PERMIT SOLUTIONSTCS PATTERN

Instructions

Before the Test:

(1) Keep only the identity card, pencil, eraser and sharpener with you. DO NOT KEEP with you books, rulers, slide rules, drawing instruments, calculators, cellular phones, stop watches or any other devices or loose paper. (2) Ensure that your name and roll number have been entered in the space provided correctly.(3) Directions for answering the questions are given before each group of questions. Read these directions carefully and answer the questions by darkening the appropriate circles on the Answer Sheet. Each question has only one correct answer.(4) All questions carry one mark each questions.(5) Each wrong answer carries .5 negative marks for each question. (6) Do your rough work only on the test booklet and NOT on the Answer Sheets

How to Answer:(1) This test contains one section with 35 questions. You have 1 hour 30 minutes to complete the 105 questions.

1. The difference between the ages of two of my three grandchildren is 3. My eldest grandchild is three times older than the age of my youngest grandchild and my eldest grandchild's age is two years more than the ages of my two youngest grandchildren added together. How old is my eldest grandchild?

(a) 12 (b) 13 (c) 10 (d) 15

Solution:Let X be the elder, Y be the younger, Z be the youngest.From qn,

1. X=3Z, 2. Y-Z=3 or X-Y=33. X=2+Y+Z. Compare 2 and 3, X-Y=3 is not possible.

We need X value so get Y value and Z value from 2 and 3 respectively.Substitute in 3, we get X=15.

2. A greengrocer was selling apple at a penny each, chickoos at 2 for a penny and peanuts at 3 for a penny. A father spent 7 pennies 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, 2 chickoos, 1 peanut(c) 1 apple, 3 chickoos, 2 peanuts(d) 1 apple, 1 chickoos, 1 peanut

Solution:Get the answer from options.No of items * no of children*cost of item=total cost for the item.A)1apple*3 =3*1 =3,2chickoos*3 =6*(1/2) =3,2peanuts*3 =6*(1/3) =2. The sum of cost is 8. . It doesn’t matches with father cost. So this is wrong answer.

B)1apple*3 =3*1 =3,2chickoos*3 =6*(1/2) =3,1peanuts*3 =3*(1/3) =1. The sum of cost is 7. It matches with father cost. So this is correct answer.

3. The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries and also write code at the same rate. Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How long will it take 72 programmers to write 72 lines of code in total?

(a) 12 (b) 18 (c) 6 (d) 72

Solution:12 programmers take 12 mins to write 12 lines of code.(Programmers = (1/ time) = lines of code ).72 programmers take 12 mins to write 72 lines of code.

4. Alok and Bhanu play the following min-max game. Given the expression

N = 9 + X + Y – Z ,where X, Y and Z are variables 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 or Z).Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the game would be

(a) 20 (b) 18 (c) 27 (d) 0

Solution:

The most appropriate answer for the equation X+Y-Z is 11

5. 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 on Thursdays, Fridays and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Rapunzel - Dwarf: Yesterday was one of those days when I lie. Byte: Yesterday was one of those days when I lie too. What day is it?

(a) Monday (b) Sunday (c) Thursday (d) Saturday

Solution: Monday Tuesday Wed Thursday Friday Saturday Sunday

Dwarf T T TByte T T T

Condition: Both of them says yesterday is one of the day I lied.They didn’t mention anything on Sunday. So left that.Monday is not possible Bcoz they didn’t mention anything on Sunday.Tue and wed is not possible Bcoz Dwarf speak true on Mon and Tue.In Thursday, Dwarf speaks lie. So the statement he said is false.In the case of Byte, he speaks true on Thursday. So the statement he said is also true and satisfies the condition. So answer is Thursday.

6. The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?

(a) 192 (b) 64 (c) 54 (d) 102

Solution:Here base is 8.

No of 8 in 10 (1,2,3,....10) is 1*base (8)0

No of 8 in 100 (1,2,3,...100) is 2*base(8)1

No of 8 in 1000(1,2,3,...1000) is 3*base(8)2 and so on...

The value of 3*(8)2 is 192.7. On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny planetoids called echina start growing on the rocks. echina

grows in the form of a circle and the relationship between the diameter of this circle and the age of echina is given by the formula d = 4 * √ (t - 8) for t ≥ 8 where d represents the diameter in mm and t the number of years since the solar blast. Jagan recorded the radius of some echina at a particular spot as 8mm. How many years back did the solar blast occur?

(a) 8 (b) 12 (c) 16 (d) 24

Solution:Given: d=8mm.

To find years:

d = 4 * √ (t - 8), substitute d value.t=12.

8. A circular dartboard of radius 1 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 centre of the circle than the periphery?

(a) 1/4 (b) 1/2 (c)3/4 (d) 1/3

Solution:Condition: probability for dart is closer to the centre of the circle than the

periphery. Let the circle be 1m radius. If the dart is lies inside the ½ m radius i.e. the dart is closer to centre is less than the periphery. So

Area of circle (radius ½ m) = π/4

Area of circle (radius 1 m ) = πP = (chances to lies inside the 1/2 circle)/ (Chances to lies inside the full circle)

P = (π/4) / ( π)= 0.25

9) A schoolyard contains only bicycles and 4 wheeled wagons. On Tuesday, the total number of wheels in the schoolyard was 166. What could the possible number of bicycles? (a) 14 (b) 10 (c) 12 (d) 11

Solution:Total no wheels =166. To find total no of bicycles.Get the answer from solution.A) 14*2=28wheels (166-28) =138B) 10*2=20 wheels (166-20) =146C) 12*2=24 wheels (166-24) =142D) 11*2=22 wheels (166-22) =144. From the above which one is divided by 4 is the correct answer. I.e. 144/4=32 four wheeler and 11 bicycles.

10) 9years ago, Andromeda’s age was twice Achilles’ age .9 years hence, Andromeda’s age will be 4/3 times the age of Achilles’. Find Andromeda’s present age in binary numbers.

(a)11011 (b) 11000 (c) 1001 (d) 1010

Solution: Let Andromeda as A, Achilles as B.A-9 =2(B-9) A-2B=-9;A+9= (4/3) (B+9) 3A-4B=9;Solve the above 2 eqn, we get A=27.Convert A value into binary, answer as 11011.

11. After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?

(a) 11/12 (b) 0 (c) 1/12 (d) 1/6

Solution:Let if she put one letter in wrong envelope, another one letter is to be

placed in wrong envelope only. So the probability of exactly one letter inserted in improper envelope is 0.

12. 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 well as womankind) had only worked with fewer digits. The problem posed at the end of the workshop is How many 5 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?

