1.Aptitude With SolutionsTCS 2009-10-11

8/13/2019 1.Aptitude With SolutionsTCS 2009-10-11

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Aptitude Questions with solutions [Trend of TCS papers in the years 2009,2010,2011]SET I

1. Let n be a natural number, then n(n2-1) is always divisible by?A. 6 (B)12 (C)24 (0)48 (E) None of theseAns: A. 6. {product of three consecutive numbers}

2. A group of housewives with average age 30 years meets with another group of housewives with average age of 40years. If the average age of the new group is 34 years, what is the ratio of the number of housewives in the first groupto the number of housewives in the second group?A. 2:3 (B) 3:5 (C) 3:2 (D) 3:4 (E) 4:3Ans: (B) 3:2{allegation rule: (40-34) : (34-30)}

3.In the city club, there are four people: Avinit, Bikash Chandan and Debjit. They were; though not necessarily in thesame order: doctor, teacher, painter and actor. Avinit and the teacher never spoke to Chandan. Bikash and the actorwere very good friends. The painter was friends with Debjit and the actor.1. Avinit is the(A) Doctor (B) Teacher (C) Painter (D) Actor (E) Data Inadequate2. Bikash is the(A) Doctor (B) Teacher (C) Painter (D) Actor (E) Data InadequateAns: Avinit-actor;Bikash-Painter;Chandan-doctor;Debjit-Teacher

4. If a number 774958A96B is to be divisible by 8 and 9, the values of A and B, respectively, will be:(A) 7, 8 (B) 8,0 (C) 5, 8 (D) 3,0 (E) None of theseAns: B ) 8,0{divisibility rules of 8 & 9}

5. A software engineer starts from home at 3 PM for evening walk on a route which has level road for some distanceand a then a hillock. He walks speed of 4kmph on level ground and then at a speed of 3kmph on the uphill and thendown the hill at a speed of 6 kmph to the level ground and then at a speed of 4kmph to the home If he reaches home at9 PM. What is the distance one way of his route?(A) 12 Km (B) 15 Km (C) 18 Km (D) 24 Km (E) Data InadequateAns: (D)24km.{average speed in the hillock =2*3*6/(3+6)=4kmph as covering the same distance during up anddownhill.Therefore 4kmph*(6PM-3PM)hr=24km}

6. From a circular sheet of paper with a radius of 20 cm, four circles of radius 5 cm each are cut out.What is the ratioof the uncut to the cut portion?(A) 1:3 (B) 4: 1 (C) 3: 1 (D) 4:3 (E) 2:3Ans: (c) 3:1;

7. Supposing a clock takes 7 seconds to strike 7. How long will the same clock take to strike 10?(A) 10 secs (B) 10.5 sees (C) 7 sees (D) 9 sees (E) 12.5 secsAns: (B) 10.5secs

8. A bag contains 5 green and 7 blue balls. Another one contains 4 green and 8 blue balls. If a bag is chosen randomlyand a ball is drawn from it at random, then find the probability that it is green(A) 3/4 (B) 1/4 (C) 5/8 (D) 3/8 (E) None of theseAns: (D)=3/8 {(1/2)*(5/12)+(1/2)*(4/12)=3/8}

9. Saniya, her brother, her daughter, and her son are tennis players. As a game of doubles is about to begin:Saniya's brother is directly across the net from her daughter.Her son is diagonally across the net from the worst player's sibling.The best player and the worst player are on the same side of the net.

1. Who is the best player?(A) Saniya (B) Saniya's brother(C) Saniya's son (D) Saniya's daughter (E) Can't be determined

2. Who is the worst player?(A) Saniya's daughter (B) Saniya (C) Saniya's son (D) either (A) or (B) (E) either (B) or (C)3. Who is partner with Saniya?(A) Saniya's daughter (B) Saniya's brother (C) Saniya's son (D) Either (A) or (B) (E) either (B) or (C)

Ans: 1.(B) Saniyas brother; 2.(B) Saniya; 3. (B) Saniyas brother

10. The price of a precious stone is directly proportional to square of its weight. What will be the loss incurred(approx) if a stone weighing 28 g and costing 28,000 breaks into two pieces whose weights are in the ratio 15: 13?

(A)No Loss (B)' 10,000 (C) , 9,500 (D) , 28,000 (E)' 14,000Ans: (E) 14000


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11. In a class of 50 students, 23 speak English, 15 speak Hindi and 18 Speak Punjabi. 3 speak only English and Hindi,6 speak only Hindi and Punjabi and 6 speak only English and Punjabi. If 9 can speak only English, how many speakall the three?(A) 1 (B) 2 (C) 3 (D) 5 (E) None of theseAns: (D) 5 {Venn diagram}

12. The average of 10 numbers is 40.2. Later it is found that 2 numbers have been wrongly added. Thefirst is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.(A) 40.2 (B) 40.4 (C) 40.6 (D) 40.8 (E) 41Ans: (A) 40.2

13. A man has 1044 candles. After burning, he can make a new candle from 9 stubs left behind. Find the maximum

number of candles that can be made.(A) 116 (B) 120 (C) 130 (D) 140 (E) 144Ans: (C) 130 { 116New-12New & 8Waste-1New & 3Waste-1New 2Waste= Total=116+12+1+1=130}

14. The sides of a triangular are in the ratio of 1/2: 1/3 : 1/4. if the perimeter is 52 cm. the length of thesmallest side is...

(A)9 cm (B) 10 cm (C) 16 cm (D) 24 cm (E) 12 cmAns: (E) 12cm

15. Find the last number of the sequence: 8,12,24,60,(A) 168 (B) 120 (C) 90 (D) 144 (E) 178Ans: (A)168

16. The cast of a benefit program will consist of exactly four actors to be selected from the seven actors P, Q,R, S, T, U and V according to the following conditions:I. Either P or T must be in the cast; but they cannot both be in the cast.II. If T is in the cast, then Q must be in the castIII. If U is in the cast, then neither P not R can be in the cast.1. If U is in the cast, then which of the following must also be in the cast?

