Sunday, August 14, 2011

New Patterns

mec placement


NEW PATTERNS

  1. 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?
    0.75                 1                      0.5                   0.25

  1. 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?
    4/9                   2/3                   1/9                   5/9



  1. 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
    12                    13                    18                    11



  1. 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 coinis the third coin from the top. Then
    In order to win, Alice’s first move should be a 0-move.
    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-move or a 1-move.




  1. 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 starts after the tortoise has covered 1/5 of its distance and that too 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?
    40                    37.80               8                      5




  1. 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



  1. 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
    27                    18                    20                    0.0

  1. Alok and Bhanu play the following min-max game. Given the expression
    N = 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
    2                      4                      9                      -18

  1. Alok and Bhanu play the following min-max game. Given the expression
    N = 38 + 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
38                    119

  1. 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 only             Neither A nor B                      Both A and B             B only


  1. A sheet of paper has statements numbered from 1 to 40. For all values of n from 1 to 40, 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 39th statement is true and the rest are false.
The odd numbered statements are true and the even numbered statements are false.
All the statements are false.


  1. A sheet of paper has statements numbered from 1 to 45. For all values of n from 1 to 45, statement n says “At most n of the statements on this sheet are false”. Which statements are true and which are false?
The odd numbered statements are true and the even numbered are false.
The even numbered statements are true and the odd numbered are false.
All statements are false.



  1. Alice and Bob play the following chip-off-the-table game. Given a pile of 58 chips, Alice first picks at least one chip but not all the chips. In subsequent turns, a player picks at least one chip but no more than the number picked on the previous turn by the opponent. The player to pick the last chip wins. Which of the following is true?
In order to win, Alice should pick 14 chips on her first turn.
In order to win, Alice should pick two chips on her first turn.
In order to win, Alice should pick one chip on her first turn.




  1. A person drives with constant speed and after some time he sees a milestone with 2 digits. Then travels for 1 hours and sees the same 2 digits in reverse order. 1 hours later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car?
54.00 mph                   45.00 mph                  27.00 mph                   36.00 mph


  1. Fermat’s Last Theorem is a statement in number theory which states that it is impossible to separate any power higher than the second into two like powers, or, more precisely- If an integer n is greater than 2, then the equation a^n b^n = c^n has no solutions in non-zero integers a, b, and c. Now, if the difference of any two numbers is 9 and their product is 17, what is the sum of their squares?
43                    45                    98                    115

  1. Alchemy is an occult tradition that arose in the ancient Persian empire. Zosimos of Panopolis was an early alchemist. Zara, reads about Zosimos and decides to try some experiments. One day, she collects two buckets, the first containing one litre of ink and the second containing one litre of cola. Suppose she takes one cup of ink out of the first bucket and pours it into the second bucket. After mixing she takes one cup of the mixture from the second bucket and pours it back into the first bucket. Which one of the following statements holds now?
There is more cola in the first bucket than ink in the second bucket.
None of the statements holds true.
There is as much cola in the first bucket as there is ink in the second bucket.
There is less cola in the first bucket than ink in the second bucket.


  1. 30 teams enter a hockey tournament. A team is out of the tournament if it loses 2 games. What is the maximum number of games to be played to decide one winner?
60                    59                    61                    30






  1. A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 4 red face and 2 blue faces. How many red and blue faces should the other die have if the both players have the same chances of winning?
3 red and 3 blue faces                                     2 red and remaining blue
6 red and 0 blue                                              4 red and remaining blue

  1. . A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 3 red faces and 3 blue faces. How many red and blue faces should the other die have if the both players have the same chances of winning?
5 red and 1 blue faces                                     1 red and 5 blue faces
3 red and 3 blue faces                                               Any of the solutions given

  1. There are two containers A and B. A is half filled with wine whereas B which is 3 times the size of A contains one quarter portion wine. If both containers are filled with water and the contents are poured into container C, what portion of container C is wine?
.30                   .31                   .42                   .25

  1. There are two statements. There is also a question. Choose 1 if the question can be answered by using either one. Choose 2 if the question can be answered using both the statements. Choose 3 if the question can not be answered using these two statements

Statement 1:  Avinash spends 30% on house rent, 20% on children’s education,40% on foods
Statement 2: Pritam spends 20% on house rent, 45% on children’s education,20% on food