(a) 375 (b) 625 (c) 500 (d) 3125

Solution:

Condition for divisibility by 4 is last 2 digits must be divisible by 4.Among the five numbers (1, 2, 3, 4, 5) have to find the combination which are divisible by 4.The combinations are 12, 24,32,44,52. First three digit is 5*5*5 and remain two digit is 5 so answer is 5*5*5*5

13. Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is

(a) 1 (b) 0 (c) 4 (d) 2

Solution:The point having equal distance in both side is equidistant.From given only one point having the same length. So answer is 1.

14) 21 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 such that the pairs (a1, a2), (a2, a3), … , (a (k-1), a k) , (ak, a1) shake hands.

(a) 17 (b) 18 (c) 19 (d) 20

Solution:

If cyclic handshake, no of handshakes= no of people.If non cyclic handshake, no of handshakes= no of people-1.

15) The ticket to Disneyland will cost anywhere from 1p to 63p. You need to produce the exact change as the ticket counter and have with you a 63p coin. So you decide to break this into change but you want to carry with you as few coins as possible. Assuming that coins of all denominations are available, how many coins (denominations) would you split the 63p into?

(a) 33 (b) 63 (c) 6 (d) 64

Solution:This problem split the coins in denomination of 2n. n be the no of coins.n=5, 20 + 21 +22 +23 +24 +25 =63

16. For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumoured that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of winning. Let's assume such rumours to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana- Bolivia game?

(a) 5/9 (b) 1/9 (c) 2/3 (d) 1/3

Solution:

Condition:If Paul picks A with some probability as A’s chance of winning.

If they having chance of losing is 1/3, Pauls predictions to be same.From the Qn, Ghana team is 2/3 strong. Probability of predicting the winning team = {(2/3)*(2/3)} + {(1/3)*(1/3)} = 5/9

17. 36 people {a1, a2, ..., a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is

(a) 18 (b) 13 (c) 34 (d) None

Solution:Condition:

Hands must be shaking in circular fashion.Have to form a small group; they must shake their hands at least with one person

in the rest.

Take the middle person from three members. Out of 36, you can able to form a small set of people is 12.

18. One the Planet, Oz, there are 8 days in a week – Sunday to Saturday and another day called Oz day. There are 36 hours in a day and each hour has 90 min

while each minute has 60 sec. As on earth, hour hand covers the dial twice every day. Find the approximate angle between the hands of clock on Oz when time is 12.40 am

(a) 89 (b) 251 (c) 111 (d) 79

Solution:Angle covered by hour hand in 1 hour = 360/18 = 20 degree.In one min 20/90=2/9 degreeAngle covered by minute hand in one min=360/90=4 degRelative deg difference=4-2/9=34/9 Now -240+34/9*40=88.88 degree.

19. The IT giant Tirnop has recently crossed a head count of 150000 and earning of $7 billion. As one of the forerunners in the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers are equal in every respect. They receive identical salaries ans also write code at the same rate Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How many lines of code can be written by 72 programmers in 72 minutes?

(a) 6 (b) 432 (c) 72 (d) 12

Solution:12 lines of code are written in 12 * 12 = 144 programmer minutes1 line of code is written in 144/12 = 12 programmer minutesWe now have 72 * 72 programmer minutes Lines of code that can be Written = 72 * 72 /12 = 432

20. 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 pained totally how many faces of the smaller cubes remain unpainted?

(a) 900 (b) 488 (c) 500 (d) 800

Solution:Formula for hollow cube=n3 –(n-2)3

Each 1*1 cube has 6 faces Total 1*1 cubes =53- (5-2) 3 = 98 Total faces of small cubes = 98*6 = 588 Now, four sides of the 5*5 cube is paintedSo, total small cube faces painted = 4*5*5 = 100 answer = 588-100 = 488

21. Planet fourfi resides in 4 – dimensional space and thus the currency used by its residents are 3 – dimensional objects. The rupees notes are cubical in shape while their coins are spherical. However the coin minting machinery lays out some stipulations on the size of the coins.

The diameter of the coins should be at least 64mm and not exceed 512mmGiven a coin, the diameter of the next larger coin is at least 50% greater.The diameter of the coin must always be an integer.

You are asked to design a set of coins of different diameters with these requirements and your goal is to design as many coins as possible. How many coins can you design?

(a) 5 (b) 8 (c) 9 (d) 6

Solution:

Given next one should be 50 % moreStart with 1st coin 642)64+32=96........3)96+48=144.4)144+72= 216........5)216+108=324........6)324+162=486.....7)486+243 is greater than 512 so we stopped here. Ans is 6

22. A hare and tortoise a race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after tortoise has covered 1/5 its distance and that leisurely. The hare and tortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so as to tie the race?

(a)8 (b) 37.80 (c) 40 (d) 5

Solution:

After tortoise covers 1/5th distance hare starts the race.

When hare covers 1/8th of distance tortoise meets hareSo distance covered by tortoise = 1-(1/5 + 1/8)= 27/40Time taken by both is same ,time = dist/speedSo (dist/ speed) of tortoise = (dist / speed) of hareLet speed of tortoise be t and of hare be h27/40t = 1/8hh = (40/(8*27) )* t = 5/27 * t  

Now for the next part hare has to cover 7/8 th distance when tortoise covers 1/8 th distanceso we get 1/8t = 7/8h h = 7tso the factor by which h's speed increases =  7t/ (5/27 * t)which we get as 37.8 

23. Anoop managed to draw 7 circles of equal radii with their centres on the diagonal of a square such that the two extreme circles touch two sides of the square and each middle circle touches two circles on either side. Find the ratio of the radius of the circles to the side of the square.

(a) 1:(2 + 7 √2) (b) 1:(4 + 7 √3) (c) (2 + 7√ 2):1 (d) 1:(2 + 6√ 2)

Solution:The extreme circles will have radius perpendicular to sides...so the part of diagonal till the centre of circle will be sqrt (2) r.

[Make diagram and it will be clear].now remaining portion is r , 5 more circles will contribute 10r and last circle will contribute sqrt(2)r + r.

Total: 12r + 2sqrt (2) r = sqrt (2) side

so ratio of radius to side = 1 :( 2+6sqrt (2))

24. Ferrari S.p.A. is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsored drivers and manufactured race cars before moving into production of streetlegal vehicles in1947 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 bought a Ferrari. It could go 2 times as fast as Mohit’s old Mercedes. If the speed of Mohit’s Mercedes is 32 km/hr and the distance travelled by the Ferrari is 952 km, find the total time taken in hours for Rohit to drive that distance.

(a) 15.88 (b) 29.75 (c) 14.88 (d)476

Solution:Rohit : Ferrari , Mohit : MercedesLet speed of car be x km/h Let speed of car be y km/hAccording to the question, x=2yWe know that y=32 km/h.x=2X32 ==>64 km/h.Total time taken in hours for Rohit to drive that distance:Distance travelled/speed = 952/64=14.875 hours.

