## Tata consultancy services placement: Quantitative aptitude (TCS 2010 dec)

1. Find the Unit’s digit in the product (76^41) * (41^14) * (14^87) * (87^76)

(a) 9 (b) 4 (c) 2 (d) 8 (e) none of these

2. If abc = ab^3 = 180 where a, b and c are positive integers, what is the value of `c’?

(a) 1 (b) 9 (c) 3 (d) 180 (e) none of these

3. Ram was asked to multiply a number by 441 and he came with an answer 70229. His

Teacher told him that all the digits except the 2’s in his answer are correct. Which of the following could be the correct answer?

(a) 70839 (b) 70749 (c) 70349 (d) 70119 (e) 70319

4. Find the number of zeroes at the end of 50!

(a) 13 (b) 11 (c) 5 (d) 12 (e) none of these

5. Find the base K of the number system, if (524)

_{8 }= (664)_{K }? (a) 2 (b) 3 (c) 5 (d) 7 (e) none of these

6. The LCM of 2 numbers is 39780 and their ratio is 13 : 15 . Then the numbers are

(a) 2652, 3060 (b) 273, 315 (c) 585, 675 (d) 2562, 6030 (e) none of these

7. Find a number such that it exceeds 18 by three times the number by which it is less than 86?

(a) 32 (b) 69 (c) 54 (d) 67 (e) none of these

8. If the operation ^ is defined by the equation x ^ y = 2x + y, what is the value of a in 2 ^ a = a ^3

(a) 0 (b) 1 (c) -1 (d) 4

9. What is the greatest possible integer of x such that 2

^{X}is a factor of 12^{10}? (a) 6 (b) 12 (c) 20 (d) 24

10. If 3

^{ n+3}– 3^{n+2}= 6, then n is equal to (a) 1 (b) 2 (c) -1 (d) -2

11. If 2

^{p }= 4^{q}= 8^{r}and ( 1/2p + 1/4q + 1/6r ) = 24/7 then the value of r is (a) 7/16 (b) 7/32 (c) 7/48 (d) 7/64

12. The value of ( 9

^{-22}– 9^{-23 }) is (a) 1 (b) 8 x 9

^{-23}(c) 9 x 9^{-22}(d) none of these13. Two cubes each with side b are joined to form a cuboids. What is the surface area of this cuboids?

(a) 12 b

^{2}(b) 10 b^{2}(c) 6 b^{2}(d) 4 b^{2}14. If each interior angle of a regular polygon is 144

^{o}, the it is (a) Octagon (b) Decagon (c) Dodecagon (d) None of these

15. It is found that the volume of a cube is numerically equal to its surface area. Then the measure of its edge in meters is:

(a) 4 (b) 6 (c) 8 (d) cannot be determined

16. If the sum of the interior angles of a regular polygon measures up to 1620 degrees, then how many sides does the polygon have?

(a) 10 (b) 16 (c) 12 (d) 11

17. The supplementary of an angle is thrice its complimentary. Find the angle.

(a) 60

^{o}(b) 45^{o}(c) 90^{o}(d) 180^{o}18. If log 0.317 = 0.3332 and log 0.318 = 0.3364, then find log 0.319 = ?

19. The value of log 5 (1/125) is:

(a) 3 (b) -3 (c) 1/3 (d) -1/3 (e) none of these

20. If log 2 = 0.3010 and log 3 = 0.4771 then the value of log 4.5 is:

(a) 0.6532 (b) 0.7727 (c) 0.3266 (d) 0.3796 (e) none of these

21. A flight takes off at 2.00 a.m. from a place at 18N 10E and landed 10 hours later at a place with co-ordinates 36N 70W. What is the local time when the plane landed?

(a) 6.00 a.m. (b) 6.40 a.m. (c) 7.00 a.m. (d) 7.40 a.m. (e) 8.00 a.m.

22. A plane moves from a place 9N 40E to a place 9N 40W taking 8 hours to travel. If the plane had left at 10.00 a.m. then what is the local time of arrival at the destination?