(A) P (B) Q (C) R (D) S (E) V2. If P is in the cast, then any of the following groups of three could make up the rest of the cast, except(A) Q, R and S (B) Q, R and V (C) R, S and V (D) S, U, and V (E) None of these

Ans: 1. (B) Q; 2. (D) S, U, and V

17. The boys and girls are in the ratio 3:7 in a school. 25% of the boys and 20% of the girls are scholarship holders.How much percent of the total students do not get scholarships?(A) 68 (B) 75 (C) 79.8 (D) 78.5 (E) 82.5Ans: (D) 78.5

18. A cistern is two-third full of water. Pipe A can fill the remaining part in 12 minutes and pipe B in 8 minutes. Oncethe cistern is emptied, how much time will they take to fill it together completely?(A) 12 minutes (B) 12.5 min (C) 14.4 min (D) 10.2 min (E) 14.66 minAns: (C) 14.4min

19. Mr. Mohit is 7 times as old as his son. 10 years hence he will be three times as old as his son. What is thedifference in their present ages?(A) 24 years (B) 30 years (C) 18 years (D) 36 years (E) 42 yearsAns: (B) 30years

20. Three terrorists are employed to shoot a renowned person Mr. X. Only one bullet is sufficient to kill him if itstrikes in the head. The probabilities of the terrorists striking Mr. X's head by their bullets are 0.2, 0.3, and 0.4. What isthe probability that Mr. X is shot dead?(A) 0.336 (B) 0.9 (C) 0.1 (D) 0.760 (E) 0.664Ans: (E) 0.664 { Prob(at least one of them will strike)=1-Prob(none will be succeded)=1-(.8)(.7)(.6)=.664}

21. Which of the following numbers is a perfect square?(A) 10201 (B) 12223 (C) 11116 (D) 55555 (E) 10101Ans: (A) 10201

22. Mr. Rajiv and Mr. Jogesh can complete a piece of work in 6 days and 8 days respectively. They started togetherbut Rajiv left the work after 2 days. In how many days will Mr. Jogesh complete the remaining work ?

(A) 19/4 days (B) 8/3 days (C) 9.5 days (D) 4 days (E) 10/3 days

Ans: (E) 10/3 days


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23. Study the given series (A) carefully and answer the incomplete series (B), in the following questions.

Assume that series B follows the same rule as series A.1. Series A: 2, 5,17,71, Series B: 1, a, b, c What will replace the symbol c?

(A)70 (B) 11 (C) 47 (D) 36 (E) 272. Series A: 2,11,47,128, .... ; Series B: 5, m, n, 0 ... The value of o is.....(A) 45 (B) 50 (C) 60 (D) 131 (E) 121

Ans: 1. (C ) 47{series B:1*1+0,1*2+1,3*3+2,11*4+3}2. (D) 131 {series B: 5,5+3^2,14+6^2,50+9^2}

24. A bag contains 4 white and 3 black balls. 2 balls are drawn one at a time, randomly in succession. What is theprobability that both the balls drawn out are white in color, if the first ball is not replaced after the first draw?

(A)9/49 (B) 3/7 (C) 2/7(D) 4/7 (E) 16/49Ans: (C ) 2/7 {(4/7)*(3/6)}

25. On rolling 6 dice, it is found that(1) Exactly 3 dice show the same number (II) Only 1 die shows 6 (III) Not more than 3 dice show 4 ormore1. What is the minimum possible total of numbers on the faces, if the three dice having same number show 2?

(A) 20 (B) 22 (C) 11 (D) 14 (E) 152. What is the maximum total, if 4 of the dice show less than 4?(A) 28 (B) 22 (C) 17 (D) 23 (E) 24

Ans: 1. (D) 14 {2,2,2,6,1,1}2. (B) 22 {3,3,3,6,2,5}

26. There arc seven family members viz, P, Q, R, S, T, U and V four of whom are females. The family runs into threegenerations. The family consists of two married couples, three daughters and two mothers. S is the brother of R. R isthe mother of U. V is Q's son in law. P is the father of R.

1. Who is the husband of R ?(A) Q (B) U (C) V (D) T (E) Either (A) or (C)

2. Which of the following is not true?(A) Q is the mother of R. (B) T may be the sister of S (C) V is the father of T (D) T and V are married(E) Options (B) and (D)

Ans: 1.(C) V; 2. (E) { Gen 1:P(M)+Q(F)Gen2: S(M) & R(F); R married with V(M)Gen 3: U(F) & T(F)}

27. The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for thepopulation to grow from 1,000 to 500,000 bacteria?(A) 10 (B) 12 (C) 14 (D) 18 (E) 20Ans: (C ) 14 {N=N0* 2

(t/2); t in mins, N=500,000,N0=1000}

28. If Sin and Cos are two roots of the equation ax2+ bx + c = 0, then which of the following is true?

(A) a2+b2 =2ac (B) a+b = c (C) a2 - b2 +2ac = 0 (D) a2 _b2 = 2ac (E) None of TheseAns: (C) a2-b2+2ac=0 {sin+cos=-(b/a); sincos=c/a}

29. From the top of a building 60 metres high the angles of depression of the top and bottom of a tower are 30 and60 respectively. The height of the tower is,

A. 40m (B) 30m (C) 20m (D) 50m (E) 23mAns: (A) 40m {60-60cot60tan30}

30. There are 6 positive and 8 negative numbers. Four numbers are chosen at random and multiplied. The probabilitythat the product is positive is

A. 500/1001 (B) 503/1001 (C) 303/1001 (D) 101/1001 (E) 505/1001Ans: (E) 505/1001 {(8C4+6C2*8C2+6C4)/14C4}

31. The average age of all boys in the class is 16.66, while the average age of all girls in the same class is 18.75. Thusthe average age of all 40 students in the class is 17.5 what is the number of girls in the class?

(A)12 (B) 16 (C) 18 (D) 20 (E) Data InsufficientAns: (B)16{apply allegation rule;{[(17.5-16.66)/(18.75-16.66)]*40=16}

32. If a+b : b+c : c+a = 6:7:8 and a+b+c = 14, then the value of c is(A) 6 (B) 7 (C) 8 (D) 14 (E) None of These

Ans: (A) 6

33. From each of the two given numbers, half of the smaller number is subtracted. Of the resulting numbers, thelargest is three times the smaller one. What is the ratio of the two numbers?

(A) 5:4 (B) 5:2 (C) 3:2 (D) 2:1 (E) 7:4


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Ans: (D) 2:1

34. Suppose n is an integer such that the sum of digits of n is 2 and 1010< n< 10ll. The number of different values for nis

(A) 11 (B) 10 (C) 9 (D) 8 (E) No Values PossibleAns: (A) 11; {11 digit number. Case 1: two 1 & nine 0 1stdigit has to be 1 remaining 10 digits can be filled up with10 ways(1 at 10 different positions).Case 2: one 2 & ten 0 2 in the first digit and remainings are 0 so one way.}

35. A car is traveling at uniform speed. The driver sees a milestone showing a two digit number which is a perfectsquare, after traveling for an hour the driver sees another milestone with the same digits in reverse order and afteranother hour the driver sees another milestone containing the same two digits as part of a three digit number. What isthe speed of the car?

(A) 30 kmph (B) 40 kmph (C) 50 kmph (D) 60 kmph (E) 45 kmphAns: (E) 45kmph { difference of a two digit number and its reverse must be divisible by 9. As the car traversed thisdistance in 1 hr therefore speed of the car will be divisible by 9.Therefore only possible answer in the option is45.Initial mile stone was 16 then 61 and finally 106.}

36. A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already full and both thetaps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filledcompletely or emptied completely as the case may be?

