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Written Test

The written paper consists mainly of puzzles followed by an essay. There are 10 puzzles to be completed within one hour and a short essay (usually based on the trends in the computer field) of 15 minutes. We suggest that after going through the sample tests given below you also take time to go through some puzzle books like “Puzzles and teasers by George W. Summers ” ,”Shakuntla Devi’s Puzzle books” , “Mind Stretching Puzzles by Stickles” etc.

The paper can be given by students from all engineering streams.

The following sets of questions are available:

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.

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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.

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1. From a vessel, 1/3rd of the liquid evaporates on the first day.

On the second day 3/4th of the remaining liquid evaporates.

What fraction of the volume is present at the end of the second day.

Ans: 50%

2. An orange glass has orange juice and white glass has apple juice both of equal volumes.

50ml of the orange juice is taken and poured into the apple juice.

50ml from the white glass is poured into the orange glass.

Of the two quantities, the amount of apple juice in the orange glass and the amount of orange juice in the white glass, which one is greater and by how much?

Ans: The two quantities are equal

3. There is a 4 inch cube painted on all sides.

This is cut down into of 1 inch cubes.

What is the no of cubes which have no pointed sides.

Ans: 8

4. Sam and Mala have a conversation.

Sam says I am certainly not over 40

Mala says I am 38 and you are atleast 5 years older than me

Now Sam says you are atleast 39

All the statements by the two are false.

How old are they really?

Ans: Mala = 38 yrs

Sam = 41 yrs.

5. Ram Singh goes to his office in the city, every day from his suburban house.

His driver Gangaram drops him at the railway station in the morning and picks him up in the evening.

Every evening Ram Singh reaches the station at 5 O’ Clock.

Gangaram also reaches at the same time.

One day Ram Singh started early from his office and came to the station at 4 O’ Clock.

Not wanting to wait for the car he starts walking home. Mangaram starts at normal time, picks him up on the way

and takes him back house, half an hour early.

How much time did Ram Singh walk?

6. In a railway station, there are two trains going.

One in the harbour line and one in the main line, each having a frequency of 10 minutes.

The main line service starts at 5 o’clock and the harbour line starts at 5.02A.M.

A man goes to the station every day to catch the first train that comes.

What is the probability of the man catching the first train?

Ans: 0.8

7. A family X went for a vacation.

Unfortunately it rained for 13 days when they were there.

But whenever it rained in the mornings, they had clear afternoons and vice versa.

In all they enjoyed 11 mornings and 12 afternoons.

How many days did they stay there totally?

Ans: 18

8. A survey was taken among 100 people to find their preference of watching T.V. programmes.

There are 3 channels. Given the no of people who watch

at least channel 1

at least channel 2

at least channel 3

no channels at all

atleast channels 1and 3

atleast channels 1 and 2

atleast channels 2 and 3

Find the no of people who watched all three.

9. Albert and Fernandes have two leg swimming race.

Both start from opposite ends of the pool.

On the first leg, the boys pass each other at 18 m from the deep end of the pool.

During the second leg they pass at 10 m from the shallow end of the pool.

Both go at constant speed but one of them is faster.

Each boy rests for 4 seconds at the end of the first leg.

What is the length of the pool?

10. Each alphabet stands for one digit in the following multiplication.

T H I S

x I S

———

X F X X

X X U X

————

X X N X X

————

What is the maximum value T can take?

Ans: T max value = 4

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1.An escalator is descending at constant speed.

A walks down and takes 50 steps to reach the bottom.

B runs down and takes 90 steps in the same time as A takes 10 steps.

How many steps are visible when the escalator is not operating?

Ans: 150 steps

2. Every day a cyclist meets a train at a particular crossing.

The road is straight before the crossing and both are travelling in the same direction.

The cyclist travels with a speed of 10 Kmph.

One day the cyclist comes late by 25 min. and meets the train 5km before the crossing.

What is the speed of the train?

Ans: 60 kmph

3. There are five persons with surnames Mukherjee, Misra, Iyer, Patil and Sharma.

There are 4 persons having first or middle name of Kumar, 3 persons with Mohan, 2 persons with Dev and 1 Anil.