23. A fisherman’s day is rated as good if he catches 9 fishes, fait if he catches 7 fishes and poor if he catches 5 fishes. The fisherman catches 53 fishes in a week that includes good, fair and poor days. How many good, fair and poor days the fisherman had during the week?

25. The ratio of incomes of C and D is 3 : 4 and their expenditures is 4 : 5. If the savings of C is one fourth of his income then what is the ratio of savings of C and D?

26. Find the third proportion to 12, 36?

27. A sum of Rs 1162.00 is divided among A, B and C such that 4 times A’s share is equal to 5 times B’s share and 7 times C’s share. What is the share of C?

28. The total expense of a boarding house is partly fixed and partly variable with the number of boarders. When the number of boarders is 25, then the charge is Rs 70 per head and the same is Rs 60 when the number of boarders is 50. What would be the charge per head if there are 100 boarders?

29. I lost Rs 68 in two races. My loss in the second race is Rs 6 more than my lose in the first race. My friend lost Rs 4 more than me in the second race. Then what is the amount lost by my friend in the second race?

30. The face of a clock is divided into three parts such that the total hours in the first part, is equal to the sum of the total hours in the other two parts. What is the total hours in the bigger part?

31. The average marks of 14 students was calculated as 71. But, it was discovered later that the marks of one student was taken as 42 instead of 56 and the marks of another student was wrongly taken as 74 while it was actually 32. If these corrections are now made then what is the average of the 14 students?

(a) 67 (b) 68 (c) 69 (d) 71

32. The average age of father and his two sons is 27 years. The difference in age between the two sons is 4 years and five years ago the average age of the two sons was 12 years. What is the present age of the father?

(a) 34 years (b) 47 years (c) 64 years (d) 27 years

33. The average weight of three men A, B and C is 84 Kg. The average weight becomes 80 Kg when D joins them. If E whose weight is 3 Kg more than D joins the group replacing A, then the average weight of B, C, D and E becomes 79 Kg. The weight of A is:

(a) 65 kg (b) 70 kg (c) 75 kg (d) 80 kg

34. The average of squares of first 11 consecutive even numbers is:

(a) 184 (b) 148 (c) 186 (d) 174

35. 27 years ago, when Mr. Waugh was asked as to whom among Steve and Mark is elder, he said, “ In two years from now Steve will be twice as old as he was two years ago and in three years from now Mark will be three times as old as he was three years ago. How old is Mark and Steve and who among the two is elder?

(a) Steve 31 years (b) Mark 37 years (c) Both are 33 years (d) cannot say

36. 19 persons went to a hotel for a combined dinner party. 13 of them spent Rs 79 each for the dinner and the rest spent Rs 4 more than the average expenditure of all the 19. What was the total money spent by them?

(a) Rs 1628.40 (b) Rs 1536 (c) Rs 1492 (d) none of these

37. Three companies working independently are saving 20%, 25% and 35% of their earnings. If these companies combine and work what would be the net percentage of savings?

38. A school having four classes only have student strength of 10, 20, 30 and 40 respectively. The pass percentages of these classes are 20%, 30%, 60% and 100% respectively. What is the pass percentage for the entire school?

(a) 56% (b) 76% (c) 34% (d) 66%

39. A number is mistakenly divided by 5 instead of being multiplied by 5. Find the percentage change in the result due t this mistake.

(a) 96% (b) 95% (c) 2400% (d) 200%

40. The entrance ticket at the Inox theatre in Chennai is worth Rs 250. The sale of tickets increased by 50% when the price of the ticket was lowered. However, the collections recorded a decrease of 17.5%. The price of the ticket is reduced by how much rupees?

(a) Rs 150 (b) Rs 112.50 (c) Rs 105 (d) Rs 120

41. Peter got 30% of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got 40% of the total marks and passed with 15 more marks than the passing marks. What was the passing marks in the examination?

(a) 35 (b) 250 (c) 75 (d) 85

42. The marks scored by a student in three subjects are in the ratio of 4 : 5 : 6. If the candidate scored an overall aggregate of 60% of the maximum marks, that is same for all the three subjects, then in how many subjects did he score more than 60% marks?