25. There are two boxes, one containing 10 red balls and the other containing 10 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 is maximized. This maximum probability is

37/38 (b) 1 / 2 (c) 14/19 (d) 3 / 4

Solution:Take one red ball in 1st bag.Put the remaining nine red ball with 10 green ball in other bagProbability of red ball in 1st bag=1/2Probability of red in other bag= (1/2)*(9/19)

The required probability=p(A)+p(B) =1/2+9/38 =28/38=14/19.

26 .Pizza shops make pizzas of same thickness but different diameter. Cost of pizza A with diameter 8 cm is 80 $, cost of the pizza B with diameter 12 cm is 240 $, cost of the pizza B with diameter 24 cm is 720 $. Which of the above mentioned pizzas gives the best value for money?

(a) A (b) B (c) C (d) Cannot be determined

Solution:A 8 cm = 80$ - 1 cm=10$B 12 cm = 240$ -1 cm =20$C 24 cm= 720$ -1 cm=30$So cheapest is A .

27. Determine the distance between x-intercept and z-intercept of the plane whose equation is 6x+8y-3z=72.

(a) 31.92 (b)26.83 (c) 32.66 (d) 25.63

Solution:Sqrt of ((d/a)^2+(d/c)^2) d=72 a=6 b=8 c=-3

(d/a)^2=144(d/c)^2=576

Sqrt(144+576)=26.83

28. Lucy finds around 25 groups of stars that appear to her as constellations. She draws 7 patterns of the constellations in her notebook and notes down the number of stars in each of them. She counts 5 stars in first constellation and 15 on next. She counts a number the third time and forgets to note it down. The next four constellations she counts 51.53,159,161. Next day her father looks at the notebook and wants to know the number of stars in the third constellation. Lucy only remembers that number of starts counted in each of the constellation followed a pattern 5,15, x, 51, 53, 159, 161.

(a) 19 (b) 17 (c) 47 (d) 31

Solution:5 x 51 159 ; 15 53 159

15*3+6=5151*3+6=159;5*3+2=1717*3+2=5353*3+2=161;

29. 6 persons standing in the queue for ROBERT movie, are wearing different colour shirts. All of them belong to different age group, after two years their average age will be 43 and seventh person joined with them, hence the current average age has become 45. Find the age of seventh person?

(a) 67 (b) 69 (c) 72 (d) 74

Solution:After 2 yrs, avg age is 43;Before 2 yrs, avg age is 41;

Sum of ages of 6 mem=41*6=246;7th mem is added, the avg =45;Sum of ages of 7 mem=45*7=315;7th mem age =315-246=69;

30. X is 6 years younger to Y. X's father is a businessman who invested 10000/- at 8% rate of interest and obtained his amount after 10 years. Y's father is a job holder who invested around 20000 at 2% rate and obtained his amount after 20 years. Now Compounded both of them get around Rs. ABC .After 5 years the ratio of ages of X and Y is 1:2. Now X's father is 20 years older to Y and Y' father is 30 years more than X. After 20 years again X's mother asks X's father to purchase a LCD TV which costs around 45000/-. What is the age of X and Y together?

(a) 12 (b) 8 (c) 18 (d) 6

Solution:X+6=Y(X+5)/(Y+5) = (1:2)

X-Y=-62X+10=Y-5 2X-Y=-5. Solve above 2 eqn we get ans as x+y=1+7=8

31. The great musician Rahman has organized a live concert. The concert is organized in a big auditorium. Rahman plays both English and Tamil songs on his Yamaha Casio. The audience in the Eastern part of the auditorium love listening to Tamil Songs and those in the western part of the auditorium. He plays songs in random. The probability that he plays English songs for 6 consecutive times is 1 in

(a) 32 (b) 16 (c) 64 (d) 128

Solution:Possible events is English and Tamil=2Favourable is English =1.So prob for playing one eng song is 1/2.For consecutive 6 times is 1/ (26) =1/64.

32. It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same colour?

(a) 3 (b) 25 (c) 48 (d) 26

33. A person was fined for exceeding the speed limit by 10mph. Another person was also fined for exceeding the same speed limit by twice the same. If the second person was traveling at a speed of 35 mph, find the speed limit.

(a) 35mph (b) 15 mph (c) 20 mph (d) 30 mph

Solution:

I st person exceeds the limit is 10mph.2nd person exceeds twice the limit i.e. 20mph2nd persons speed is 35 mph.So the speed limit is (35-20) =15mph.

34. A person drives with constant speed and after some time he sees a milestone with 2 digits. Then travels for 1 hour and sees the same 2 digits in reverse order. 1 hour later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car?

(a) 54 (b) 45 (c) 27 (d) 36

Solution:

Let x = the 1st digit on the first mile stoneLet y = the 2nd digit Let s = speed of the car"Then travels for 1 hour and sees the same 2 digits in reverse order."10x + y + 1s = 10y + x10x - x + s = 10y - y9x + s = 9y 1"1 hours later he sees that the milestone has the same 2 digits with a 0 between them."10y + x + s = 100x + y10y - y + s = 100x - x9y + s = 99x 2Rearrange the above two equations for elimination9x - 9y + s = 0-99x+9y + s = 0 ----------------adding eliminates y-90x + 2s = 02s = 90x s = 45xx has to equal 1, then s = 45 mph (If x=2 and s=90 mph, when added toa two digit milestone, could not be at another two digit milestone.)Find y9x + s = 9y9(1) + 45 = 9y9 + 45 = 9y simplify divide by 9y=6Speed is 45 mph

Answer:1st milestone: 16travel one hr +452nd milestone: 61travel one hr: +453rd milestone: 106

35. With four fifths of then tank full, a vehicle travels 12 miles. How much distance will the vehicle travel with one third tank full?

a)8.05 km (b) 6.05 km (c) 12km (d) 5 km

Solution:

4/5 of full tank travels=12 miles.Full tank travels =15 miles.One-third full tank=15/3=5 miles. 1 miles =1.609km. So 5miles =5*1.609=8.05km.

36) Peter is twice as old as Paul was when Peter was as old as Paul is now. The combined age of Peter and Paul is 42 years. How old is peter now?

(a) 21 (b) 18 (c) 24 (d) 26

37) 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 1/16 filled after 17 hours, what is the total durations required to fill it completely?

(a) 4 hours (b) 21hours (c) 22 hours (d) 24 hours

Solution:Every hour amount of water in tank B gets doubled than previous hour.

If the time increases by an hour, then the amount of water in the tank gets doubled.Initially 1/16 of tank in 17hrs.2*(1/16)=1/8 of tank in 18 hrs.2*(1/8) = 1/4 of tank in 19 hrs2*(1/4) =1/2 of tank in 20 hrs2*(1/2) =1 i.e. of full tank in 21 hrs.

