Book 4 - TestFunda

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Book 4
We all fit like pieces of a puzzle. Everybody's input and their journeys and where they've been
help put that puzzle together.
- Melody Thorntonzz
Table of Contents
Puzzle #01: Miss Braganza and her Special Grid ....................................... 1
Puzzle #02: Be ready to beat about the bush during CAT 2010 ............... 2
Puzzle #03: Phoebe's Phoebia! ................................................................. 3
Puzzle #04: Good Old Mr. Luis .................................................................. 4
Puzzle #05: The Complicated Corporate World ........................................ 5
Puzzle #06: The Mathematician's Stairs ................................................... 6
Puzzle #07: Find the number counting numbers ...................................... 7
Puzzle #08: Letters for numbers ............................................................... 7
Puzzle #09: Three Mice ............................................................................. 8
Puzzle #10: The caselet of the Air-Freight-Carrier planes......................... 8
Puzzle #11: Entangled Wires? ................................................................... 9
Puzzle #12: Transporting a thief ............................................................. 10
Puzzle #13: The case of the cheating husbands...................................... 11
Puzzle #14: Diwali Chocolates ................................................................. 12
Puzzle #15: Sentencing the Thief ............................................................ 12
Puzzle #16: A Tale from the South .......................................................... 13
Puzzle #17: Hoping for Sunny Weather .................................................. 14
Puzzle #18: Shuchi's Birthday Party ........................................................ 14
Puzzle #19 : Shuchi's Birthday Party 2 .................................................... 15
Puzzle #20 : The Lazy Ant ........................................................................ 16
Puzzle #21 : LINKing your rent ................................................................ 16
Puzzle #22 : The case of the blue bandanas ........................................... 17
Puzzle #23 : At which table have you been seated? ............................... 17
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Puzzle #24 : Use all your devices ............................................................ 17
Puzzle #25 : Another Taj Mahal .............................................................. 18
Puzzle #26 : The Engineer and the Marketing Manager ......................... 18
Puzzle #27 : Q21. of CAT 2012 ................................................................ 19
Puzzle #28 : Q42. of CAT 2012 ................................................................ 20
Puzzle #29 : Of Dads and Sons ................................................................ 20
Puzzle #30 : To which party do I belong?................................................ 21
ANSWERS ................................................................................................ 22
Puzzle #01: Miss Braganza and her Special Grid ..................................... 23
Puzzle #02: Be ready to beat about the bush during CAT 2010 ............. 23
Puzzle #03: Phoebe's Phoebia! ............................................................... 24
Puzzle #04: Good Old Mr. Luis ................................................................ 25
Puzzle #05: The Complicated Corporate World ...................................... 26
Puzzle #06: The Mathematician's Stairs ................................................. 28
Puzzle #07: Find the number counting numbers .................................... 30
Puzzle #08: Do NOT Disturb the Dead .................................................... 30
Puzzle #09: Three Mice ........................................................................... 31
Puzzle #10: The caselet of the Air-Freight-Carrier planes....................... 32
Puzzle #11: Entangled Wires? ................................................................. 33
Puzzle #12: Transporting a thief ............................................................. 34
Puzzle #13: The case of the cheating husbands...................................... 35
Puzzle #14: Diwali Chocolates ................................................................. 36
Puzzle #15: Sentencing the Thief ............................................................ 38
Puzzle #16: A Tale from the South .......................................................... 39
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Puzzle #17: Hoping for Sunny Weather .................................................. 40
Puzzle #18: Shuchi's Birthday Party ........................................................ 40
Puzzle #19 : Shuchi's Birthday Party 2 .................................................... 41
Puzzle #20 : The Lazy Ant ........................................................................ 42
Puzzle #21 : LINKing your rent ................................................................ 43
Puzzle #23 : At which table have you been seated? ............................... 44
Puzzle #24 : Use all your devices ............................................................ 45
Puzzle #25 : Another Taj Mahal .............................................................. 45
Puzzle #26 : The Engineer and the Marketing Manager ......................... 46
Puzzle #27 : Q21. of CAT 2012 ................................................................ 46
Puzzle #28 : Q42. of CAT 2012 ................................................................ 47
Puzzle #29 : Of Dads and Sons ................................................................ 48
Puzzle #30 : To which party do I belong?................................................ 49
About TestFunda.com ............................................................................. 50
PREFACE
For the past couple of years, CAT and other MBA entrance exams have
shown a trend towards questions testing a student’s ability to apply
Mathematical Principles and Analytical Reasoning to solve problems.
