Test 6

1.    One day Alice meets Pal and Byte in fairyland. She knows that Pal  lies on Mondays, Tuesdays and Wednesdays and tells the truth on the other days of the week and 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 Alice – Pal “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) Thursday   b) Tuesday   c) Monday d) Sunday

2.    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 * sqrt (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 time of some echina at a particular spot is 24 years then what is diameter?
a) 8 b) 16 c) 25 d) 21

3.    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 center of the circle than the periphery?
a) 0.75    b) 1    c) 0.5    d) 0.25

4.    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 winning. 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 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?
a)1/9    b)4/9    c)5/9    d)2/3

5.    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 coins the third coin from the top. Then
a) In order to win, Alice's first move should be a 1-move.
b) In order to win, Alice's first move should be a 0-move.
c) In order to win, Alice's first move can be a 0-move or a 1-move.
d) Alice has no winning strategy.

6.    Here 10 programmers, type 10 lines with in 10 minutes then to type 60 lines in 60 minutes. how many programmers are needed?
a) 16 b) 6 c) 10 d) 60

7.     We all know that Aryabhatta is the greatest mathematics belongs to India. When his Daughter Mayabati was in her teen age he discovered a problem. At that time the age of Mayabati is a prime number, let that age is a. After some years her age becomes b. Then AryaBhatta was able to solve that problem with the help of her daughter Mayabati.  If a-b=5 and product of a and b is 26 then what is the sum of two squares?

a)      77 b) 45 c)89 d)67

8.    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 each color?

     a) 2

     b) 3

     c) 26

     d) 25

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

     a) his son

     b) his father

     c) he himself

     d) his brother

10. Entry ticket to an exhibition ranges from 1p to 7p. You need to provide exact change at the counter. You have 7p coin. In how many parts will u divide 7p so that u will provide the exact change required and carry as less coins as possible?

      a) 8 b) 7 c) 5 d) 3

11. 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)3  c)4  d)0

12. There are 11 boys in a family. Youngest child is a boy. What is the probability of all the remaining children are boys? a) 1/2 b) 1/2! C) 1/2048 d) 1/1024

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

(a)First half of the statements are true and the rest are false

(b) The odd numbered statements are true the even numbered are false

(c) First half of the statements are false and the rest are true

(d) The even numbered statements are true and the odd numbered are false

14. The citizens of planet nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street in nigiet contains 1000 (in base 6) buildings numbered 1 to 1000.

How many 3s are used in numbering these buildings?

(a)    108 (b) 192 (c) 54 (d) 102

15. Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a circle with each coin touching two other coin. 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.

16. 66 people {a1, a2, ..., a66} meet and shake hands in a circular fashion. In other words, there are totally 66 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a65, a66}, {a66, 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)22 (b)33 (c)65 (d) 11

17. After the typist writes 25 letters and addresses 25 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope? (a) 23/25 (b) 0 (c) 2/25 (d) 1

18. You have a jar containing water absorbing marbles which will take 21 hours to set completely when fixed with white cement. There are 50 red marbles, 52 blue marbles and 63 black marbles. The jar is kept inside a dark room. What is the minimum number of marbles that you need to pick to make sure that you have a pair of marbles in each color?

(a)    117 (b) 98 (c) 120 (d) 114

19. 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 7 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)5000 (b) 15625 (c) 2500 (d) 3179

20. Middle- earth is a fictional land inhabited by hobbits, elves, dwarves and men. The hobbits and elves are peaceful creatures that prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows. A tournament is one where out of the 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 9 rounds played in knock out tournament, how many matches were played?

(a)    511 (b) 512 (c) 256 (d) 255

21. 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 and also write code at the same rate Suppose 12 such programmers take 12 minutes to write 12 lines of code in total. How many programmers will complete 96 lines in 96 minutes?(a)12 (b)96 (c)1152 (d)32

22. 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 10 points in the plane is (a)5 (b)10 (c)3 (d)9

23. 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 ball is maximized. This maximum probability is
a)1/2    b)14/19     c)37/38 d)3/4 

24. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely3. A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the Hare in the other. 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) 37.80  b)8  c) 40  d) 5

25. There are 45 cans out of them one is poisoned. If a person tastes very little of this he will die within 14 hours so they decided to test it with mice. Given that a mouse dies in 24 hours and you have 24 hours in all to find out the poisoned can, how many mice are required to find the poisoned can?

(a)    44 (b) 6 (c) 5 (d) 15

26. It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 26 red and 24 blue, 34 brown socks. How many socks do I have to take from the drawer to get atleast two socks of the each color?

(a)    6 (b) 74 (c) 61 (d) 62

27. One train travels 200km from A to B with 70kmph and returns to A with 80kmph. Find the average speed of the train.

a)      75kmph

b)      74.99kmph

c)       74.67kmph

d)      74.33kmph

28. 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) 0 b) 27 c) 18 d) 20

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

a)      4 boys and 3 girls

b)      3 boys and 4 girls

c)       2 boys and 4 girls

d)      2 boys and 5 girls

30. 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) 280.5625 b) 240.5625 c) 280.125 d) 240

31. A person has to make 146 pieces of a long bar. He takes 4 seconds to cut a piece. What is the total time taken by him in seconds to make 146 pieces?
a) 584 b) 580 c) 730 d) 725

32. A horse chases a pony 2 hours after the pony runs. Horse takes 3 hours to reach the pony. If the average speed of the horse is 81Kmph.Then what is the average speed of the pony?
a) 46.4 b) 51 c) 53.4 d) 48.6

33. Consider two tumblers, the first containing Water and next contains coffee. Suppose you take one spoon of water out of the first tumbler and pour it into the second tumbler. After moving you take one spoon of the mixture from the second tumbler and pour it back into the first tumbler. Which one of the following statement holds now?

a) There is less coffee in the first tumbler than water in the second tumbler
b) There is more coffee in the firs 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

34. Six friends decide to share a big cake. Since all of them like the cake, they begin quarreling who gets to first cut and have a piece of the cake. One friend suggests that they have a blindfold friend choose from well shuffled set of cards numbered one to six. You check and find that this method works as it should simulating a fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfold 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 to a number between 2 and 12. Which total would be likely to appear more often
a) 8 b) All are equally likely c) 7 d) 10

35. In a market 4 men are standing .The average age of the four before 2 years is 55, after some days one man is added and his age is 45. What is the average age of all?
a) 55 b) 54.5 c) 54.6 d) 54.7

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