(A) Emptied; 16 mins (B) Filled; 8 mins (C) Emptied; 12 mms (D) Filled; 12 mins (E) None of TheseAns: (E) None of these{ emptied the 1/2full tank in (1/2)*[(1/8)-(1/16)]-1=8min}

37. How many numbers can be formed using all of 1,2,3,4,5 (without repetition), when the digit at the units place mustbe greater than that in the tenth place?

A. 54 (B) 40 (C) 60 (D) 48 (E) 36Ans: (C ) 60. {4!+(4!-3!)+( (4!-2*3!)+ (4!-3*3!)=60}

38. A man is standing in front of a painting of a man, and he tells us the following: Brothers and sisters have I none,but this man's father is my father's son. Who is on the painting?His fatherA. His grandfather B. His son C. He himselfAns: B.His son

39. A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4 facesof the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

A. 900 B.488 C.500 D.800Ans: B. 488 { 130*2+76*3=488}

40. Alok and Bhanu play the following min-max game. Given the expression N=X-Y-Z where X, Y and Z arevariables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it.Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y orZ). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the valuefor the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the game wouldbeA.4 B.2 C. -18 D.9Ans:B. 2 {Strategy of the game for B : if the 1stnumber less than 3 then make it X if not make it Y or Z;if X is vacant2ndnumber will be allotted to X if it is less than or equal to (7-1 stnumber). Strategy of A: 1stnumber should be 2 and2ndnumber will be 0 if 1stnumber is assigned to X, if not then 4 or 5.}

41. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre evelY hourin A, it gets filled up like 10,20, 40, 80, 160 .. in tank B. (At the end of first hour, B has 10 litres, second hour it has

20, and so on). If 1/32 of B's volume is filled after 3 hours, what is the total duration required to fill it completely?A. 10 hours B.9 hours C.8 hours D.7 hoursAns:C. 8hours { Volume of B=32*40lt=10*27lt; Again nth term of the series 10,20,40is 10*2(n-1)where n is timeelapsed in hour.Therefore solving n=8}

42. The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of theforerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, allprogrammers are equal in every respect. They receive identical salaries and also write code at the same rate. suppose12 such programmers take 12 minutes to write 12 lines of code in total. How long will it take 72 programmers to write72 lines of code in total?A.72 B. 12 C.6 D. 18Ans:B. 12mins


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43. The difference between the ages of two of my three grandchildren is 3. My eldest grandchild is three times olderthan the age of my youngest grandchild and my eldest grandchild's age is two years more than the ages of my twoyoungest grandchildren added together. How old is my eldest grandchild?A 12 B 15 C 10 D13Ans: B. 15 { ages are 15,8,5}

44. There are two "boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed tomove the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box,the probability of getting a red ball is maximized. This maximum probability isA 14/19 B 37/38 C D 3/4Ans: A 14/19,[Box1:1R,Box2:9R+10G]

45. Ferrari S.p.A. is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 asScuderia Ferrari, the company sponsored drivers and manufactured race cars before moving into production of street-legal vehicles in 1947 as Ferrari S.p.A.. Throughout its history, the company has been noted for its continuedparticipation in racing, especially in Formula One, where it has enjoyed great success. Rohit once bought a Ferrari. Itcould go 2 times as fast as Mohit's old Mercedes. If the speed of Mohit's Mercedes is 32 km/hr and the distancetravelled by the Ferrari is 952 km, find the total time taken for Rohit to drive that distance.A15.88 B 14.88 C 476 D 29.75Ans: B. 14.88hr

46. The teacher is testing a student's proficiency in arithmetic and poses the following question. 1/3 of a number is 3more than 1/6 of the same number. What is the number? Can you help the student find the answer?A 18 B 21 C 6 D 12Ans:A. 18

47. A greengrocer was selling apple at a penny each, chickoos at 2 for a penny and peanuts at 3 for a penny. A fatherspent 7p and got the same amount of each type of fruit for each of his three children. What did each child get?A) 1 apple, 2 chickoos, 2 peanuts B) 1 apple, 3 chickoos, 2 peanuts C) 1 apple, 2 chickoos, 1peanutD) 1 apple, 1 chickoo, 1 peanutAns: C) 1 apple, 2 chickoos, 1peanut {let 3x,3y,3z are the total no of ap,ch and peanut, therefore 6x+3y+2z=14, x hasto be 1it cant be more than that,between y and z by trial it is found that y=2,z=1}

48. A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and thehare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely. The hare andtortoise meet when the hare has covered only l/8 of the distance:. By what [actor should the hare increase its speed soas to tie the race?A 8 B40 C 37.80 D 5Ans: C. 37.80{

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49. Rearrange the following letters to make a word and choose the category in which it fits.RAPETEKAA Bird B Vegetable C Fruit D CityAns: A. Bird(PARAKEET)

50. One day Rapunzel meets Dwarf and Byte in the Forest of forgetfulness. She knows that Dwarf lies on Mondays,Tuesdays and Wednesdays, and tells the truth on the other days of the week. Byte, on the other hand, lies onThursdays, Fridays and Saturdays, but tells the truth on the other days of the week. Now they make the followingstatements to Rapunzel- Dwarf: Yesterday was one of those days when I lie. Byte: Yesterday was one of those dayswhen I lie too. What day is it?A Sunday B Monday C Thursday D Tuesday

Ans: C. Thursday {After the statement of Dwarf it is clear that the day will be either Monday or Thrusday, Bytesstatement prove that it cant be Monday}

51. A hunter leaves his cabin early in the morning and walks one mile due south. There he sees a bear and startschasing it for one mile due east before he is able to shoot the bear. After shooting the bear, he drags it one mile due

north back to his cabin where he started that morning. What color is the bear?


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A Grey B Black C Brown D WhiteAns: D. White { This is possible only when you are at the north pole, so bear must be a polar bear which is white incolor}

52.In school there are some bicycles and 4 wheeler wagons. One Tuesday there are 190 wheels in the campus. Howmany bicycles are there?Ans: Must be an odd number exists(say,1bicycle & 47 wagons, or 2 bicycles & 46 wagons.etc){x+2y=95, x=no.ofbicycle,y=no. of 4 wheelers}

53.In a market 4 man are standing .the average age of the four before 4 years is 45, after some days one man is addedand his age is 49. What is the average age of all?Ans:49{now the average age is(45+4)=49,therefore if the man added is of 49 average age will remain same}

54. In a school for a student out of a 100 he got 74 of average for 7 subjects and he got 79 marks in 8th subject. Whatis the average of all the subjects?Ans:75.625{average will be increased by (79-74)/8=0.625}

55. In a city, there are 100 buildings numbered by corporation between 0-100, how many twos are shown in door?Ans:20{1 in unit digit,19 in two digits}

56. 6 persons standing in queue with different age group, after two years their average age will be 43 and seventhperson joined with them. hence the current average age has become 45.Find the age of seventh person?Ans: 69 {present average age 43-2=41.average age increased by (45-41)=4.So 7thperson is 7*4=28 years older thanthe present average age of 6 persons. His age will be 41+28=69.}

57. 3,22,7,45,15,?, 31Ans: 91{ series A:3,7,15,31;series B:22,45,45*2+1=91}

58. if a person moves 15km straight and turns 45km right and moves 15km straight then how much distance he needsto walk to reach starting point?