The unpredictable nature of CAT has ensured that most students are
never fully prepared to ace the exam. This is because students limit their
preparation to just the learning and practice of core concepts of
Mathematics, Verbal Ability and Data Interpretation & Logical
Reasoning. However, to bell the CAT, divergent thinking is required
which is why experts also recommend solving an eclectic mix of Puzzles,
Crosswords, Riddles and Brain Teasers. These enhance the problemsolving skills of CAT aspirants and encourage them to think out-of-thebox.
We, at TestFunda.com, feel that solving puzzles not only helps sharpen
one’s logical acumen, but also gives immense pleasure and satisfaction.
The puzzles in this book will give students that extra edge and
confidence needed to be ready for any surprise that CAT might throw
their way.
We are sure that our readers will benefit greatly from these books. They
shall provide a much-needed break from long study hours as well as
high-quality cerebral recreation.
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Puzzle #01: Miss Braganza and her Special Grid
Miss Braganza once decided to play a game with her students in class, who
were beginning to look bored. She asked a peon to get an overhead projector
(OHP) and focused a transparency sheet on a screen on the whiteboard. On the
transparency sheet was a grid. There were 9 numbers in shaded squares on the
grid in such a way that there were 8 non-shaded squares around each number.
The game was that a student should fill each of the non-shaded squares with a
number from 1 to 7.
The 8 numbers around the number in the shaded square should sum up to the
shaded number.
Also, no row nor column should contain a duplicate number in the non-shaded
square. For example, the top row may be 1 2 3 4 5 6 7.
Fill in the non-shaded squares with appropriate numbers and complete the
grid.
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Puzzle #02: Be ready to beat about the bush during CAT
2010
Here's a snippet of the DILR section of the CAT 2010 question paper.
Questions 21-24 are related.
Q21. The first question to have option C as the correct option is:
A. 23
B. 24
C. 21
D. 22
Q22. The first question to have option A as the correct option is:
A. 24
B. 22
C. 23
D. 21
Q23. The first question to have option D as the correct option is:
A. 21
B. 22
C. 24
D. 23
Q24. The first question to have option B as the correct option is:
A. 22
B. 24
C. 23
D. 21
What would the answers to the above questions be? Remember a seat in the
IIMs is at stake. :P
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Puzzle #03: Phoebe's Phoebia!
Phoebe plays the lottery every week and also plays the same numbers every
week as advised by her psychic, who had also predicted that she would be
killed by a pigeon. (But that's beside the point!) Phoebe has always been very
superstitious as a person and is extremely wary of prime numbers. She says
that while she and her sister were growing up, her mom had killed herself on a
day when the date was a prime number! Now, in order to win the lottery, a
player has to choose six integers between 1 and 49 (1 and 49 are both
included!). However, because of her "Prime Number Phobia" (or should we say
Phoebia!), she chooses her numbers such that:
1. All six numbers are composite.
2. All of the digits in the six numbers are non-prime.
3. The differences between any two of the six numbers are always composite.
Using the given data, figure out the combination of numbers that she always
plays. Provide a detailed explanation along with your answer.
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Puzzle #04: Good Old Mr. Luis
Mr. Joseph Arthur Luis was fond of puzzles right from his childhood. A few
months ago, he was caught puzzling his son's father-in-law, Mr. D'Costa. Mr.
D'Costa just wanted to know Mr. Luis's age, but what Mr. Luis said was, "My
grand-daughter, my son and I together are 140 years old. My grand-daughter is
about as many days old as my son is weeks, and my grand-daughter is as many
months old as I am in years. Now, Mr. D'Costa, I think you can figure out my
age by yourself." What was his age? Provide a detailed explanation along with
your answer.
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Puzzle #05: The Complicated Corporate World
From the information given below, can you identify each industrialist's firm,
firm CEO, and number of employees?
