Ans: 66 sec.                 (2 marks)

2. Three friends divided some bullets equally.
    After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division.
    Find the original number divided.

Ans: 18                         (2 marks)

Initially   .    x          x        x
Now          x-4       x-4     x-4
Equation is   3x-12 = x

3. A ship went on a voyage.
    After it had travelled 180 miles a plane statrted with 10 times the speed of the ship.
    Find the distance when they meet from starting point.

Ans: 200miles.              (2 marks)
        Distance travelled by plane = 1/10 distance travelled by ship + 180

4.  Complete the Table given below:

      Three football teams are there. Given below is the group table. Fill in the x's

Ans: The filled table is given below                                (4 marks)

5. There are 3 societies A, B, C. 
   A lent cars to B and C as many as they had already.
   After some time B gave as many tractors to A and C
as many as they have.  After sometime c did the same thing. At the end of this transaction each one of them had 24.
Find the cars each orginally had.

Ans: A had 39 cars, B had 21 cars & C had 12 cars                   (4 marks)

6. There N stations on a railroad.
    After adding X stations on the rail route 46 additional tickets have to be printed.
    Find N and X.

Ans. x=2  and N=11

Let initially, N(N-1) = t
After adding,  (N+X)(N+X-1) =  t+46
By trail and error method                                       (4 marks)

7. Given that April 1 is tuesday.
    A, B, C are 3 persons told that their farewell party was on

• A  - May 8, thursday
• B  - May 10,tuesday
• C  - June 5, friday

Out of A, B, C only one made a completetly true statement concerning date,day and month
The other told  two one told the day right and the other the date right..
What is correct date, month, day.

Ans:  B - (May 10) SUNDAY
        C  - June 6 (Friday).                                     (5 marks)

8. The Bulls, Pacers, Lakers and Jazz ran for a contest.
    Anup, Sujit, John made the following statements regarding results.

• Anup said either Bulls or Jazz will definitely win
• Sujit said he is confident that Bulls will not win
• John said he is confident that neither Jazz nor Lakers will win

When the result cameit was found that only one of the above three had made a correct statement.
Who has made the correct statement and who has won the contest. 

Ans: Sujith; Lakers                      (5marks )

9. Five people A ,B ,C ,D ,E are related to each other.
    Four of them make one true statement each as follows.

(i)  B is my father's brother.       
(ii) E is my mother-in-law.
(iii)C is my son-in-law's brother
(iv)A is my brother's wife.

Ans: (i)   D
        (ii)  B
        (iii) E
        (iv) C                                 (10 marks)

10.  Some statements are given below:

• L says all of my other four friends have money
• M says that P said that exactly one among them has money
• N says that L said that precisely two among them have money
• O says that M said that three of the others have money
• P, L and N said that they have money

All the above statement are false..
Who has money & who doesn't have any money?

(5 marks)

1. Mr.Mathurs jewels have been stolen from his bank locker .
    The bank has lockers of 12 people which are arranged in an array of 3 rows and 4 columns like:

• The locker belonging to JONES was to the right of BLACK'S locker and directly above MILLAR'S.
• BOOTH'S locker was directly above MILLAR'S.
• SMITH'S locker was also above GRAY's (though not directly).
• GREEN'S locker was directly below SMITH'S.
• WILSON'S locker was between that of DAVIS and BOOTH.
• MILLAR'S locker was on the bottom row directly to the right of HERD'S.
• WHITE'S locker was on the bottom right hand corner in the same column as BOOTH'S.

Which box belonged to Mr.Mathurs?

Ans: Box number 9 belongs to Mr.Mathurs.

2. Fifty minutes ago if it was four times as many minutes past three o'clock,how many minutes is it to six o'clock?

Ans: Twenty six minutes.

3. If a clock takes 7seconds to strike 7, how long will the same clock take to strike 10?

Ans: The clock strikes for the first time at the start and takes 7 seconds for 6 intervals-thus for one interval time
        taken=7/6.
        Therefore, for 10 seconds there are 9 intervals and time taken is 9*7/6=10 and 1/2 seconds.

4. Three criminals were arrested for shop lifting.
    However, when interrogated only one told the truth in both his statements, while the other two each told one true  
    statement and one lie.
    The statements were:

• ALBERT :(a)Chander passed the merchandise.  (b)Bruce created the diversion.
• BRUCE   :(a)Albert passed the merchandise.      (b)I created the diversion.
• CLIVE     :(a)I took the goods out of the shop.    (b)Bruce passed them over.