(a) 2 (b) 1 (c) 3 (d) none of these

43. In a group of students, 70% can speak English and 75% can speak Hindi. If 10% of the students can speak none of the two languages, what percentage of students can speak both the languages?

(a) 45% (b) 55% (c) 60% (d) 65%

44. The population of a town is 176400. If it increases at the rate of 5% per annum, what will be the population 2 years hence, and what was the population 2 years ago?

45. A bag contains 600 coins of 25p denomination, and 1200 coins of 50p denomination. If 12% of 25p coins and 24% of 50p coins are removed, what is the percentage of money removed from the bag?

46. An Emperor at his 11

^{th}hour called his three wives and distributed his gold in the following manner. He gave 50% of the Gold to his first wife, 50% of the remaining to his second wife and 50% of the rest to his third wife. If the combined share of the three wives is 1,30,900 kg Gold, What was the total quantity of Gold the Emperor had in the beginning? (a) 1,50,000 (b) 1,49,600 (c) 1,51,600 (d) 1,52,600

47. The profit earned when an article is sold for Rs 800 is 20 times the loss incurred when it is sold for Rs 275. At what price should the article be sold to make a profit of 25%?

(a) Rs 300 (b) Rs 350 (c) Rs 375 (d) Rs 400

48. A dishonest dealer marks up the price of his goods by 20% and gives discount of 10% to the customer. He also cheats both his supplier and buyer by 100 gm while buying or selling 1 kg. What is the profit earned by the dealer?

(a) 20% (b) 25% (c) 32% (d) 27.5%

49. A tempo dealer buys 30 tempos for Rs 4725. Of these, 8 are four-seaters and the rest 2 seaters. At what price he must sell the 4 seaters so that at ¾ of this price if he sells the 2 seaters, then overall he makes a profit of 40% on his outlay?

(a) Rs 180 (b) Rs 270 (c) Rs 360 (d) Rs 450

50. In a business village consisting of 2000 persons, 55% are male and the rest female. The male and the female population earns 5% and 8% respectively on an investment of Rs 50 per person. Population of the business village remaining the same, what would be the change in the profit percentage of the village, if the ratio of male and female population gets reversed in the next year?

(a) Drop of 0.3% (b) Increase of 0.3 (c) Increase of 0.45 (d) drop of 0.45

51. Debby bought 100 kg of wheat at Rs 1100. She sold the same at a loss, for as much money she received for 20 kg wheat. At what price dis she sell the wheat?

(a) Rs 9/kg (b) Rs 9.166/kg (c) Rs 9.5/kg (d) Rs 10.33/kg

52. A shopkeeper purchased two tables both marked at Rs 2000 – one at successive discount of 10% and 15% and the other at successive discount of 15% and 10%. He spent Rs 140 on transportation and sold the two tables each for Rs 2000. What is his percentage gain in the transaction?

(a) 20% (b) 30% (c) 24% (d) 15% (e) 25%

53. A shopkeeper buys 50 dozen eggs at Rs 24 per dozen. Out of them 40 eggs were found broken. At what rate should the shopkeeper, sell the remaining eggs per dozen so as to gain an overall profit of 5%?

(a) Rs 25.20 (b) Rs 26.10 (c) Rs 27 (d) Rs 27.90 (e) None

54. A retailer buys 100 watches for Rs 13,500. His overhead expenses are Rs 500. He sells 20 watches for Rs 150 each. Determine the increase in price he should apply for the remaining watches, if he wants to gain an overall profit of 10% .

(a) Rs 5 (b) Rs 15 (c) Rs 12 (d) Rs 10 (e) None of these

55. A manufacturer whose cost of production was Rs 720 per tonne , sell the same to his agent at a profit of 20%. The agent in turn sells it to the retail dealer at a profit of 10%. The retail dealer after marking up the price and allowing a discount of 12% still makes a profit of 10%. What is the marked price?