1. Industrialists' Names: Frazer, Mary, Alwyn. Ross, and Mario.
2. CEOs names: Mona, Ashley, Warren, Esha, and Howard.
3. The firms: Firm (A), Firm (B), Firm (C), Firm (D) and Firm (E).
4. The firms have: 150, 190, 230, 270 and 310 employees.
5. Ashley works for the firm who has the most employees.
6. Esha is the CEO of the firm owned by Mario, whilst Howard works for firm
(B)
7. Firm (D) has 230 employees. The smallest number of employees do not
work in the firm owned by Mary.
8. Alwyn has 190 employees in his firm. His firm is not Firm (E), and his firm's
CEO is not Mona.
9. Firm (A) is owned by Frazer, who has 80 employees more than those
directed by Warren.
10. Mona has more employees to direct than Howard. The latter's firm owner
has a four letter name.
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Puzzle #06: The Mathematician's Stairs
A mathematician, while going home, had to walk up a flight of stairs. The stairs
consisted of twenty steps. One day, the mathematician, to get over monotony,
decided to paint the stairs maroon and orange in accordance with the following
rules he came up with:
1.
2.
Every step was to be either painted maroon or orange.
Orange steps would never succeed each other.
In how many ways can the mathematician paint these stairs? Also, what was
his name? Provide a detailed explanation along with this answer.
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Puzzle #07: Find the number counting numbers
There exists a number ZYXWVUTSRQ such that each letter represents one and
only one digit between 0-9. However, different letters can represent the same
digit. For example, both R and S can represent 9 but R cannot represent 9 and
8. Z is the count of the number of zeroes in the number, Y is the count of the
number of ones, X is the count of the number of twos and so on. Find the
number.
Puzzle #08: Letters for numbers
Here are 5 equations using 5 variables P, Q, R, S & T. Each letter represents one
number:
P-Q=Q
Q*R =P
S:Q=T
R*R=T
R+T=P
Find P*Q*R*S*T. Provide a detailed explanation along with your answer.
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Puzzle #09: Three Mice
Three mice were trapped in a triangular cage. The cage was an equilateral
triangle of side 1 metre. Once, each one of them was at a different corner of
the triangle. Suddenly, each mouse set off running after the mouse in the
adjacent corner to its left. Thus each mouse followed a curved course that
terminated at the centre of the cage. Also, all three mice arrived at the same
time. Now it's obvious that the three mice ran at the same speed. Using this
data, calculate the distance travelled by each mouse.
Puzzle #10: The caselet of the Air-Freight-Carrier planes
There are 5 planes at an airport stationed parallel to each other.
1. The Danish plane leaves at one and carries chocolates.
2. The plane in the middle has an auburn wing.
3. The Japanese plane leaves at four.
4. The Indian plane with a peach wing is to the left of the plane that carries
chocolates.
5. To the right of the plane carrying cheese is a plane going to Geneva.
6. The Austrian plane is heading for Moscow.
7. Next to the plane carrying electronic goods is a plane with a gold wing.
8. A plane going to Sydney leaves at twelve.
9. The Egyptian plane leaves at two and is to the right of the plane going to
Geneva.
10. The plane with a magenta wing goes to Los Angeles.
11. Next to the plane leaving at two is a plane with a grey wing.
12. The plane on the border carries gems.
13. The plane with an auburn wing leaves at three.
14. The plane carrying gems is stationed next to the plane carrying electronic
goods.
15. The plane to Los Angeles leaves at one.
Deduce which plane carries condiments and which plane goes to La Paz.
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Puzzle #11: Entangled Wires?
TestFunda Telephone Limited (TTL) laid a wire cable consiting of 120 wires
underground between two of its telephone exchanges that were 8 km apart.
However, after the cable was laid, they realised that individual wires could not
be identified as they were not labeled. Now, the cable was underground and so
identifying each wire would be a tedious job and would require ripping the
entire ensemble up. Akhil, the senior technician at TTL, was handed the
responsibility of identifying and labelling the wires at both ends without having
to rip it all up. All he had at his disposal were a battery and a light bulb. He was
also given a tape and a marker to label the wires. He didn't have any mode of
transport and had to walk the entire distance. Deduce the shortest distance
that he had to walk so as to identify and label each wire correctly. Provide a
detailed explanation along with your answer. (Assume the wire resistance to be
negligible.)