Ans: Albert passed the goods.Bruce created the diversion..Clive took the goods out of the shop.

5. Everyday in his business a merchant had to weigh amounts from 1 kg to 121 kgs, to the nearest kg.
    What are the minimum number of weight required and how heavy should they be?

Ans: .The minimum number is 5 and they should weigh 1,3,9,27 and 81 kgs.

6. A hotel has 10 storeys.Which floor is above the floor below the floor, below the floor above the floor, below the
    floor above the fifth.

Ans: The sixth floor.

7. Seven members sat around a table for three days for a conference.
    The member's names were Abhishek, Amol, Ankur, Anurag,Bhuwan ,Vasu and Vikram.
    The meetings were chaired by Vikram.
    On the first evening members sat around the table alphabetically.
    On the following two nights, Vikram arranged the seatings so that he could have Abhishek as near to him as
    possible and abesent minded Vasu as far away as he could.
    On no evening did any person have sitting next to him a person who had previously been his neighbour.
    How did Vikram manage to seat everybody to the best advantage on the second and third evenings?

Ans:
Second evening:Vikram,Ankur,Abhishek,Amol,Vasu,Anurag and Bhuwan.
Third evening   :Vikram,Anurag,Abhishek,Vasu,Bhuwan,Ankur,Amol.

8. Two trains start from stations A and B spaced 50 kms apart at the same time and speed.
    As the trains start, a bird flies from one train towards the other and on reaching the second train, it flies back to the
    first train.This is repeated till the trains collide.
    If the speed of the trains is 25 km/h and that of the bird is 100km/h.
    How much did the bird travel till the collision.

Ans: 100 kms.

9. Four prisoners escape from a prison.
    The prisoners, Mr East, Mr West, Mr South, Mr North head towards different directions after escaping.
    The following information of their escape was supplied:

• The escape routes were The North Road, South Road, East Road and West Road.
• None of the prisoners took the road which was their namesake.
• Mr.East did not take the South Road
• Mr.West did not the South Road.
• The West Road was not taken by Mr.East

What road did each of the prisoners take to make their escape?

Ans: Mr.East took the North Road
        Mr.West took the East Road
        Mr.North took the South Road
        Mr.South took the West Road.

10. Complete the series:
        5, 20, 24, 6, 2, 8, ?

Ans: 12 (as 5*4=20, 20+4=24, 24/4=6, 6-4=2, 2*4=8, 8+4=12).

1) A man collects cigarette stubs and makes one full cigarette with every 8 stubs.
   If he gets 64 stubs how many full cigarettes can he smoke.

Ans: 8+1=9


2) A soldier looses his way in a thick jungle. At random he walks from his camp but mathematically in an interesting fashion. First he walks one mile East then half mile to North. Then 1/4 mile to West, then 1/8 mile to South and so on making a loop.
Finally how far he is from his camp and in which direction.

Ans: Distance travelled in north and south directions
        1/2 - 1/8 + 1/32 - 1/128 + 1/512 - and so on
        = 1/2/((1-(-1/4))
       Similarly in east and west directions
        1- 1/4 + 1/16 - 1/64 + 1/256 - and so on
        = 1/(( 1- ( - 1/4))
Add both the answers

3)  How can 1000000000  be written as a product of two factors neither of them containing zeros

Ans: 2 power 9 x 5 power 9

4)  Conversation between two mathematcians:
First : I have three childern. The product of their ages is 36.
          If you sum their ages, it is exactly same as my neighbour's door number on my left.
The second mathematician verfies the door number and says that it is not sufficient.
Then the first says " Ok one more clue is that my youngest is really the youngest". Immmediately the second mathematician answers .
Can you answer the question asked by the first mathematician?
What are the childeren ages?

Ans 1,6 and 6

5) Light glows for every 13 seconds . How many times did it glow between 1:57:58 and 3:20:47 am.

Ans : 383 + 1 = 384

6) 500 men are arranged in an array of 10 rows and 50 columns according to their heights.
     Tallest among each row of all are asked to fall out.
     And the shortest among them is A.
     Similarly after resuming that to their original podsitions that the shortest among each column are asked to fall out.
     And the tallest among them is B .
     Now who is taller among A and B ?