Question: If pritam spends more than avinash on foods who spends more on children’s education? The question can be answered by
a)  1   b) 2   c)3                                        

Ans: c


  1. Alok and Bhanu play the following min-max game. Given the expression            
1.    N = 15 + X*(Y – Z)

  1. 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
Ans: 15+18 =33

( questions of the same type  with different equations for N  )





  1. In planet OZ planet there are 8 days, sunday to saturday and 8th day is Oz day. There is 36 hours in a day. What is angle between 12.40?
27. 
 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 hours 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 15.40 am?
28.  On the planet Oz, there are 8 days in a week Sunday to Saturday and another day call Oz day. There are 36 hours in a day and each hour has 90 mins while each minute has 60 sec. As on earth, the hour hand covers the dial twice every day. Find the approximate angle between the hands of a clock on Oz when the time is 10.40 am.
Ans: Aroung 59 degrees

  1. In planet OZ planet there are 8 days, sunday to saturday and 8th day is Oz day. There is 36 hours in a day. What is angle between 12.40?
    a) 80  b) 81  c) 87  d) 89                                   
    Ans: 89

  1. After the typist writes 12 letters and addresses 12 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) 0      b) 12/212    c) 11/12     d) 1/12     
Ans: a



  1. 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 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?

a) 256     b) 54      c) 192       d) 108                      
Ans: d

  1. A and B play a game between them. The dice consist of colors on their faces(instead of number). When the dice are thrown, A wins if both show the same color, otherwise B wins. One die has 3 red faces and 3 blue faces. How many red and blue faces should the other die have if the both players have if the both players have the same chances of winning?
5 red and 1 blue faces.
1 red and 5 blue faces.
3 red and 3 blue faces.
Ans: c


  1. A manufacturer undertakes to supply 2000 pieces of a particular component at Rs.25 per piece. According to his estimates, even if 5% fail to pass the quality tests, then he will make a profit of 25%. However, as it turned out, 50% of the components were rejected. What is the loss to the manufacturer?
(a) Rs.12000    (b) Rs.13000    (c) Rs.14000     (d) Rs.15000


  1. A manufacturer undertakes to supply 2000 pieces of a particular component at Rs.25 per piece. According to his estimates, even if 5% fail to pass the quality tests, then he will make a profit of 25%. However, as it turned out, 50% of the components were rejected. What is the loss to the manufacturer?

(a) Rs.12000            (b) Rs.13000            (c) Rs.14000              (d) Rs.15000



  1. A Roman was born the first day of the 35th year before Christ and died the first day of the 35th year after Christ. How many years did he live?

(a) 70            (b) 69            (c) 71        (d) 72

  1. Adam sat with his friends in the Chinnaswamy stadium at Madurai to watch the 100 metres running race organized by the Asian Athletics Association. Five rounds were run. After every round half the teams were eliminated. Finally, one team wins the game. How many teams participated in the race?

(a) 30         (b) 32               (c) 41               (d) 54


  1. A garrison of 3300 men has provisions for 32 days when supplied at the rate of 850 g per head. At the end of 7 days, a reinforcement arrives, and it is found that the provisions can last for 17 days more when supplied at the rate of 825 g per head. What is the strength of the reinforcement?

(a) 1700     (b) 1000           (c) 3000           (d) 2700


  1. Two unemployed young men decided to start a business together. They pooled in their savings, which came to Rs. 2,000. They were both lucky, their business prospered and they were able to increase their capital by 50 per cent every three years. How much did they have in all at the end of eighteen years?

(a) Rs. 22,781.25      (b) Rs. 24,150.25         (c) Rs. 28,140.50        (d) Rs. 18,000


  1. A man divides Rs.8600 among 5 sons, 4 daughters and 2 nephews. If each daughter receives four times as much as each nephew, and each son receives five times as much as each nephew, how much does each daughter receive?

(a) Rs.800            (b) Rs.600           (c) Rs.200              (d) Rs.700     



  1. A train starts full of passengers. At the first station, it drops one-third of the passengers and takes 280 more. At the second station, it drops one-half of the new total and takes 12 more. On arriving at the third station, it is found to have 248 passengers. Find the number of passengers in the beginning.

(a) 240       (b) 248             (c) 280             (d) 288



41.  A box of 150 packets consists of 1kg packets and 2kg packets. Total weight of box is                     264kg. How many 2kg packets are there?