38) Middle-earth is a fictional land inhabited by hobbits, Elves, dwarves and men. The Hobbits and the Elves are peaceful creatures who prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows. A tournoi is one, where out of two teams that play a match, the one that loses get eliminated. The matches are played in different rounds where in every round; half of the teams get eliminated from the tournament. If there are 10rounds played in a knock-out tournoi how many matches were played?

(a)1024 (b) 1023 (c)1026 (d)1011

Solution:No of players = 2^n.No of matches=(2^n)-1

39) Ferrari S. p. A. is an Italian sports car manufacturer based in Maranello. Italy. Founded by Enzo Ferrari in 1928 as Scuderia 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 continued participations in racing, especially in Formula One, where it has enjoyed great success Rohit once bought a Ferraris. It could go 4 times as fast Mohit’s old Mercedes. If the speed of Mohit’s Mercedes is 35 km/hr and the distance travelledby the Ferrari is 968km, find the total time taken for Rohit to drive that distance.

(a) 242 hours (b) 27 hours (c) 7 hours (d) 6.91 hours

Solution:

Rohit: Ferrari, Mohit: MercedesLet speed of Ferrari car be x km/h Let speed of car Mercedes be y km/hAccording to the question, x=4yWe know that y=35 km/h.x=4X35 ==>140km/h.Total time taken in hours for Rohit to drive that distance:

Distance travelled/speed = 968/140=6.914hours.

40) Two blocks of copper with density of 100 kg/m^3 are twisted into wires of length 100 km and thickness 0.1mm. Copper is a very ductile material. Its ductility is measured in terms of percentage elongation upon application of tensile forces. The conductivity of the copper wire is extremely high rendering it useful in the construction of many electronic circuits. If the voltage through one such circuit is 18 V and the current flowing in the circuit is 190 ma. What is the resistance of the wire?

(a) 208.00 K Ohms (b) 3420.00 K Ohms (c) 0.09 k Ohms (d) 10.56 K Ohms

Solution: Ohms law, V=IR.V= 18,I=190mA.

R=0.09kohms.

41) 5 men and 5 women meet and men dance with women. Which of the following are always true? A. there are 2 men who have danced with same number of women. B. There are 2 women who have danced with same number of men.

(a) Both A and B (b) A only (c) B only (d) Neither A nor B

Solution:

It’s just logical.

42) Three boys John, Tom and Oliver and two girls Rachel and Kim are to be seated in a row. Rachel always sits to the left of John. No girl sits at the extreme positions and at the middle positions. Tom always sits at the extreme positions. Who sits to the right of Kim?

(a) Oliver (b) Tom (c) Tom or Oliver (d) John

Solution:Given, girls won’t sit in extreme and middle. So 2girls in 2 and 4 position only .Rachel sits left of john. So john is in middle. Right of Kim is extreme position. So tom or Oliver is answer.

43) The thank giving banquet at No.2, Ritcher Street, had 49 guests which consisted of 6 statesmen, 26 relatives and their families. At the end of a banquet 19 people shake hands with other , some of which were between the statesmen alone, some between relatives alone and some between the statesmen and relatives. How many handshakes will there be in total?

(a) 342 (b) 171 (c) 180 (d) 162

Solution:nCr.

n=19, r=2 ==171.

44) There are 7 children. You are told that the youngest child is a boy. The probability that all of them are boys is 1 in

(a) 64 (b) 21 (c) 2 (d) 128

Solution:Possible events is boy and girl=2Favourable is boy =1.So prob for getting one boy is 1/2.For consecutive 6 times is 1/ (26) =64.

45) Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e. the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The minimum value of n1(P) over all configurations P of 5 points in the plane in general position (.i.e. no three points in P lie on a line) is

(a) 3 (b) 5 (c) 2 (d)7

Solution:Consider plane is like triangle. Separating one point and rest by a line.Minimum lines required will be 3 .

46) Given a collection of points P in the plane, a 1-set is a point in P that can be separated from the rest by a line, .i.e. the point lies on one side of the line while the others lie on the other side. The number of 1-sets of P is denoted by n1(P). The maximum value of n1(P) over all configurations P of 5 points in the plane in general position (.i.e. no three points in P lie on a line) is

(a) 3 (b) 5 (c) 2 (d)7

Solution:Maximum value will be 5 it will occur when all points are aligned in a circle

47) There is a pie to be divided among 20 people. A man eats3 pizza, a women eats two pieces and a child eats half a piece of pie. Find the number of men, women and children so that they are 20 people in total and everyone gets some pie. There are 20 pieces of pie in all.

(a) 7 women, 1 men and 12 children (b) 5 women, 1 men and 14 children (c) 6women, 2 men and 12 children (d) 4women, 2 men and 14 children

Solution:Backtracking from the answer.a) 7w*2=14 1m*3=3 12*1/2 =6, total=23people.b) 5w*2=10 1m*3=3 14*1/2=7, total=20 people.

48)A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21 . What is the remainder left, when twice the number is divided by 3D?

(a) 13 (b) 42 (c) 3 (d) cannot be determined

Solution:Number=Divisor * Quotient + Remainder.N=D*Q+8N=3D*Q1+21D=13/ (Q-3Q1)Q-3Q1! =0.Take Q=4, Q1=1,D=13.Substitute in above eqn, get N=60.2N/3D=? Remainder is 3.

49)In a pizza restaurant, you get a basic pizza with two toppings, cheese and tomato. You can also make up your own pizza with extra toppings. You can also choose from 10 different toppings, e.g. olives, ham, mushroom, salami etc. Ross wants to order a pizza with 2 different extra toppings. How many different combinations are possible?

(a) 100 (b) 1024 (c) 90 (d) 45

Solution:Its a combination problem. nCr,n=10,r=2. Answer is 45

50) The Thousand Pillar Temple of Hyderabad was built by the Kakatiyans of Chalukyan dynasty in the 12th century. Each pillar has carvings made of block monolithic rocks of basalt which are polished to give it a brilliant look. One sunny morning, three tourists visit the temple. Samantha is taller than Lily and taller than two of the thousand pillars and Kelly is shorter than Samantha and the pillars. Which of the following statements would be more accurate?

(a) Its impossible to tell (b) Kelly is as tall as Lily(c) Lily is shorter than Kelly (d) Lily is taller than Kelly

Solution: Given statements are not sufficient to answer. So answer is a.