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Puzzle #12: Transporting a thief
Biraj, a local thief, once entered the Pereira household. However, he wasn't
adept at theft and half way through the robbery, he got caught in the act. The
Pereiras were a family of 6, comprising a father, mother, 2 boys and 2 girls. A
policeman arrived and caught the thief. He asked the whole family to come
down with him to the police station to lodge a case against the thief. However,
they had to cross a creek to get to the police station on the other side. All that
was available was a raft that could only carry 2 people at any given time. They
chained Biraj up so that he wouldn't get away. But it was still advisable not to
leave any of the family members with him in the absence of the policeman, lest
Biraj should cause them any harm. Also, Mr. Pereira, the father, could not be
left with any of the daughters unless Mrs. Pereira was present, as the girls kept
arguing in the absence of their mother. Also, Mrs. Pereira could not be left with
any of the sons unless Mr. Pereira was present, as they kept hitting each other
and Mrs. Pereira just could not control them. Only Mr. and Mrs. Pereira, Biraj
and the policeman knew how to use a raft. But, Biraj obviously couldn't raft as
he had been chained. Using the given data, deduce a plan to quickly get them
all to cross the creek and have Biraj behind bars as soon as possible.
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Puzzle #13: The case of the cheating husbands
In ancient Potidaea, society was more matriarchal in nature. Women never
trusted their husbands, as infidelity was on the rise. However, the laws
empowered a woman to throw her husband out of the house if he were proved
to be an adulterer. Women at that time believed in Oracles. Once, an Oracle
was invited to Potidaea. The female inhabitants of the town wanted
confirmation from the Oracle that their husbands were loyal to them. However,
the Oracle had a few conditions as she wanted to avoid any controversies.
1. She would simply say "Nai (yes)" or "Ohkee (No)" and not announce the
number of men who were adulterers nor would she identify them.
2. Also, if she arrived and made her announcement, the women would have to
follow a particular rule. Once, the Oracle has announced her answer, if on any
day a lady figured out that her husband was an adulterer, she would throw him
out of the house the very next day at noon.
Now, the entire episode would be visible to every inhabitant of Potidaea. Also,
every woman already knew what every man, other than her husband, was up
to. However, she could not reveal that information to any other woman. Also,
obviously, a cheating husband would not reveal his infidelity.
When the Oracle visited, she just said, "Nai" and left immediately. At noon on
the 15th day after the Oracle left, for the first time, some women threw their
husbands out of their homes. How many men were thrown out? Provide a
detailed explanation along with your answer.
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Puzzle #14: Diwali Chocolates
Mrs. Bakshi had five daughters. For Diwali, each girl gifted boxes of chocolate
to one or more of her sisters. Each of them gifted 4 boxes and each one
received 4 boxes. However, no two daughters presented boxes to her sister(s)
in the exact same way. For example, only one sister gifted two boxes to one
sister and two to another. Krithika gifted all 4 of her boxes to Sunila while
Chandini gave three to Pooja. Using the given information, deduce which
sister(s) gave Disha the four boxes that she received.
Puzzle #15: Sentencing the Thief
After being taken to the police station (Puzzle #102 - Transporting a thief), Biraj
was taken to court where he was convicted. In that primitive town, the penalty
for theft was death. However, the magistrate, needless to say a puzzle lover,
decided to give him a chance to save himself. He was blindfolded and was told
that he would have to pick a pill from either of two small cups. There would be
a total of 100 pills - 50 blue and 50 green pills. Green pills contained potassiuym
cyanide and consuming them would cause instant death. The blue pill was a
very strong laxative as the judge felt that in case he chose that pill, at least a
small, yet memorable punishment was imminent. He asked for one last wish to
be granted. He said that he would like to divide the pills amongst the 2 cups
before he was blindfolded. The judge granted his wish, but added a stipulation
that after the division was done, the cups would be sealed and Biraj would
have to choose a cup whilst being blindfolded and once he chose a cup, he
could not exchange the cup and would have to pick a pill from that very cup.
