ) sum + difference 25 5 5.The ratio of the two numbers are = = = . sum − difference 15 3 30 30 6.Let A’s speed be x km/hr. Then, − = 3 ⇔ 6 x = 30 ⇔ x = 5km / hr . x 2x 600 600 7.Let the duration of the flight be x hours. Then, − = 200 x 1 x+ 2 600 1200 2 ⇔ − = 200 ⇔ x(2x + 1) = 3 2x + x – 3 = 0 (2x +3)(x – 1)= 0 x = 1 hr. x 2x + 1 8.Let the speed of the train be x km/hr and that of the car be y km/hr. 120 480 1 4 1 200 400 25 1 2 1 Then, + = 8 or + = . And + = or + = . x y x y 15 x y 3 x y 24 Solving (i) and (ii) we get x = 60 and y = 80. ∴ Ratio of speeds = 60: 80 = 3:4. 9.Clearly, the two will meet when they are 726 m apart. To be (4.5 + 3.75 =) 8.25 km apart, 100 726 242 they take1hour. To be 726m apart, they take × hrs = × 60 min= 5.28 min 825 1000 2750 10. At the time of meeting, let the distance travelled by the second train be x km. Then, x x + 100 distance covered by the first train is (x + 100) km. ∴ = 40 50 50x = 40x + 4000 x = 400. R0304 B 1. D. I + I leads to no conclusions, both this conclusions are invalid. 2. D. A + E = E. Thus the conclusion should be ‘No beautiful girls are smart’. 3. D. I + I = no conclusion. Thus both are invalid. 4. A. I + E = O which leads to the conclusion ‘Some shirts are not red’. But if we consider only statement I, then we find that it is the same as conclusion I. 5. D. A + I = No conclusion. 6. B. The word ‘only’ makes the first argument weak. 7. C. 8. C. 9. A. The failures of experiment initiates steps to rectify the mistakes in the privatisation 10. B. The situation may not be the same in all countries makes argument I weaker.