51) Franchois Pachet, a researcher at Sony Computer Science Laboratories is also a jazz musician. He decided to build a robot able to improvise like a pro. Named Continuator, the robot duet can with alive musician in real- time. It listens to a musical phrase and then computes a complementary phrase with the same playing style. If the cost of making the robot is divided between materials, labour and overheads is the ratio of 4:5:2. If the materials cost $ 84.0, the cost of the robot is

(a) 184.80 $ (b) 189.00 $ (c) 231.00 $ (d) 462.00 $

Solution:Given:Material cost is 84$. In ratio material is 4x. So x=21.Total sum of ratio is 11x.Total cost =11*21=231$

52) The great Indian mathematician Bhaskaracharya formulated this problem in the twelfth century for his teenaged prime number aged daughter Lilavati. He also authored the eponymous Lilavati, a compendium of mathematical puzzles, in which the number of problems that use this formula is the sum of two prime numbers. The product of the two prime numbers is smaller than the total number of problems in the Lilavati. Now, if the difference of any two numbers is 4 and their product is 18, what is the sum of their squares?

(a) 34 (b) 40 (c) 52 (d) 42

Solution:Formula :(a-b)2=(a2+b2-2ab)

Given a-b=4 ab=18, substitute in above eqn , get answer as 52

53) A taxi driver commenced his journey from a point, and drove 10 km towards north, and turned to his left and drove another 20 km. After waiting to meet a friend here he turned to his right and continued to drive another 50 km. In which direction is he now?

(a) North (b) South (c) West (d) East

Solution:

Starting towards north.Ending also in north only.

54) A result of global warming is that the ice of some glaciers is melting. Twelve years after the ice disappears tiny plants, called lichens, start to grow on the rocks. Each lichens 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 = 13 * (t-11) for t > 11 where d represents the diameter of the lichen in millimetres, and t represents the number of years after the ice disappeared. Using the above formula, calculate the diameter of the lichen, 36 years after the ice has disappeared.

(a) 468 mm (b) 457 mm (c) 325 mm (d) 11 mm

Solution:

Given t=36 years, we need to find d using the formula in question.

55) The British mathematician Lewis Caroll also loved to make up fantastic stories in which he embedded a number of clever puzzles and curious riddles. For example, his popular story, Alice in Wonderland, is about young girl called Alice who dreams of a strange world where she meets several unusual characters including the Red Queen and the March hare. In our story, after 2 years of time, Paul will be twice as old as Alice. Presently he is 6 times as old. How old is Paul now?

(a) 2 (b) 4 (c) 3 (d) 6

Solution: Let present age of Paul be P and Alice be A.From qn :

A=P/6;P- 2A=2;

Sub A value, we get P=3.

56) A long, thin strip of width 10cm is kept on a flat surface. Another identical strip is kept on it as an overlapping manner such that the combined width of the two is 15cm.What is the width if 22 such strips kept like this?

(a) 115 cm (b) 110 cm (c) 200 cm (d) 95 cm

Solution:Let X be the initial width of strip, Y be the width of the newly added strips, Z is the no of strips. (Z-1)*(Y-X)+X.From qn. X=10, Y=15, Z=22.

57) A toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters, at 10 meters per minute. However, the toy train is defective and it now produces only two different tunes at random. What are the odds that the toy train produces3music tunes of the same type (1 in _____ ) ?

(a) 3 (b) 9 (c) 8 (d) 4 58) Fill dirt or fill soil is usually the sub-soil removed from an excavation side and is used to level a place or create artificial mounds. If the average density of sub—soil removed from a site is 3gm/cu cm and it weight 400 kg. How many hemispherical pits each of volume 240 cubic cm, can this sub-soil fill?

(a) 555 (b) 277 (c) 556 (d) 554

Solution:It’s very simple.No of hemispheres =amt of soil in cu.cm/ vol of hemisphere in cu.cm.Amount of soil=400kg=400000gm.Amount of soil in cu.cm=400000/3=133333.33 cu.cmVolume of 1 hemispherical pits=240 cu.cm.No of hemispheres=133333.33/240=555 pits.

59) The New York Public library is on of the world’s greatest repositories of books and journals. It has a beautiful reading room facing Manhattan’s famous Fifth Avenue. In the reading rooms are 10 reading spots. Each reading spot consists of a round table with 4 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 10 readers, how many reading spots are empty?

(a)None (b)6 (c)5 (d)4

Solution:1st spot=1reader2nd spot=2 reader3rd spot=3 reader4th spot=4 reader.10 readers can occupy 4 spots only. So answer is 6

60) A group of friends Tom, Tim, Dick, Diana, Harry, and Harriet go out to a fair three hundred meters from the Mc.Donalds which is five KMs away. They see a weighing machine and decide to have some fun. However the girls refuse to step on the weighting machine. So Tom,Dick and harry, weigh themselves in a particular order. First Tom, Dick, and Harry weigh themselves individually and then tom and Dick, Dick and Harry, Tom and Harry and then Tom, Dick and harry together respectively. The recorded weight for the last measure is 158 kgs. The average of all the 7 measures is

(a) 112.86 (b)52.67 (c)90.29 (d)67.71

Solution:1st Tom 2nd dick 3rd harry4th tom + dick5th dick + harry6th tom + harry7th tom + dick + harry.Average of 7 measures=4(T+D+H)/7=4*158/7=90.29

61) In the year 2002, Britain was reported to have had 4.3m closed-circuit televisions (CCTV) cameras–one for every 14 people in the country. This scrutiny is supposed to deter and detect crime. In one criminal case, the police interrogates two suspects. The ratio between the ages of the suspects is 6:5 and the sum of their ages is 66 years. After how many years will the ratio be 8:7?

(a) 11 years (b) 12 years (c) 6 years (d) 7 years

Solution:A/6 =B/5=x;A=6x;B=5x;A+B=66; == x=6;A=36, B=30;After X years ,((A+X)/(B+X))=(8/7)Solve the above eqn, we get X=12.

62. A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At least n of the statements on this sheet are true." Which statements are true and which are false?

a) All statements are falseb) The odd numbered statements are true the even numbered are falsec) All statements are trued) The even numbered statements are true and the odd numbered are false

Solution: its just logical.

63. 10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects 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 suspects are lying or the leftmost suspect is innocent.(B) All suspects are lying and the leftmost suspect is innocent.

(a) A only(b) B only (c) Both A and B(d) Neither A nor B

64. The pace length P is the distance between the rear of two consecutive footprints. For men, the formula, n/P = 144 gives an approximate relationship between n and P where, n = number of steps per minute and P = pace length in meters. Bernard knows his pace length is 164cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed kmph.