Ans:15 13 { 22 45)1515( ++ }

59. if pqrstu implies qrstuv then abcdefg implies what?Ans: bcdefgh{shift one letter}

60. There are 30 cans and out of them only one is poisoned. If a person tastes very little he will die within 14 hours soif there are mice to test and 24 hours, how many mice are required to find the poisoned can?Ans: 5[30


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67. There are 11 children in a family. Youngest child is a boy. What is the probability of all are boys?Ans: 1/1024 {(1/2)10}

68. A boy bought a roll A of 56 inches wide and 141 yards long. Time taken for cutting A into 1 yard piece is 2secondsTime taken to cut into 141 pieces of 1 yard each is?Ans: 140*2=280sec

69. A Person buys a horse for 15 pounds, after one year he sells it for 20 pounds. After one year, again he buys thesame horse at 30 pounds and sells it for 40 pounds. What is the profit for that person?Ans: 15pound{(15+30)-(20+40)}

70. John buys a cycle for 31 dollars and given a cheque of amount 35 dollars. Shop Keeper exchanged the cheque withhis neighbor and gave change to John. After 2 days, it is known that cheque is bounced. Shop keeper paid the amountto his neighbor. The cost price of cycle is 19 dollars. What is the profit/loss for shop keeper?Ans: 23dollar {only loss is the cost price of the cycle & 4dollar change}

71. In a family there are some boys and girls. All boys told that they are having equal no of brothers and sisters andgirls told that they are having twice the no. of brothers than sisters. How many boys and girls present in a family?Ans: 4boys & 3 girls

72. There are certain numbers of gloves in a box. They are of 41 red, 23 green, 11 orange. Power gone. How manydraws are required to obtain a pair of each color?Ans: 66 {41+23+2=66}

73. Metal strip of width 'x' cm. 2 metal strips are placed one over the other, then the combine length of 2 strips is 'y'. If'z' strips are placed in that manner. What is the final width of that arrangement?Ans:x+(z-1)(y-x)

74. A game is played between 2 players and one player is declared as winner. All the winners from first round areplayed in second round. All the winners from second round are played in third round and so on. If 8 rounds are playedto declare only one player as winner, how many players are played in first round?Ans: 28{ in the xth round the number of players =29-x}

75. There are 3 boys A, B, C and 2 Girls D, E. D always sit right to A. Girls never sit in extreme positions and in themiddle position. C always sits in the extreme positions. Who is sitting immediate right to E?Ans: C { A,D,B,E,C}or A {B,E,A,D,C}

76. Entry ticket to an exhibition ranges from 1p to 31p. You need to provide exact change at the counter. You have31p coin. In how many parts will u divide 31p so that u will provide the exact change required and carry as less coinsas possible?Ans: 5 {1,2,4,8,16}

77. Block has 10, 9,5 size, how many unit cube is needed to make a block of that size?Ans: 450

78. Sangakara and Ponting selects batting by using a dice, but dice is biased. So to resolve, Ponting takes out a coin.What is the probability that dice shows correct option?Ans: 1/2{ x*0.5+(1-x)*0.5, where x is the biased ness of the dice }

79. There is a toy train that can make 10 musical sounds. It makes 2 musical sounds after being defective. What is theprobability that same musical sound would be produced 5 times consecutively?

Ans: 1/16 { 2*()5}


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SET II

1. Alok and Bhanu play the following min-max game. Given the expression N=40+ X+Y -Z, where X, Y and Z arevariables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it.Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y orZ). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the valuefor the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the game wouldbe 49 51 31 5Ans:51(Remember if X+Y-Z then =11,if X-Y-Z then =2, if X*(Y-Z) then =18 )

2.The IT gaint Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of theforerunners in the technology front, Timop continues to lead the way in products and services in India. At Tirnop, allprogrammers are equal in every respect. They receive identical salaries and also write code at the same rate. Suppose14 such programmers take 14 minutes to write 14 lines of code in total. How long will in take 5 programmers to write5 lines of code in total? 19 5 14 70

Ans:14

3.14 people meet and shake hands. The maximum number of handshakes possible if there is to be no 'cycle' ofhandshakes is (A cycle of handshakes is a sequence of people aI, 31, ... ak, k>2 such that the pairs {al ,a2}, {a2,a3}, ..., {a(k-l), ak}, {ak, al} shake hands). 11 12 10 13Ans: 13 {k-1}

4. 45 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspectsare made to stand in a line and each person declares that the person next to him on his right is guilty. The rightmostperson is not questioned. Which of the following possibilities are true? A. All the suspects are lying. B. The leftmostsuspect is guilty. C. The rightmost suspect is guilty. A only A and C B only A and B

Ans: A & B

5.The dynamics of crowd behavior are hard to study because usually people are not reliable witnesses of their ownbehavior. Now consider 4 people standing in the queue of a supermarket. You want to predict their behavior based ontheir age group. You get to know from the supermarket records that their average age 4 years ago was 43 years. After awhile, another person joins the queue and the present average of all the 5 is 40 years. The present age of the last personin the queue is :28 years 12yrs 32 yrs 24rs

Ans: 12yrs

6. One day Snowwhite meets Pal and Unicorn in the Fairyland. She knows the Pal lies on Mondays, Tuesdays andWednesdays, and tells the truth on the other days of the week. Unicorn, on the other hand, lies on Thursdays, Fridaysand Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Snowwhite- Pal: Yesterday was one of those days when I lie. Unicorn: Yesterday was one of those days when I lie too. What dayis it?Tuesday Monday Thursday SundayAns:Thursday

7.The Barnes Foundation in Philadelphia has one of the most extra-ordinary and idiosyncratic collections in Frenchimpressionist art. Dr. Barnes who put together this collection has insisted that the paintings be hung in a particularmanner specified by him at a museum designed by the French architect Paul Philippe Cret who also designed the

Rodin Museum. The museum has, say, seven galleries - Eugene Boudin, Cassatt, Boudin, Forain, Gonzales, Manet andMonet. Visitors reach the main Eugene Boudin by an elevator, and they can enter and leave the exhibition onlythrough Eugene Boudin gallery. Once inside, visitors are free to move as they choose. The following list includes allof the doorways that connect the seven galleries: There is a doorway between Eugene Boudin and Cassatt, a doorwaybetween Eugene Boudinand Boudin, and a doorway between Eugene Boudin and Gonzales galleries. There is adoorway between Cassatt and Boudin galleries. There is a doorway between Gonzales and Forain and a doorwaybetween Gonzales and Manet galleries. There is a doorway between Manet and Monet galleries. Which of thefollowing rooms CANNOT be the third gallery that any visitor enters?Monet Boudin Forain CassattAns:Monet