Ans A


7)  A person with some money spends1/3 for cloths, 1/5 of the remaining for food and 1/4 of the remaining for travel.
     He is left with Rs 100/- .
     How much did he have with him in the begining ?

Ans: Rs 250/-

8)  There are six boxes containing 5 , 7 , 14 , 16 , 18 , 29 balls of either red or blue in colour.
     Some boxes contain only red balls and others contain only blue.
     One sales man sold one box out of them and then he says
   " I have the same number of red balls left out as that of blue ".
     Which box is the one he solds out ?

Ans: Total no of balls = 89 and (89-29 /2) = 60/2 = 30
and also 14 + 16 = 5 + 7 + 18 = 30

9)  A chain is broken into three pieces of equal lenths containing 3 links each.
     It is taken to a backsmith to join into a single continuous one .
     How many links are to to be opened to make it ?

Ans : 2.

10)  Grass in lawn grows equally thick and in a uniform rate.
       It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass.
       How many cows are needed to eat the grass in 96 days.?

Ans : 20
g - grass at the beginning
r - rate at which grass grows, per day
y - rate at which one cow eats grass, per day
n - no of cows to eat the grass in 96 days
g + 24*r = 70 * 24 * y
g + 60*r = 30 * 60 * y
g + 96*r = n * 96 * y
Solving, n = 20.
 

Section B

1.  Replace each letter by a digit.
     Each letter must be represented by the same digit and no beginning letter of a word can be 0.

O N E
O N E
O N E
O N E
-------
T E N

Ans:  0 =1, N = 8 ,E = 2, T = 7

2. Ann, Boobie, Cathy and Dave are at their monthly business meeting.
    Their occupations are author, biologist, chemist and doctor, but not necessarily in that order.
    Dave just told the biologist that Cathy was on her way with doughnuts.
    Ann is sitting across from the doctor and next to the chemist.
    The doctor was thinking that Boobie was a goofy name for parent's to choose,but didn't say anything.
    What is each person's occupation?

Ans: Since Dave spoke to the biologist and Ann sat next to the chemist and across the doctor, Cathy must be the author 
        and Ann the biologist.
        The doctor didn't speak, but David did, so Bobbie is the doctor and Dave the chemist.

3. Sometime after 10:00 PM a murder took place.
    A witness claimed that the clock must have stopped at the time of the shooting.
    It was later found that the postion of both the hands were the same but their positions had interchanged.
    Tell the time of the shooting (both actual and claimed).

Ans: Time of shooting = 11:54 PM
        Claimed Time     = 10:59 PM

4. Next number in the series is
      1 , 2 , 4 , 13 , 31 , 112 , ?

Ans: 224.
        No number has digits more than 4. All of them are 1 , 2, 4, 8 , 16 , 32 , 64 converted to numbers in base 5

5. Shahrukh speaks truth only in the morning and lies in the afternoon, whereas Salman speaks truth only in the afternoon.      A says that B is Shahrukh. Is it morning or afternoon and who is A - Shahrukh or Salman.

Ans: Afternoon ; A is Salman.

6. Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their 
    destination 1 hr and 4 hours respectively after passing each other. How nuch faster is one train from other?

Ans: Twice

7. There are 6 volumes of books on a rack kept in order ( ie vol.1, vol. 2 and so on ).
     Give the position after the following changes were noticed.

• All books have been changed
• Vol.5 was directly to the right of Vol.2
• Vol.4 has Vol.6 to its left and both weren't at Vol.3's place
• Vol.1 has Vol.3 on right and Vol.5 on left
• An even numbered volume is at Vol.5's place

Find the order in which the books are kept now.

Ans: 2 , 5 , 1 , 3 , 6 , 4

8. I bought a car with a peculiar 5 digit numbered licence plate which on reversing could still be read.
    On reversing value is increased by 78633.Whats the original number if all digits were different?

Ans: Only 0 1 6 8 and 9 can be readupside down.So on rearranging these digits we get the answer as 10968

9. The shape in the sketch below is that of a square attached to half of a similar square.Divide it into four equal pieces

Ans: Hint : the figure can be divided into 12 equal triangles 

10. Supposing a clock takes 7 seconds to strike 7. How mlong will it take to strike 10?

Ans: 10 1/2 seconds