(a) 236.16 (b) 11.39 (c) 8.78 (d) 23.62

Solution:P be the pace length in metres, N be the no steps per minute.N/1.64 = 144N = (144 * 1.64) = 236.16

No. of steps per minute = 236.16Distance per minute = N*P= (236.16 * 164) cmDistance per minute = 0.3873024 km Distance per hour = 23.238144

Speed = 23.238144 km/h

65. Alice and Bob play the following coins-on-a-stack game. 20 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 of moving the coin on the top to a position i below the top coin (0 ≤ i ≤ 20). 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 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

(a) In order to win, Alice’s first move should be a 0-move.(b) In order to win, Alice’s first move should be a 1-move.(c) Alice has no winning strategy.(d) In order to win, Alice’s first move can be a 0-move or a 1-move

Solution: I don’t know explanation. All the staff saying this one is correct.

66) Paul the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous accuracy has now been invited to predict ICC world cup matches in2011. We will assume that the world cup contenders have been divided into 2 groups of 9 teams each. Each team in a group plays the other teams in the group. The top two teams from each group enter the semi finals (after which the winner is decided by knockout). However, Paul has a soft spot for India and when

India plays any team, Paul always backs India. Alas, his predictions on matches involving India are right only 2 out of 3 times. In order to qualify for the semi finals, it is sufficient for India to win 7 of its group matches. What is the probability that India will win the ICC world cup?

(a) (2/3)^10 (b) (2/3)^9 + 8/3 * (2/3)^9

(c) 8/3 * (2/3)^9 (d) (2/3)^10 + 8/3*(2/3)^9

Solution: (2/3)^10 + 8/3*(2/3)^9

67) A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At least n of the statements on this sheet are true." Which statements are true and which are false?

a) The first 26 statements are false and the rest are true.b) The odd numbered statements are true the even numbered are falsec) The first 13 statements are true and the rest are false.d) The even numbered statements are true and the odd numbered are false

Solution: none of the above.

68) There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter 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 liters, second hour it has 20, and so on). If tank B is 1/32 filled after 11 hours, what is the total durations required to fill it completely?(a)5 Hours (b) 15 Hours (c) 17 Hours (d)16 Hours

Solution:Every hour amount of water in tank B gets doubled than previous hour.

If the time increases by an hour, then the amount of water in the tank gets doubled.Initialiy 1/16 of tank in 11hrs.2*(1/16)=1/8 of tank in 12 hrs.2*(1/8) = 1/4 of tank in 13 hrs2*(1/4) =1/2 of tank in 14 hrs2*(1/2) =1 i.e. of full tank in 15 hrs.

69) A sheet of paper has statements numbered from 1 to 10. For all values of n from 1 to 10, statement n says At most n of the statement on this sheet is false. Which statements are true and which is false?(a) All the statements are FALSE(b) The odd numbered statements are true and the even numbered are false.(c) The first half statements are true and the rest are false.(d) The even numbered statements are true and the odd numbered are false.

70) A schoolyard contains only bicycles and 4 wheeled wagons. On Tuesday, the total number of wheels in the schoolyard was 90. What could be possible number of bicycles?

(a)12 (b) 14 (c) 10 (d)11

Solution:

Total no wheels =90. To find total no of bicycles.Get the answer from solution.A) 12*2=24wheels (90-24) =66B) 14*2=28 wheels (90-28) =62C) 10*2=20 wheels (90-20) =70D) 11*2=22 wheels (90-22) =68. From the above which one is divided by 4 is the correct answer. I.e. 68/4=17 four wheeler and 11 bicycles.

71.Six friends decide to share a big cake. Since all of them like the cake, they begin quarreling as to who gets to first cut and has a piece of the cake. One friend suggests that they blindfold a friend and then choose from a well shuffled set of cards numbered from one to six. You check and find that this method works as it should be simulating a fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfolding and throwing a die. You note that the number shown by the method of picking up a card and throwing a real world die, sums up to a number between 2 and 12. Which total would be likely to appear more often – 8, 9 or 10?

(a) 8 (b) 9 (c) 10 (d) All are equally likely.

Solution:Combination of 8 is 2+6,3+5,4+4,5+3,6+2.Combination of 9 is 3+6,4+5,5+4,6+3.Combination of 10 is 4+6,5+5,6+4.

72. Consider two tumblers, the first containing one litre of coffee. Suppose you take one spoon of water out of the first tumbler and pour it into the second tumbler and after which you take one spoon of the mixture from the second tumbler and pour it back into the first tumbler. Which one of the following statements holds true?

(a) There is less coffee in the first tumbler than water in the second tumbler.

(b) There is more coffee in the first tumbler than water in the second tumbler (c) There is as much coffee in the first tumbler as there is water in the

second tumbler (d) None of the statements holds true.

Solution: Think logically.

73.A lady has fine gloves and hats of different colours in her closet- 18 blue, 32 red and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes an item out of the closet only if she is sure that it is a glove. How many gloves must she take out to make sure that she has a pair of each colour?

(a) 6 (b) 8 (c) 60 (d) 59

Solution: This problem we cant take exactly what we need. So go for worst case i.e. if we take Maximum of different colours. From the given red color is highest. So take the count .Then take the next highest is yellow. Totally we get 32+25= 57, in that surely we can get exactly 2 pair of socks of different color among three color. To get one more pair ,take one pair . so totally she have to take 32+25+2=59.

74.It was the semester exam day, Vidhya caught the college bus. She enjoyed

travelling by bus. Moving at 6 mph, the bus took Vidhya to college at the right time. She finished her exam and had a chit chat with her friends and suddenly she realized that it was 6 pm and she had missed the college bus. She decided to walk back home at 4 mph. What is her average speed for the day?

(a) 4 mph (b) ) 5 mph (c) 2.4 mph (d) 4.8 mph

Solution: Its just to find average speed = (2*6*4)/(6+4)

= 4.8mph

75. Spores of a fungus, called late blight, grow and spread infection rapidly. These pathogens were responsible for the Irish potato famine of the mid-19 century. These seem to have attacked the tomato crops in England this year. The tomato crops have reduced and the price of the crop has risen up. The price has already gone up to $45 a box from $27 a box a month ago. How much more would a vegetable vendor need to pay to buy 27 boxes this month over what he would have paid last month?

(a) $27 (b) $ 18 (c) $45 (d) $ 486

Solution: Vendor paid extra = amount paid this month – amount paid last month.

=27*45 -27*27=486

76.A car manufacturer produces only red and blue models which come out of the final testing area completely at random. What are the odds that 5 consecutive cars of the same color will come through the test area at a time?

(a) 1 in 16 (b) 1 in 125 (c) 1 in 32 (d) 1 in 25

77.Given a collection of 36 points in the plane P and a point “X” equidistant from all points in P, which of the following are necessarily true?

A. The points in P lie on a circle. B. The distance between any pair of points in P is larger than the distance

between X and a point in P (a) A only (b) B only (c) Both A and B (d) Neither A nor B

78.Susan made a block with small cubes of 8 cubic cm volume. To make the block she used 3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?