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8.Mr. Beans visited a magic shop and bought some magical marbles of different colours along with other magicalitems. While returning home whenever he saw a coloured light, he took out marbles of similar colours and counted

them. So he counted the pink coloured marbles and found that he has bought 25 of them. Then he counted 14 green

marbles and then 21 yellow marbles. He later counted 30 purple coloured marbles with him. But when he reached a

crossing, he looked at a red light and started counting red marbles and found that he had bought 23 Red marbles. Assoon as he finished counting, it started raining heavily and by the time he reached home he was drenched. After

reaching home he found that the red, green and yellow marbles had magically changed colours and became white,

while other marbles were unchanged. It will take 1 day to regain its colours, but he needs to give at least one pair ofmarbles to his wife now. So how many white marbles must be choose and give to his wife so as to ensure that there is

at least one--pair of red, yellow and green marbles?

46 35 29 48

Ans:46 {23+21+2=46}

9. A greengrocer was selling watermelon at a penny each, chickoos at 2 for a penny and peanuts at 3 for a penny. A

father spent 7p and got the same amount of each type of fruit for each of his three children, Jane, Joe and Jill. Jane is

three years older than Jill and Joe is exactly half the age of Jane and Jill together. What did each child get? 1 watermelon, 3 chickoos, 2 peanuts I watermelon, 1 chickoo, 1 peanus

I watermelon, 2 chickoos, 2 peanuts I watermelon, 2 chickoos, 1 peanut

Ans: 1 watermelon, 2 chickoos, 1 peanut{6x+3y+2z=14}

10. Given 3 lines in the plane such that the points of intersection from a triangle with sides of length 20, 20 and 20, the

number of points equidistant from all the 3 lines is

4 3 0 1

Ans:4{1 incentre and 3 excenters}

11. 33 people {a1, a2, ... ,a33} meet and shake hands in a circular fashion. In other words, there are totally 33

handshakes involving the pairs, {al,a2}, {a2,a3}, ... ,{a32, a33}, {a33, a I}. Then the size of the smallest set of peoplesuch that the rest have shaken hands with at least one person in the set is

10 11 16 12

Ans: 11{ k/3 if k is multiple of three;(k+1)/3 or (k+2)/3 if k is not multiple of three;where k is no.of people}

12.Consider two vessels, the first containing on litre of water and the second containing one litre of pepsi. Suppose

you take one glass of water out of the first vessel and pour it into the second vessel. After mixing you take one glass of

the mixture from the second vessel and pour it back into the first vessel. Which one of the following statements holds

now?

None of the statements holds true. There is less pepsi in the first vessel than water in the second vessel.

There is more pepsi in the first vessel than water in the second vessel. There is as much pepsi in the first vessel as there is water in the second vessel.

Ans: There is as much pepsi in the first vessel as there is water in the second vessel.

13.Alok is attending a workshop 'How to do more with less' and today's theme is Working with fever digits. The

speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as well as womankind) had only

worked with fever digits. The problem posed at the end of the workshop is 'How many 10 digit numbers can be formed

using the digits 1,2,3,4,5 (but with repetition) that are divisible by 4?' Can you help Alok find the answer?1953125 781250 2441407 2441406

Ans: 1953125{58 x 5=59}

14.For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is

rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of wining.Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a

probability of 11/12 of winning the game. What is the probability that Paul with correctly pick the winner of theGhana-Bolivia game?

.92 .01 .85 .15

Ans 0.85{P(Paul correct)=P(Paul correct/Ghana Win)P(Ghana Win)+P(Paul correct/Bol win)P(Bol

win)=12

1

12

1

12

11

12

11+ }

15. There are two boxes, one containing 39 red balls and the other containing 26 green balls. You are allowed to move

the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the

probability of getting a red ball is maximized. This maximum probability is. .60 .50 .80 .30


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Ans: .80{All the red balls has to be transferred to the other box keeping only one red in that box .So box 1:1Red

0Green and box2 :38Red 26Green. So probability will be 8.064

385.0

1

15.0 =+ }

16.After the typist writes 40 letters and addresses 40 envelopes, she inserts the letters randomly into the envelopes (1

letter per envelope). What is the probability that exactly I letter is inserted in an improver envelope?

1-1/40 1/40 1/401 0

Ans:0

17.A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the are

in the other. The hare starts after the tortoise has covered 1/3 of its distance and that too leisurely. The hare and

tortoise meet when the hare has covered only 1/4 of the distance. By what factor should be hare increase its speed so asthe win the race?

4 3 12 5

Ans:

5


;53/53'

;3'

)2.........(4

11

'

4

1;3/5)1........(

3

1

4

11

4

1

====

======

ofveluWhere

v

v

u

v

u

v

v

u

v

u

18.

A sheet of paper has statements numbered from 1 to 20. For each value of n from I to 20, statements n says

'At least n of the statements on this sheet are true.' Which statements are true and which are false?

The odd numbered statements are true and the even numbered are false.

The first 13 statements are false and the rest are true. The first 6 statements are true and the rest are false.

The even numbered statements are true and the odd numbered are false.

Ans: The first 6 statements are true and the rest are false.

19.

The question is followed by two statements, A and B. Answer the question using the following instructions:

Choose 1: ifthe question can be answered by using one of the statements alone but not by using the other statementalone.

Choose 2: if the question can be answered by using either of the statements alone.

Choose3: if the question can be answered by using both statements together but not by either statement alone.Ch.oose 4: if the question cannot be answered on the basis of the two statements.Zaheer spends 30% of his income on his children's education, 20% on recreation and 10% on healthcare. The

corresponding percentages for Sandeep are 40%,25% and 13%. Who spends more on children's education? A" Zaheerspends more on recreation that Sandeep B: Sandeep spends more on health care than Zaheer.

3 2 1 4

Ans: 1

20. Subha Patel is an olfactory scientist working for lnternationa! Flavors and Fragrances. She specializes in findingnew scents recorded and reconstituted from nature thanks to Living Flower Technology. She has extracted fragrance

ingredients from different flowering plants into bottles labeled herbal, sweet, honey, anisic and rose. She has learned

that a formula for a perfume is acceptable if and only if it does not violate any of the rules listed: If the perfume

contains herbal, it must also contain honey and there must be twice as much honey as herbal. If the perfume contains

sweet, it must also contain anisic, and the amount of anisic must equal the amount of sweet. honey cannot be used incombination with anisic. anisic cannot be used in combination with rose. lfthe perfume contains rose, the amount

ofrose must be greater than the total amount of the other essence or essences used. Which of the following could beadded to an unacceptable

perfume consisting of two parts honey and one part rose to make it acceptable?