(a) 100            (b) 114            (c) 200            (d) 208



  1. A man, a woman, and a child can do a piece of work in 6 days. Man only can do it in 24 days. Woman can do it in 16 days and in how many days child can do the same work?
(a) 8          (b) 14            (c) 16          (d) 18



43.  A bus started from bus stand at 8.00a m and after 30 min staying at destination, it returned back to the bus stand. The destination is 27 miles from the bus stand. The speed of the bus 50 percent fast speed. At what time it returns to the bus stand.

(a) 11a.m         (b) 12a.m         (c) 10a.m      (d) 10.30p.m

  1. If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage.


(a) 40%          (b) 55%       (c) 35%         (d) 30%  


  1. Two trains move in the same direction at 50 kmph and 32 kmph respectively. A man in the slower train observes the 15 seconds elapse before the faster train completely passes by him. What is the length of faster train?
(a) 100m        (b) 75m       (c) 120m           (d) 50m



  1. A man spends half of his salary on household expenses, 1/4th for rent, 1/5th for travel expenses, the man deposits the rest in a bank. If his monthly deposits in the bank amount 50, what is his monthly salary?
    (a) Rs.500 (b) Rs.1500 (c) Rs.1000 (d) Rs. 900



  1. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

(a) 360          (b) 480           (c) 720       (d) 5040



  1. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

(a) 1 hour               (b) 2 hours           (c) 3 hours        (d) 4 hours


  1. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

(a) 23 years        (b) 24 years           (c) 25 years          (d) None of these

  1. Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

(a) 4         (b) 10           (c) 15          (d) 16

  1. The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?

(a) 240            (b) 270          (c) 295         (d) 360

52. 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?

( I got this ques 3 times with values changed)

53. . The pacelength 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 = pacelength in meters. Bernard knows his pacelength is 111cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed kmph.



54.  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 16mm and not exceed 64mm·
 Given 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?


55. 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.
2)Öa) 1:(2 + 7
3)Öb) 1:(4 + 7
2):1Öc) (2 + 7
2) ( For me they changed 7 circles to 9 circles)Öd) 1:(2 + 6



56. 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 woman kind) 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) 3125  c) 500  d) 625

  1. There are two statements. There is also a question. Choose 1 if the question can be answered by using either one. Choose 2 if the question can be answered using both the statements. Choose 3 if the question can not be answered using these two statements

  1. Statement 1:  Avinash spends 30% on house rent, 20% on children’s education,40% on foods
    Statement 2: Pritam spends 20% on house rent, 45% on children’s education,20% on food

    Question: If pritam spends more than avinash on foods who spends more on children’s education? The question can be answered by
    a)  1   b) 2   c)3                                        

    Ans: c


  1. a block has 14cm width. if we combine 2 blocks the width will b 25cm. then if we put 150 blocks in similar manner. then wat is the resultant width.



  1. a man has age in years equal to his daughters age in months and daughter age is equals to his grand daughter age in weeks and her age in weeks total age of 3 members is given we need to find out the mans age



  1. New town is straight to the north of  New york. A high way M runs from newtown making an angle of 61 degree [^]south east. from newyork there is also an high way N which runs Northeast 61 degrees. If high ways M and N are straight then findout the acute angle made at their intersection point.
Ans: 180-(61+61)=58 (the high ways make a triangle the addition of 3 angles of a triangle is 180)
62. There are 7 meetings A,B,C,D,E,F,G. One meeting should happen in one day. Meeting A is on Sunday c and the meetings should happen after B. Then E ,F,G meetings should occur in three conjucutive days. And meeting g is on Saturday. Then meeting the should occur on which day?
a) Sun  b) Mon  c) Wed d) Friday
Ans: c

63. There are 9 weights like 16,19.156.26, 106,15,24,36 (in kg). There are three persons like rohit, sameer and imran. each lifts 3 types of weights. Rohit”s  total lifted  weight is 2 times than the weight lifted by  Rohit. What is the weight lifted by imran?
Ans: Total weight=16+19+156+26+106+15+24+36=398 kg

  1. Suppose option is y kg lifted by imran(choose from option)  then  3x+y=398
    =>x=(398-y)/3  here x should be a whole number then y is  the weight lifted by imran.



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