(a) 114 (b) 135 (c) 21 (d) 71

Solution: Formula for making hollow cube= (3*9*5) - ((3-2) (9-2) (5-2))

=135-21 =114.79.A seamstress buys a certain amount of Gingham cloth which comes in rolls that are exactly 56 inches wide. She has also bought a certain length of Seek sucker cloth and 35 inches wide. The seamstress first focuses on the Gingham roll ad discovers that she has 116 yards of Gingham and she wants to divide the gingham into 116 lengths of 1 yard each. She wants to have twice as many pieces of seek sucker as she does of the Gingham. It takes 4 seconds to cut

each length of Gingham. Working non-stop, how long (in seconds) will it take her to cut all 116 pieces?

(a) 464 (b) 460 (c) 463 (d) 465

Solution:To make 116 pieces, we have to cut 115 times, for each cut it takes 4 secs.For 115 cuts =115*4=460

80.A man goes north 37km,turns left goes 2km,turns right goes 17 km again turns right goes another 2km. Find distance between the starting & the ending point.

(a) 56 (b) 52 (c) 58 (d) 54

Solution:

2

17 2 37+17=54

37

N

81.A research lab in Chennai requires 100 mice and 75 sterilized cages for a certain set of laboratory experiments. To identify the mice, the lab has prepared labels with numbers 1 to 100, by combining tags numbered 0 to 9. The SPCA requires that the tags be made of toxin-free material and that the temperature of the cages be maintained at 27 degree Celsius. Also, not more than 2 mice can be caged together and each cage must be at least 2 sq.ft in area. The 5 experiments to be conducted by lab are to be thoroughly documented and performed only after a round of approval by authorities. The approval procedure takes around 48 hours. How many times is, the tag numbered '4' used by the lab in numbering these mice?

(a) 9 (b) 19 (c) 20 (d) 21

Solution: No of 4 in 10 (1,2,3,....10) is 1*base (10)0

No of 4 in 100 (1,2,3,....100) is 2*base (10)1

82. A triangle is made from a rope. The sides of the triangle are 25 cm, 11 cm and 31 cm. What will be the area of the square made from the same rope?

(a) 280.561 (b) 280.563 (c) 280.564 (d) 280.562

Solution:Area of the Square= ((perimeter of triangle)/4)2

i.e. perimeter of triangle is sum of the sides.

83. Mr. Alex is the father of children Jane, Joe, and Jill. He goes to a nearby park twice a week. He loves his children very much. On a certain day, on his

way to the park he finds fruit vendors selling different fruits. Watermelon is one penny each, dates at 2 for a penny and plums at 3 for a penny. Mr.Alex spent 7 pennies and got the same amount of each type of fruit for each of his three children. What did each child get?

(a) 1 Watermelon, 2 Dates, 1 plum (b) 1 Watermelon, 1 Date, 1 plum (c) 1 Watermelon, 3 Dates, 2 plums (d) 1 Watermelon, 2 Dates, 2 plums

Solution:Get the answer from options.No of items * no of children*cost of item=total cost for the item.A)1watermelon*3 =3*1 =3,2dates*3 =6*(1/2) =3,1plum*3 =3*(1/3) =1. The sum of cost is 7. . It’s matches with Mr.Alex’s cost. So this is correct answer.

84.An athlete decides to run the same distance in 1/4th less time that she usually took. By how much percent will she have to increase her average speed?

(a) 25% (b) 50% (c) 33.33% (d) 20%

Solution:Speed is inversely proportional to time.Let he takes time t at speed s.now new time is 3/4t , so speed will become 4/3sso speed is 1.33s , that is speed increases by 33.3%

85. Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a circle with each coin touching two other coins. Two of the coins are special and the rest are ordinary. Alok starts and the players take turns removing an ordinary coin of their choice from the circle and bringing the other coins closer until they again form a (smaller) circle. The goal is to bring the special coins adjacent to each other and the first player to do so wins the game. Initially the special coins are separated by two ordinary coins O1 and O2. Which of the following is true?

(a) In order to win, Alok should remove O1 on his first turn. (b) In order to win, Alok should remove one of the coins different from O1

and O2 on his first turn (c) In order to win, Alok should remove O2 on his first turn. (d) Alok has no winning strategy.

Solution:There are two special coins separated by two ordinary coin. If Alok removes one out of these two ordinary coin say O1 or O2, Bhanu will remove the other ordinary coin and join both the special coins and win the game. Hence choice (a) is ruled out. Total 99 coins. Reducing the two ordinary coin and the two special coins, the remaining ordinary coins other than O1 and O2 and special coins S1 and S2, is 95 ordinary coins surrounded by special coins. If Alok starts removing one out of these 95ordinary coins and Bhanu will remove the second ordinary coin and this will continue and Alok will remove the 95 th ordinary coin and join the two special coin from out side and win the game.

86. A racehorse starts chasing a wild pony 3 hours after the pony bolts the stable. The pony runs through the entire country of Alb. Texas jumping 3 streams and crossing four 10 meter roads. The racehorse finally catches up with the pony after four hours by the time the sun had set and the moon was up in the sky for 4 hours. If the average speed of the racehorse is 73kmph then average speed of the wild pony is?

(a) 54.75 kmph (b) 42.71 kmph (c) 31.29 kmph (d) 41.71 kmph

Solution:Time taken to catch the pony by horse is 4 hrs. So distance is 73*4.

The average speed of pony is distance/time=(73*4) / (4+3)= 41.71 kmph

87.On planet Korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids called echina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of this circle and the age of echina is given by the formula d= 4*v (t-9) for t = 9 , where d represents the diameter in mm and t, the number of years since the solar blast. Anubhav recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur?

(a) 17 (b) 21.25 (c) 12.25 (d) 12.06

Solution:Given: d=7mm.

To find years:

d = 4 * √ (t - 9), substitute d value.t=21.25.

88.How many 13 digit numbers are possible by using the digits 1, 2, 3, 4, 5 which are divisible by 4 if repetition of digits is allowed?

(a) 4*5 (b) 5 12 (c) 5*12! (d) 5

Solution:

Condition for divisibility by 4 is last 2 digits must be divisible by 4.Among the five numbers (1, 2, 3, 4, 5) have to find the combination which are divisible by 4.The combinations are 12, 24,32,44,52. First eleven digits are 511 and remain two digit is 5 so answer is 511*5

89.In a family there are some boys and girls. All boys told that they are having equal number of brothers and sisters and girls told that they are having twice the number of brothers than sisters. How many boys and girls are present in a family?

(a) 5 boys & 3 girls (b) 7 boys & 2 girls (c) 4 boys & 3 girls (d) 6 boys & 2 girls

Solution:It’s just logical. Go from answer. c) Satisfying the given condition.