(a) Rs 1188 (b) Rs 1008 (c) Rs 1100 (d) Rs 1166 (e) Rs 1221

56. A vendor of fruits buys 11 for Rs 10 and sells 10 for Rs 11. What is his profit or loss percentage?

(a) Nil (b) 20% profit (c) 21% profit (d) 22% profit (e) None

57. Two men and three boys can do a piece of work in 20 days. Three men and two boys can do the same work in 16 days. How long would it take for two men and one boy to do the same work?

(a) 28 (b) 30 (c) 24 (d) 25 (e) none of these

58. A man, a woman and a child can do a piece of work in 6 days. Man alone can do it in 24 days, and the woman alone can do it in 16 days. In how many days achild alone can do the work?

59. Anand can do a piece of work in 7 days, while Bittu and Chandu can do the same work in 8 days and 6 days respectively. They work in turns everyday with Anand starting the work on the first day followed by Bittu on the second day and Chandu on the third day. On which day the work will get over completely?

(a) 3 (b) 6 (c) 9 (d) 7

60. A and B can do a job in 15 and 10 days respectively. After a few days of working together A leaves and B completes the remaining work in 5 more days. After how many days did A leave?

(a) 4 (b) 3 (c) 2 (d) 5 (e) None of these

61. It was estimated that 75 men could complete a piece of work in 20 days. When the work was about to commence, it was found necessary to send 25 men to another project. How much longer would it take now to complete the work by the remaining men?

62. A man was engaged on a job for 30 days on the condition that he would get a wage of Rs 10 for the day he works, but will have to pay a fine of Rs 2 for each day of his absence. If at the end of the period he received an amount of Rs 216, then how many days was he absent?

63. A contractor agreed to complete a project in 150 days and employed 75 men on condition that they work 8 hours daily. After 90 days it was found that only 2/7 of the work is completed. In order to complete the whole work within the stipulated time schedule, how many more men should the contractor employ, if the working hour is increased to 10 hours per day?

64. A boat takes 4 hours for travelling downstream from point A to B and coming back upstream from B to A. If the speed of the stream is 2 km/hr and the speed of the boat in still water is 4 km/hr, what is the distance between A & B?

65. A man rows 13 Km upstream in 5 hours and 28 Km downstream in 5 hours. Find the speed of the stream.

66. A man rows to a place 48 km away and returns in 14 hours. His speed with the current is 4 km/hr while the same against the current is 3 km/hr. What is the speed of the stream/current?

67. Two trains starting from stations A and B are travelling towards each other at speeds of 50 km/hr and 60 km/hr respectively. At the time of their meeting, the second train had travelled 120 km more than the first train. Find the distance between the stations A & B.

68. A motorist covers a distance of 39 km in 45 minutes. His speed during the first 15 minutes is x km/hr. During the next 20 minutes the speed is doubled and during the last 10 minutes the speed again is reduced to x km/hr. Find the speed `x’.

69. A train with speed 72 km/hr crosses a platform in 30 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?

(a) 240 mtrs (b) 360 mtrs (c) 420 mtrs (d) 600 mtrs

70. Two boys starting from the same place, walk at speeds of 5 km/hr and 5.5 km/hr respectively in the same direction. How much time would it take for the two boys to be 8.5 km apart?

71. A car travelling at 30 km/hr takes 2.5 hours more than another car travelling at 45 km/hr to reach the destination. How far away is the destination?

(a) 300 kms (b) 400 kms (c) 350 kms (d) 225 kms (e) none of these

72. Two trains of same length but with different speeds pas a static pole in 6 seconds and 7 seconds respectively. If they move in the same direction in what time will they cross each other completely?

73. Two trains of different lengths moving at the same speed pass a pole in 6 seconds and 8 seconds respectively. If the trains are moving in the opposite direction, in what time will they cross each other completely?

74. A car can finish a certain journey in 10 hours moving at a speed of 48 km/hr. If the journey were to be competed in 8 hours, then the speed of the car is to be increased by how much?

75. Vikas gets on to the elevator at the 11

^{th}floor of a building and rides up at the rate of 57 floors per minute. At the same time, Ashok gets on another elevator at the 51^{st}floor of the same building and rides down at the rate of 63 floors per minute. If they continue riding at these rates, then at which floor their paths would cross?76. Two trains running in the same direction at speeds of 65 km/hr and 47 km/hr completely pass one another in one minute. If the length of one train is 125 meters, then what is the length of the other train?