Now we know that Biraj was a novice (considering that he wasn't adept at
robbery) and, hence, a death penalty would be utterly barbaric. He could be
given a chance to amend his ways without taking away his life. So, help him
figure out a plan to maximise his chances of survival. Provide a detailed
explanation along with your answer.
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Puzzle #16: A Tale from the South
In the village of Alappuzha, there lives a great old man named Mathew. Every
time he has visitors, he makes sure he acquaints them with a famous love story
that is now a part of the town's history. It was the story of Mr and Mrs.
Puthussery who fled from their village in North Kerala to Thiruvanathapuram in
South Kerala to get married against their parents wishes. Like every love story,
this one too involved a lot of bloodshed between the families and half the
village property went up in smoke. But their courageous move to run away still
serves as an inspiration to all budding love stories in that village. When
Mathew is prodded for further details, he poses a puzzle to the questioner and
says that he'll supply details only if the puzzle is answered. The puzzle of course
is about Mr. and Mrs. Puthussery and their two children.
He just states four sentences:
1.
Vimble and Mariam are blood relatives.
2. Thomas is older than Vimble.
3. Jincy is younger than Thomas.
4. Jincy is older than Mariam.
And then, he coolly adds that exactly two of those statements are true. Using
the information, he expects one to identify the father, mother, son and
daughter. Solve the puzzle and provide a detailed explanation along with your
answer.
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Puzzle #17: Hoping for Sunny Weather
London has very weird weather. On an average, for two days out of every
three, the sky is overcast. Charmaine will be travelling there for a conference.
She'll be staying in London from the 1st to the 5th of the month. Since the
conference would be held only in the evening, she wanted to laze around in the
sun on the beach the whole day. What is the probability that the sky will be
clear and sunny on at least 4 out of the 5 days of her stay there? Provide a
detailed explanation along with your answer.
Puzzle #18: Shuchi's Birthday Party
Shuchi invited 49 of her friends home to celebrate her birthday. By midnight,
they were all tired and decided to play a game. Each player was assigned a
unique integer from 1 to 50. In the first game, player 1 won. In the second,
player 2 won. In the third, player 3 won. The pattern continued till in the 50th
game, player 50 won.
Now the rules of the game were such that, if player 1 won a game, he would
have to forfeit some money to the other 49 players. The amount of he would
give would be equal to the amount that the other person had in his pocket at
that time.
For example, if player 1 won, he would give the other 49 players some money.
He would give player 2 the amount of money that player 2 had in his pocket.
Player 3 would be given the amount of money that player 3 had in his pocket.
The rest would be paid accordingly.
Finally, after the player 50 won, the amount of money left with every player is
the same and is "X".
Calculate in terms of"X" the value of money which 13th player had in
beginning.
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Puzzle #19 : Shuchi's Birthday Party 2
As the birthday party continued, Shuchi and Kasturi played a little game after
everyone else had fallen asleep. THey took turns to call out integers. The rules
of the game were as follows:
1. The first player who would call out “50” would win the game.
2. Whosoever starts the game must call out an integer between 1 and 10, (both
numbers included).
3. Whenever a new number is called out, it must exceed the number called out
most recently by at least one and by no more than 10.
Shuchi decides to go first. What should her strategy be in order to win the
game? Provide a detailed explanation along with your answer.
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Puzzle #20 : The Lazy Ant
I am a very lazy ant. I've been trapped in a large cubic cage. The walls of the
cage are made of plastic. I'm currently seated at one corner of the cube. I know
that there is a grain of sugar at the corner farthest from me. I think it's a lot of
effort going all the way for a single grain of sugar. Help me devise the shortest
route to the grain so that I may exert as little effort as possible. Also send me a
detailed explanation of why you consider that route to be the shortest.
Puzzle #21 : LINKing your rent
Amanda recently lost her job and has been unable to pay her rent ever since.
As a last resort, she decided to pay using her only 23-link chain. After several
calculations, she realised that her monthly rent was equal to the price of one
gold link. As she is emotionally attached to her chain, she wants to make as
little cuts in the chain as possible. What is the fewest number of cuts that can
be made in this chain so as to be sufficient for her rent for the next 23 months?