Two parts rose One part herbal Two parts honey One part sweet

Ans: Two parts rose

21.

The citizens of planet Oz are 6 fingered and thus have developed a number system in base 6. A certain

street in Oz contains 1000 buildings numbered from 1 to 1000. How many 3's are used in numbering thesebuildings? Express your answer in base 10.

144 54 108 36


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Ans:108{single digit(1)+double digit(6+5)+3 digits(6*6+6*5+6*5)=1+11+96}

22. Recent reports have suggested that sportsmen with decreased metabolic rates perform better in certain sports. After

reading one such report, Jordan, a sportsperson from Arlington decides to undergo a rigorous physical training

program for 3 months, where he performs Yoga for 3 hours, walks for 2 hours and swims for I hour each day. He says:I began my training on a Wednesday in a prime number month of2008. I lost 1% of my original weight within the first

30 days. In the next two months combined, I lost 1 Kg. If he walks at 5 mph over a certain journey and walks back

over the same route at 7 mph at an altitude of 200 meters, what is his average speed for the journey? 5.83 2.92 6.00 35.00

Ans: 5.83{2*5*7/(5+7)}

23. A schoolyard contains only bicycles and 4 wheeled wagons. On Tuesday, the total number of wheels in theschoolyard was 134. What could be possible number of bicycles?

16 15 18 14

Ans: 15{must be an odd number, clear from the equation}

24.A sheet of paper has statements numbered from 1 to 20. For all values ofn from 1 to 20, statement n says:

'Exactly n of the statements on this sheet are false.' Which statements are true and which are false? The even numbered statements are true and the odd numbered statements are false.

All the statements are false.

The odd numbered statements are true and the even numbered statements are false.

The second last statement is true and the rest are false.

Ans: The second last statement is true and the rest are false.

25. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour

in A, it gets filled up like 10,20,40, 80, 160 .. in tank B. (At the end of first hour, B has 10 litres, second hour it has 20,

and so on). If tank B is 1/8 filled after 5 hours, what is the total duration required to fill it completely? 9 hours 7 hours 3 hours 8 hours

Ans:8hrs{5+log28}

26. A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If 4 faces

of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

900 488 500 800

Ans:488

27. Alice and Bob play the following coins-on-a-stack game. 100 coins are stacked one above the other. One of them

is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly

moving the topmost coin to another position in the stack. Alice starts and the players take turns. A turn consists ofmoving the coin on the top to a position i below the top coin (for some j between 0 and 100). We will call this an i-

move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated; for example once a

player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gold coin happens to be on topwhen it's a player's turn then the player wins the game. Initially, the gold coin is the third coin from the top. Then

In order to win, Alice's first move should be a 1-move.

In order to win, Alice's first move should be a 0-move.

Alice has no winning strategy.

In order to win, Alice's first move can be a 0-move or a 1-move.

Ans: In order to win, Alice's first move should be a 1-move.

28.The teacher is testing a student's proficiency in arithmetic and poses the following question: 1/2 of a number is 3

more than I/6 of the same number. What is the number?Can you help the student find the answer?

9 8 10 3Ans:9

29.A circular dashboard of radius 1.0 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the

dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circle than the

periphery?

1.00 .75 .25 .50

Ans:0.25{( )

2

22/

r

r=1/4}

30.A result of global warming is that the ice of some glaciers is melting. 13 years after the ice disappears, tiny plants,

called lichens, start to grow on the rocks. Each lichen grows approximately in the shape of a circle. The relationship

between the diameter of this circle and the age of the lichen can be approximated with the formula: d=l O*(t - 13) for


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t> 13, where d represents the diameter of the lichen in millimeters, and t represents the number of years after the icehas disappeared. Using the above formula, calculate the diameter of the lichen, 45 years after the ice has disappeared.

450 437 13 320

Ans:320

31.25 people meet and shake hands. The maximum number of handshakes possible if there is to be no 'cycle' of

handshakes is (A cycle of handshakes is a sequence of people a1, a2, ... , ak, k>2 such that pairs {a1, a2}, {a2, a3}, ... ,

{a(k-I), ak}, {ak, a1} shake hands). 24 22 21 23 32.

Ans:24

32.Consider two cans, the first containing one litre of water and the second containing one litre of pepsi. Suppose youtake one cup of water out of the first can and pour it into the second can. After mixing you take one cup of the mixturefrom the second can and pour it back into the first can. Which one of the following statements holds now?

There is less pepsi in the first can than water in the second can.

There is more pepsi in the first can than water in the second can. None of the statements holds true.

There is as much pepsi in the first can as there is water in the second can.

Ans: There is as much pepsi in the first can as there is water in the second can.

33. A greengrocer was selling orange at a penny each, olives at 2 for a penny and grapes at 3 for a penny. A father

spent 7p and got the same amount of each type of fruit for each of his three children, Jane, Joe, and Jill. Jane is three

years older than Jill and Joe is exactly half the age of Jane and Jill together. What did each child get?

1 orange, 2 olives, 2 grapes I orange, 3 olives, 2 grapes 1 orange, 1 olive, 1 grape 1 orange, 2 olives, 1grape

Ans: 1 orange, 2 olives, 1 grape

34.A sheet of paper has statements numbered from 1 to 20. For each value of n from 1 to 20, statement n says 'At leastn of the statements on this sheet are true.' Which statements are true and which are false?

The even numbered statements are true and the odd numbered are false

The first 13 statements are false and the rest are true. The fist 6 statements are true and the rest are false.

The odd numbered statements are true and the even numbered are false.

Ans: The first 6 statements are true and the rest are false.

35. 45 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. Thesuspects are made to stand in a line and each person declares that the person next to him on his right is guilty. The

rightmost person is not questioned. Which of the following possibilities are true? A. All the suspects are lying. B. The

leftmost suspect is guilty. C. The rightmost suspect is guilty.A and C A and B A only B only

Ans: A and B

36.Ferrari S.p.A. is an Italian sports car manufacturer base in Maranello, Italy. Founded by Enzo Ferrari in 1928 as

Scuderia Ferrari, the company sponsored driver and manufactured race cars before moving into production of street -

legal vehicles in 1947 as Ferrari S.p.A ..Throughout its history, the company has been noted for its continued

participation in racing, especially in Formula One, where it has enjoyed great success. Rohit once brought a Ferrari. It

could go 2 times as fast as Mohit's old Mercedes. If the speed of Mohit's Mercedes is 40 Km/hr and the distancetraveled by the Ferrari is 913 Km, find the total time taken for Rohit to drive the distance.

12 Hours 22 Hours 456 Hours 11.41 Hours

Ans: 11.41 Hours

37.The teacher is testing a student's proficiency in arithmetic and poses the following question: 1/3 of a number is 6mote than 1/6 of the same number. What is the number? Can you help the student find the answer?