77. Find the angle between the hour hand and the minute hand of a clock at 9.40.

(a) 290

^{o}(b) 240^{o}(c) 50^{o}(d) None of these78. Find at what time between 9 and 10 the hands of a clock will be in the same straight line but not together.

(a) 9.16 (b) 9.10 (c) 9.15 (d) None of these

79. At what time between 7 and 8 both the hands of the clock will be together with no angle between them?

80. Today is Tuesday. After 59 days it will be

(a) Monday (b) Thursday (c) Friday (d) Tuesday

81. The calendar for the year 2005 will also serve for the year

(a) 2007 (b) 2012 (c) 2010 (d) None of these

82. How many three digits number can be formed using the digits 9876541?

(a) 56 (b) 210 (c) 7! (d) 7! – 3!

83. In how many different ways can the letters of the word “

**REACTION”**be arranged so that the vowels may occupy only the odd positions? (a) 4! (b) 4! + 4! (c) 4! X 4! (d) None of these.

84. In how many ways can the letters of the word

**“REVIEW”**be rearranged such that the vowels always appear together? (a)

__3 !__(b) 3 ! * 3 ! (c)__3 ! * 3 !__(d)__4 ! * 3 !__ 2 2 2 !

85. A college has 15 members cricket team. A 10 member team and a captain will be selected out of the 15 players. How many different selections are possible?

(a) 1260 (b)

^{15}C_{11}x^{11}C_{1}(c)^{15}C_{10}x^{10}C_{1}(d)^{15}C_{10}86. Out of 5 Girls and 3 Boys, a group of 5 is to be formed on condition that that group includes at least one boy. In how many ways this can be formed?

(a) 15 (b) 55 (c)

^{5}C_{4}x^{3}C_{1}(d) None of these

__PART B__

__Direction for Questions 1 & 2 :__Read the data given below and answer the questions that follow.

A market survey was conducted to ascertain brand switching parameters among toothpaste users. The initial and the current usage of the 4 brands of toothpaste - Close Up, Cibaca, Pepsodent and Colgate were checked out and presented as follows :

__Current__

__Initial__

Close Up 80 74

Cibaca 26 30

Pepsodent 72 10

Colgate 49 60

No toothpaste 25 16

Total 252 190

The people surveyed were known to use only one brand of toothpaste per person.

1. In the sample surveyed, what is the increase in the number of people using the brand Close Up as

percentage of the total current sample population?

(a) 6% (b) 2.38% (c) –4.5% (d) –7%

2. If the total number of people using any of these 4 brands of toothpaste is defined as the size of the

toothpaste market, what has been the increase in the size of the toothpaste market, based on the

data obtained in the survey?

(a) 30.45 % (b) 15.55 % (c) 20.6 % (d) 33.33 %

__Direction for the Questions 3 to 6:__Read the following information and answer the questions that follow.

Five of the integers from 1 to 16 have been placed in the various squares of a 4 × 4 grid as shown.

3 | |||

14 | |||

6 | 12 | ||

7 |

The remaining integers from 1 to 16 are to be placed in the remaining squares of the grid, subject to

the following conditions:

1. No even number is to be placed in the first or fourth row.

2. No multiple of 5 is to be placed in the first and fourth column.

3. The sum of the integers in one of the diagonals is 18.

4. No square or cube of an integer is to be placed in third column.

5. The sum of the integers in the column which contains 10, should not be less than sum of integer

in the column containing 1.