Either Mukherjee and Patil have a first or middle name of Dev or Misra and Iyer have their first or middle name of Dev.

Of Mukherkjee and Misra, either both of them have a first or middle name of Mohan or neither have a first or

middle name of Mohan.

Either Iyer or Sharma has a first or middle name of Kumar but not both.

Who has the first or middle name of Anil?

Ans: Kumar Misra Dev

Mohan Iyer Dev

Kumar Patil Mohan

Mohan Sharma Kumar

4. Boys are allowed to watch football at C.V.Raman auditorium subjected to conditions.

The boy over age 16 can wear overcoat

No boy over age 15 can wear cap

To watch the football either he has to wear overcoat or cap or both

A boy with an umberella or above 16 or both cannot wear sweater.

Boys must either not watch football or wear sweater.

What is the appearence of the boy who is watching football.

5. A bird keeper has got P pigeons, M mynas and S sparrows.

The keeper goes for lunch leaving his assistant to watch the birds.

Suppose p=10, m=5, s=8 when the bird keeper comes back, the assistant informs the x birds have escaped. The bird keeper exclaims: “Oh no! All my sparrows are gone.”

How many birds flew away?

When the bird keeper comes back, the assistant told him that x birds have escaped. The keeper realised that atleast 2 sparrows have escaped.

What is minimum no of birds that can escape?

6. Answer the following questions based on the conditions from the choices A, B, C, D, E as described below:

(A) if a definete conclusion can be drawn from condition 1

(B) if a definete conclusion can be drawn from condition 2

(C) if a definete conclusion can be drawn from condition 1 and 2

(D) if a definete conclusion can be drawn from condition 1 or 2

(E) no conclusion can be drawn using both conditions

person 1 says N<5 person says N>5

person 3 says 3N>20

person 4 says 3N>10

person 5 says N<8 What is the value of N? a) 1. No of persons who speak false being less than no of persons who tells the truth. 2. Person 2 is telling the truth. b) 1. no of persong telling the truth is greater than no of persons telling lies 2. person 5 is telling the truth. 7. There are N coins on a table and there are two players A & B. You can take 1 or 2 coins at a time. The person who takes the last coin is the loser. A always starts first. If N=7 (a) A can always win by taking two coins in his first chanse (b) B can win only if A takes two coins in his first chance. (c) B can always win by proper play (d) none of the above 2. A can win by proper play if N is equal to (a) 13 (b) 37 (c) 22 (d) 34 (e) 48 Ans: (e.) 3. B can win by proper play if N is equal to (a) 25 (b)26 (c) 32 (d) 41 (e) none 4. if N<4, can A win by proper play always? (a) Yes (b) No 8. Two twins have vertain peculiar charcteristics. One of them always lies on Monday, Wednesday, Friday. The other always lies on Tuesdays, Thursdays and Saturdays. On the other days they tell the truth. You are given a conversation. Person A– today is Sunday my name is Anil Person B — today is Tuesday, my name is Bill What day is today? Ans: Today is Tuesday. 9. There is a safe with a 5 digit number as the key. The 4th digit is 4 greater than second digit, while 3rd digit is 3 less than 2nd digit. The 1st digit is thrice the last digit. There are 3 pairs whose sum is 11. Find the number. Ans: 65292 10. A hotel has two wings,the east wing and the west wing. Some east wing rooms but not all have an ocean view. All west wing rooms have a harbour view. The charge for all rooms is identical, except as follows : Extra charge for all harbour view rooms on or above the 3rd floor Extra charge for all ocean view rooms except those without balcony Extra charge for some harbour rooms on the first two floor & some east wing rooms without ocean view but having kitchen facilities. Which of the following cannot be determined on the basis of the nformation given: I. Whether there are any rooms without a balcony for which an extra charge is imposed. II. Whether any room without a kitchen or a view involves an extra charge. III. Whether two extra charges are impsed for any room. (A) I only (B) II only (C) III only (D) II and III only (E) I, II and III (This question is from 1999 Barrons GRE Guide model Test 3 – section 6, question 22) Ans: (A)