35 6 37 36

Ans: 36

38.Recent report have suggested that sportsmen with decreased metabolic rates perform better in certain sports. After

reading one such report, Jordon, a sportsperson from Arlington decides to undergo a rigorous physical training

program for 3 months, where he performs Yoga for 3 hours, walks for 2 hours and swims for 1 hour each day. Hesays: I began my training on a Wednesday in a prime number month of2008. I lost 1% of my original weight within

the first 30 days. In the next two months combined, 1 lost 1 Kg. If he walks at 5 mph over a certain journey and walks

back the same route at 8 mph at an altitude of 200 meters, what is his average speed for the journey? 6.15 3.08 6.50 26.67

Ans:6.15


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39.The result of global warming is the ice of some glaciers is melting. 19 years after the ice disappears, tiny planets,

called lichens, start to grow on the rock. Each lichen grows approximately in the shape of a circle. The relationship

between the diameter of the circle and the age of the lichen can be approximated with the formula: d =12* (t-19) for t>

19, where d represents the diameter of the lichen in millimeters, and t represents the number of years after the ice hasdisappeared. Using the above formula, calculate the diameter of the lichen, 32 years after the ice has disappeared.

384 156 19 365

Ans:156

40.There are two boxes, one contains 12 red balls and the other containing 47 green balls. You are allowed to move

the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the

probability of getting a red ball is maximized. This maximum probability is:.59 .20 .10 .50

Ans:0.59 {box1:1R and0G box2:11R and 47G. probability=.5*1+.5*(11/58)=0.59}

41.The citizens of planet Oz are fmgered and thus have developed a number system in base 6. A certain street in Ozcontains 1000 buildings numbered from 1 to 1000. How many 2's are used in numbering these buildings? Express your

answer in base 10.

144 24 108 36

Ans:108

42.The question is followed by two statements, A and B. Answer the question using the following instructions:

Choose 1: if the question can be answered by using one of the statements alone but not by using the other

statement alone.Choose2: if the question can be answered by using either of the statements alone.

Choose3: if the question can be answered by using both statements together but not by either statement

alone. Choose4: if the question cannot be answered on the basis of the two statements. Zayed spends 30%

of lLis income on his children's education, 20% on recreation and 10% on health care. The correspondingpercentage for Sandeep are 40%,25% and 13%. Who spends more on children's education? A: Zayed

spends more on recreation than Sandeep B: San deep spends more on healthcare than Zayed.

4 3 2 1

Ans:1


Choose 1: if the question can be answered by using one of the statements alone but not by using the other

statement alone.

Choose2: if the question can be answered by using either of the statements alone.Choose3: if the question can be answered by using both statements together but not by either statement

alone. Choose4: if the question cannot be answered on the basis of two statements. Tamn is standing 2

steps to the left of a green mark and 3 steps to the right of a black mark. He tosses a coin. If it comes upheads, he moved one step to the right, otherwise he moves one step to the left. He keeps doing this until he

reaches one of the two marks, and then he stops. At which mark does he stops? A: he stops at 21 coin

tosses. B: he obtains three more tails than heads.1 3 4 2

Ans:1

44.There are two water tank A and B, A is much smaller than B. While water fills at rate of one liter every hour in A,

it gets filled up like 10,20, 40, 80, 16..in tank B. (At the end offrrst hour, B has 10 litres, second hour it has 20, and soon). If tank B is l/8 filled after 7 hours, what is the total duration required to fill it completely?

10 hours 9 hours 11hrs 3hrs

Ans: 10hrs{7+log2 8}

45.A sheet of paper has statements numbered from 1 to 10. For a1l values of n from 1 to 10, statement n says:< 'Exactly n ofthe statements on this sheet are false.' Which statements are true and which are false?

The even numbered statements are true and the odd numbered statements are false. The second last statement is true and the rest are false.




46. Alok is attending a workshop 'How to do more with less' and today's theme is Working with fewer digits. The

speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as we as womankind) had onlyworked with fewer digits. The problem posed at the end of the workshop is 'How many 6 digit numbers can be formed

using the digits 1,2,3,4,5, (but with repetition) that are divisible by 4?' Can you help Alok find the answer?


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3906 3907 3125 1250

Ans:3125{54*5=55}

47.The dynamics of crowd behaviour are hard to study because usually people are not reliable witness of their own

behaviour. Now consider 4 people standing in the queue of a supermarket. You want to predict their behaviour basedon their age group. You get to know fro the supermarket records that their average age 3 years ago was 48 years. After

a while, another person joins the queue and the present average of all the 5 is 46 years. The present age of the last

person in the queue is:38 years 35yrs 41yr 26yrs

Ans:26yrs

48.Alice and Bob play the following coins-on-a-stack game. 100 coins are stacked one above the other. One of them isa special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top of the repeatedlymoving the topmost coin to another position in the stack. Alice starts and the players take turns. A turn consists of

moving the coin on the top to a position I below the top coin (for some I between 0 and 100). We will call this as i-

move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated, for example once aplayer makes a 2-move, on subsequent turns neither player can make a 2-move.lfthe gal coin happen to be on the top

when it's a player's turn then the player wins the game. Initially, the gold coin is the third coin from the top. Then

In order to win, Alice's first move should be a 1-move. Alice has no winning strategy.

In order to win, Alice's first move can be a 0-moveor a 1-move.

In order to win, Alice's frrst move should be a 0-move.

Ans: In order to win, Alice's first move should be a 1-move.

49.There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour in

A, it gets filled up like 10, 20, 40, 80, 160 .. in tank B. (At the end of first hour, B has 10 litres, second hour it has 20,

and so on). Iftank B is 1/16 filled after 16 hours, what is total duration required to fill it completely?

19 20 hours 4 hours 21 hrs

Ans:20hrs{16+log216}

50.Consider two tumblers, the first containing one litre of milk ad the second containing one litre of coffee. Supposeyou take one glass of milt out of the frrst tumbler and pour it into the second tumbler. After mixing you take one glass

of the mixture from the second tumbler and pour it back into the first tumbler. Which one of the following statements

holds now?

None of the statements holds true.

There is less coffee in the first tumbler than milk in the second tumbler. There is as much coffee in the first tumbler as there is milk in the second tumbler.

There is more coffee in the first tumbler than milk in the second tumbler.

Ans: There is as much coffee in the first tumbler as there is milk in the second tumbler.

51.A circular dashboard of radius 2.0 foot is at a distance of20 feet from you. You throw a dart at it and it hits the

dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circle than theperiphery?

.75 1.00 .25 .50

Ans: 0.25

52.A sheet of paper has statements numbered from I to 10. For all values ofn from I to 10, statement n says:'Exactly n of the statements on this sheet are false.' Which statements are true and which are false?