90.Mr Behera wants to build a house for his wife. In his dream house there are 5 rooms each having equal area. The length of each room is 4 m, breadth is 5 m

and the height is 2m. For every single unit of area, he requires 17 bricks, how many bricks are required to make the floor of a particular room?

(a) 340 (b) 420 (c) 280 (d) 400

Solution: They asked for floor alone. So we need to find the area for floor. Take length and breadth ,calculate area?L=4m, B=5m, A=20m2. Per unit 17 bricks needed , for 20 = 20*17=340

91. The Mehta’s have decided to launch their perfumes and have narrowed down to five ingredients for the perfume: Lilac, Balsamic, Lemon, Woody and Mimosaic. The customer can order for specific variety of perfume. To make a perfume that is in demand the Mehta’s adhered to the following conditions: Lilac and Balsamic go together. Woody and Mimosaic go together; Woody and Balsamic never go together. Lemon can be added with any material. All of the following combinations are possible to make a perfume except___.

(a) Balsamic and Lilac (c) Mimosaic and Woody (b) Woody and Lemon (d) Mimosaic and Lilac

Solution:Conditions:Perfume combinations: Li+ B, W+M , W+B wont ,L can be added to all.From the given option d) option wont satisfy the given conditions.

92.If ‘a’ and ‘b’ are mixed in 3:5 ratio and b, c are mixed in 8:5 ratio and if the final mixture is 35 litres. Find the amount of b in the mixture.

(a) 15.73 (b) 14.73 (c) 15.24 (d) 14.24

Solution:a/c=a/b *b/c=24/25.a:b:c=24:40:25

Totally (24 + 40 + 25)x=35;The amount of B in the mixture is =40*(x=35/89) =15.73

93. The Chennai corporation has a particular strategy for assigning numbers for buildings. The Corporation had strict rules that every building should have a number. In T Nagar, a place in Chennai there many buildings were under residential category. For buildings, the Corporation numbered from 1 to 100. For shops, corporation numbered between 150 and 200 only in prime numbers. How many times does the number “6” appear in the building numbers?

(a) 20 (b) 19 (c) 10 (d) 13

Solution: No of 6 in 10 (1,2,3,....10) is 1*base (10)0

No of 6 in 100 (1,2,3,...100) is 2*base(10)1

No of 6 in 1000(1,2,3,...1000) is 3*base(10)2 and so on...

The value of 1*(10) is 10.

94.A Person buys a horse for 15 pounds, after one year he sells it for 20 pounds. After one year, again he buys the same horse at 30 pounds and sells it for 40 pounds. What is the profit for that person?

(a) 20 pounds (b) 15 pounds (c) 25 pounds (d) 10 pounds

Solution:Simple calculation.First time he gets 5 pounds.Next time he gets 10 pounds. Totally he got 15 pounds as profit.

95.A scientist was researching on animal behaviour in his lab. He was very interested in analyzing the behaviour of bear. For some reason he travelled 1 mile in the north direction & reached the North Pole. There he saw a bear and then followed the bear around 1 hr with a speed of 2km/hr in east direction. After that he travelled in south direction & reached at his lab in 2 hrs. Then what colour is the bear?

(a) White (b) black (c) brown (d) grey

Solution:It’s just logical. Going north = white; south =black.

96. Three boys Bob, Pete and Oliver and two girls Samantha and Kristie are to be seated in a row. Samantha always sits to the left of Bob. No girl sits at the extreme positions and at the middle positions. Peter always sits at the extreme positions. Who sits to the right of Kristie?(a)Peter or Oliver (b) Bob (c) Peter (d)Oliver

Solution:Given, girls won’t sit in extreme and middle. So 2girls in 2 and 4 position only.Samantha sits left of Bob. So Bob is in middle. Right of Kristie is extreme position. So Peter or Oliver is answer.

97.If x/2y =2a, then 2x/x-2ay=? (a) 4 (b) ay (c) 2 (d) 2a

Solution:From given x=4ay. Sub x value in (2x/x-2ay) =4

98.A man looks at a painting and tells “Neither have I any brother nor any sister, but the person in the painting is my father’s son”. Then who is in the painting?

(a) Father (b) Daughter (c) Son (d) Himself

Solution: Its just logical. Himself is answer.

99.Inspired by Fibonacci series, Sanket decided to create his own series which is 1,2,3,7,7,22,15,67,..... What number comes immediately before 63?

(a) 31 (b) 61 (c) 57 (d) 202

Solution:Split as 1, 3, 7, 15, --, 63

2, 7, 22, 67.Take the first one the difference between no is formed as multiples of 2. 2, 4, 8, 16, 32.

100) Determine the distance between the x-intercept and the z-intercept of the plane whose equation is 2x+9y-3z=18(a) 6.32 (b)10.82 (c)3.00 (d)5.00

Solution:Sqrt of ((d/a)^2+(d/c)^2) d=18 a=2 b=9 c=-3

(d/a)^2=81(d/c)^2=36

Sqrt(81+36)=10.82

101.A game is played between 2 players and one player is declared as winner. All the winners from first round, played in the second round. All the winners from second round played in third round and so on. If 8 rounds were played to declare only one player as winner, how many players played in first round?

(a) 256 (b) 128 (c) 255 (d) 127

Solution:

No of players= 2^8

102.1/3 rd of a number is more 3 than the 1/6 of the same number, then find the number?

(a) 24 (b) 12 (c) 18 (d) 20

Solution:Let X is the number.(1/3) X-(1/6) X=3,Solving these we can get the answer.

103.It is the class with the seating arrangement in 4 rows and 8 columns. When the teacher says 'start' the girl who is sitting in first row and first column will say 1, then the next girl sitting behind her will say 4, the next girl sitting behind that girl will say 7, in a particular order each girl is telling a number, the following girls told 10, 13 next turn is yours what you will say?

(a) 14 (b) 16 (c) 20 (d) 17

104.If Valentine’s day of 2005 was celebrated on a Monday. What day is Feb 14 ,2010 ?

(a) Monday (b) Sunday (c) Tuesday (d) Wednesday

Solution: In leap year 2 odd daysOrdinary year 1 odd days.From 2005 to 2010, there is one leap year and 4 ordinary year. So totally 6 odd days.So answer is Sunday.

105.If a pipe can fill the tank in 6 hrs but unfortunately there was a leak in the tank due to which it took 30 more minutes .Now if the tank was full how much time will it take to get emptied through the leak?

(a) 39 hrs (b) 78 hrs (c) 72 hrs (d) 70 hrs

Solution:Work done by the leak in 1 hour = [(1/6)-(2/13)]

= 1/78 hrs.

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