6. No more than one square of an integer is to be placed in any diagonal.

7. The sum of the integers in the first row is equal to 30.

Based on the above information, answer the questions below by identifying the integers to be placed

in each row, where the numbers in the options indicate their position in the row from left to right

(excluding the integers already shown in the grid)

3. The integers which are to be placed in the remaining squares of the first row are

(a) 5, 9, 13 (b) 1, 15, 11 (c) 11, 15, 9 (d) 5, 13, 1

4. The integers which are to be placed in the remaining squares of the second row are

(a) 2, 4, 10, (b) 2, 8, 10 (c) 4, 10, 16 (d) 8, 10, 16

5. The integers which are to be placed in the remaining squares of the third row are

(a) 2, 8 (b) 4, 2 (c) 2, 16 (d) 4, 10

6. The integers which are to be placed in the remaining squares of the fourth row are

(a) 15, 11 1, (b) 1, 9, 13 (c) 9, 5, 13 (d) 5, 13, 11

**Each question consists of a question and two statements, I and II. Choose**

a. if one of the two statements (I or II) alone is sufficient to answer the question, but cannot be

answered by using the other statement alone.

b. if each statement alone is sufficient to answer the question asked.

c. if I and II together are sufficient to answer the question but neither statement alone is sufficient.

d. if even I and II together are not sufficient to answer the question.

7. A game is played between two intelligent students, A and B. The student who starts has to pick out

one folded chit out of eight chits each with one number between 1 to 8 (both inclusive) and then the

other student can speak out any number by adding any natural number 1 to 8 to the number picked

last. The students continue speaking out numbers in this manner by adding 1 to 8 to the number

last spoken. The student who speaks 100 first wins the game. Who wins the game?

I. A starts the game and picks chit with number 1.

II. B speaks second and speaks 10.

8. Books numbered 1, 2, 3 and 4 are placed in racks 1, 2, 3 and 4 not in that order such that there is

one book in each rack, and every even numbered book is in an odd numbered rack. What is the

exact way in which books are placed?

I. Rack numbered 3 has book 2.

II. Rack numbered 2 has book 3.

9. How much cardboard will it take to make an open cubical box with no top?

I. The area of the bottom of the box is 4 square feet.

II. The volume of the box is 8 cubic feet.

10. If x + y + z > 0, is z > 1 ?

I. z > x + y + 1

II. x + y + 1 < 0

__Direction for questions 11 to 14:__Read the passage given below and answer the questions that follow:

There were 6 gentlemen who were out at Megacity Shopping Mall Each one of them bought one item only.

The 6 gentlemen are – Mr. Gupta, Mr. Pandey, Mr. Sharma, Mr. Chowbey, Mr. Haathi, Mr. Handa.

The items bought (not necessarily in the order) were – Dress, Sweater, Dresser, Telephone, Tires, Bicycle.

The original prices of these items (not necessarily in the order) was – Rs. 200, Rs. 1500, Rs. 300, Rs. 2000, Rs. 900 and Rs. 1200 and the prices paid (after various discounts) were – Rs. 800, Rs. 600, Rs. 1200, Rs. 1000, Rs. 75, Rs. 50. The following information is available to us:

1. Mr. Gupta found a clothing item..

2. The bicycle was bought at 50% off the buyer name starts with H.

3. Mr. Chowbey bought the item priced at Rs. 1500 for 4/5 ths of the amount.

4. The tires set was sold for Rs. 100 less than the asking price.

5. The item that was sold for Rs. 50 was an article of clothing.

6. Mr. Pandey spent Rs. 400 less than Mr. Chowbey.

7. Mr. Haathi paid for the dress with a Rs. 100 note (value equal to 50% the original price) and

received Rs. 25 in change.

8. Mr. Gupta spent less for the item, than Mr. Sharma, who spent less than Mr. Pandey.

9. The item originally priced the highest did not sell for the highest price. Nor did the lowest priced

item sell for the lowest amount.

10. The paid price for telephone was more than the dresser.

11. Who bought the dresser?

(a) Mr. Gupta (b) Mr. Pandey (c) Mr. Sharma (d) Mr. Handa

12. Who paid the highest price?

(a) Mr. Sharma (b) Mr. Handa (c) Mr. Haathi (d) Mr. Chowbey

13. What did Mr. Handa buy?

(a) The dresser (b) The sweater (c) The tires (d) The bicycle

14. What was the percentage discount on the highest original price item?

(a) 70% (b) 50% (c) 25% (d) 75%

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