The even numbered statements are true and the odd numbered statements are false.

The odd numbered statements are true and the even numbered statements are false.Ans: The second last statement is true and the rest are false.

53.Consider two vessels, the fIrst containing one litre of oil and the second containing one litre of coffee. Suppose you

take one spoon of oil out of the fIrst vessel and pour it into the second vessel. After mixing you take one spoon of

mixture from the second vessel ap.d pour it back into the first vessel. Which one of the following statements holds

now?

None of the statements holds true. There is less coffee in the fIrst vessel than oil in the second vessel.

There is more coffee in the fIrst vessel than oil in the second vessel.

There is as much coffee in the fIrst vessel as there is oil in the second vessel.

Ans: There is as much coffee in the first vessel as there is oil in the second vessel.


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54.There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour inA, it gets filled up like 10,20,40,80, 160 .. in tank B. (At the end of first hour, B has 10 litres, second hour it has 20,

and so on). Iftank B is 1/32 fIlled after 19 hours, what is total duration required to fill it completely?

5 hours 23 hours 24 hours 25 hours

Ans:24hrs{19+log2 32}


Choose 1: if the question can be answered by using one of the statements alone but not by using the otherstatement alone.

Choose2: if the question can be answered by using either of the statements alone.

Choose3: ifthe question can be answered by using both statements together but not by either statement

alone. Choose4: ifthe question cannot be answered on the basis of two statements. Zayed spends 30% ofhis income on his children's education, 20% on recreation and 10% on healthcare. The corresponding

percentage for Sandeep are 40%,25% and 13%. Who spends more on children's education? A: Zayed

spends more on recreation than Sandeep B: Sandeep spends more on healthcare than Zayed.

1 3 4 2

Ans:1

56.The question is followed by two statements, A and B. Answer the question using the following instructions:Choosel: if the question can be answered by using one of the statements alone but not by using the other

statement alone. Choose2: if the question can be answered by using either ofthe statements alone.

Choose3: if the question can be answered by using both statements together but not by either statement

alone. Choose4: if the question cannot be answered on the basis of two statements. Tarak is standing 2

steps to the left of a yellow mark and 3 steps to the right of a grey mark. He tosses a coin. If it comes upheads, he moves one step to the right, otherwise he moves one step to the left. He keeps doing this until he

reaches one of the two marks, and then he stops. At which mark does he stops? A: he stops at 21 coin

tosses. B: he obtains three more tails than heads.

2 3 4 1

Ans:1

57. A sheet of paper has statements numbered from 1 to 10. For all values ofn from 1 to 10, statement n says:'Exactly n of the statements on this sheet are false.' Which statements are true and which are false?

The even numbered statements are true and the odd numbered statements are false.





58.There are two boxes, one contains 47 red balls and the other containing 46 green balls. You are allowed to movethe balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the

probability of getting a red ball is maximized. This maximum probability is

.75 .50 .25 .5

Ans:0.75

59. Consider two vessels, the first containing one litre of ink and the second containing one litre of cola. Suppose you

take one glass of ink out of the first vessel and pour it into the second vessel. After mixing you take one glass of

mixture from the second vessel and pour it back into the first vessel. Which one of the following statements holds

now? There is as much cola in the first vessel as there is ink in the second vessel.

None of the statements holds true.

There is more cola in the first vessel than ink in the second vessel.

There is less cola in the first vessel than ink in the second vessel.

Ans: There is as much cola in the first vessel as there is ink in the second vessel.

60. 36 people {a1, 31, ..... , a36} meet and shake hand in a circular fashion. In other words, there are totally 36handshakes involving in the pairs, {al,a2}, {a2,a3}, ..... , {a35, a36}, {a36, al}. Then the size of the smallest set of

people such that the rest have shaken hands with at least one person in the set is

1 18 12 13

Ans:12{k/3}


16/29

SET III

Ans: 37

Ans: 10800[ 108003*400;3400

3600; 3302

0

====== kkkkt eNNeee

NN

Ans:1[

x 3 y

F(x) 1/4 3/4

E(x)=3(1/4)+y(1/4)=0; y=-1

x 3 -1

F(x) 1/2 1/2

E(x)=3(1/2)+(-1)(1/2)=1]


17/29

Ans: Ans:89deg [angle between any two consecutive hour is 360/18=20deg.Each 20degcorresponds to 90/18=5mins.At 12:40 min hand is on 40/5=8 and hr hand is on approx

12(Actually it will travel further by 20*40/90=8.88 deg).Therefore angle between them is

(12-8)*20=80deg(actually it should be 80+8.88=88.88deg)]

Ans:83

Ans:255[28-1]


18/29

Ans:In order to win, Alices first move should be 1-move.

Ans:637

Ans;1100[12]


19/29

Ans:12(k/3 )

Ans:25

Ans:0.75

Ans:48[24+22+2=48]


20/29

Ans:33[21+12=33]

Ans:30208[23600*1.6*.8=30208]

Ans:1095

Ans:6min


21/29

Ans:11011[27(correction:4/3 times not 413 times)]

Ans:6.86 [H.M. of 6 and 8=2*6*8/(6+8)=6.86]

Ans:11


22/29

Ans: 4[one in center and 3 ex centers ]

Ans:0.76[6/7*6/7+1/7*1/7=37/49]

Ans:185


23/29

Ans:625[53*5=625]

Ans:72lt[(2/3)x=x-(6+x/4)]

Ans:2[4mm,6mm]

Ans:8[1(one digit)+7(4+3,two digits)=8]


24/29

Ans:13

Ans:

Ans:2[actual answer should be one mouse]


25/29

Ans:5.79thousand dollar[22*10

6/3800=5789.5]

Ans:93[46+45+2=93]

Ans:47.43[83*4/7=47.43]


26/29

Ans:4[total 58 shake hands therefore shake hands with host is 39therefore 2 hostess are

there(1between themselves and 38 with invitees)Therefore S{H1,H2,Inv1,Inv2}so that

every pair shake hands between themselves]

Ans:488[53-3

3=98 small cubes.total faces=98*6=588.Painted face=25*4=100.Therefore

unpainted faces=588-100=488]

Ans:7.6:1 [ 6.72422

822:;2622 =+=

+=++++= rarrrrra ]


27/29

Ans: Two parts rose

Ans:11[(1-1/5)*(1-1/5-1/4)*(1/5)-2

=11


;)5

1()

5

11()

4

1

5

11(

')2.........(

5

11

'

5

1);1........(

4

1

5

11

5

1 2

====

===

ofveluWhere

v

v

u

v

v

u

]

Ans: A and B


28/29

Ans:0.25

Ans:0

Ans:19.44[n=125p; vel=np=125p2m/min=125p

2(60/1000)kmph]

Ans:15[11+log216=15]


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1.Aptitude With SolutionsTCS 2009-10-11

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