Provide a detailed explanation along with your answer.
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Puzzle #22 : The case of the blue bandanas
Three men were blindfolded and a blua bandana was tied around each of their
heads. The were made to sit in a circle They were told that the bandana might
be black or blue. Upon removal of the blindfolds, each was to raise his hand, if
he saw at least one blue bandana. If he could logically deduce the colour of his
own bandana, he could lower his hand. The moment the bandanas were
removed, all three hands were quickly raised. A minute later, one of them
lowered his hand. How did he figure this out? Provide a detailed explanation
along with your answer.
Puzzle #23 : At which table have you been seated?
At a party, Darmes and Rakesh were seated at tables 120 and 124 respectively.
What were the table numbers of Manish's and Rohit's tables? Provide a
detailed explanation along with your answer.
Puzzle #24 : Use all your devices
Here's a secret code that you need to decipher. Hint: Use all your devices to
figure out what we mean.
A3Q9Z6A11Q5 Z5Q3A9Q8Q3Z4Q3 A1A9A9 Q5A6A1Q5 Q6Q9Q7 A2Q3Q3.
Q2A6A1Q5 Q6Q9Q7 A2Q3Q3 Q8A2Z6A11Q5 A1A9Q2A1Q6A2 Q2A6A1Q5
Q6Q9Q7 A5Q3Q5Z9
Provide a detailed explanation along with your answer.
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Puzzle #25 : Another Taj Mahal
King Iolaus of Newtonia once visited India. He marvelled at the Taj Mahal.
When he went back, he decided to build a palace similar to the Taj Mahal to
please his wife, Sarah. He employed 3552 workers to build the monument for
him. However, soon after completing the construction, the city was hit by an
epidemic. Eight ninth of the male workers and eleven twelth of the female
workers perished during the epidemic without collecting their dues from the
Royal Treasury. Only the ones who survived got their dues. How much money
did the King finally pay the survivors if he was supposed to pay each man 45
Newtons and each woman 60 Newtons? (Newton was the currency of
Newtonia.) Provide a detailed explanation along with your answers.
Puzzle #26 : The Engineer and the Marketing Manager
One of Mr. Singhania, his wife, their son and Mr. Singhania's mother is an
engineer and another is a marketing manager.
1. If the engineer is younger than the marketing manager, then the engineer
and the marketing manager aren't blood relatives.
2. If the engineer is a woman, then the engineer and the marketing manager
are blood relatives.
3. If the marketing manager is male, then the engineer is also male.
Whose occupation do u know? Provide a detailed explanation along with your
answer.
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Puzzle #27 : Q21. of CAT 2012
The following question appeared as Question 21 in the DILR section of CAT
2012.
7
letters
were
arranged
in
a
particular
grid.
Each letter represents a different digit. Also, AxBxC, BxGxE and DxExF are equal.
What digit does letter G represent? Help the examinee crack the solution and
gain 4 precious marks. Provide a detailed solution along with your answer.
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Puzzle #28 : Q42. of CAT 2012
The following question appeared in the QA section of the CAT 2012 exam.
Q42. Find three distinct integers, A, B and C, where A + B, A + C, B + C, A - B, A c, and B - C are all squares of integers.
The three integers aren't necessarily positive.
Find the set [A, B, C] with the smallest A + B + C.
Puzzle #29 : Of Dads and Sons
Statement 1: Both dads always tell the truth or both dad always tell lies.
Statement 2: One of the sons always tell the truth while one son always lies.
Statement 3: Statement 1 and Statement 2 are not both lies.
About the 3 statements:
a. Tarun made one statement, his son made another and his dad made the
remaining.
b. Each son and dad mentioned in the three statements refers to one of the
three men mentioned above.
c. Each of them either always lies or always tells the truth.
Among statements 1, 2 & 3, which one was made by Tarun? Provide a detailed
explanation along with your answer.
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Puzzle #30 : To which party do I belong?
Of Akanksha, Bhavika and Chitra, each belongs to either the XYZ political party
whose members are always truthful or to the ABC party, whose members are
perpetual liars.
Akanksha says, "Either I belong or Bhavika belongs to a different party from the
other two.
Whose party do we know the name of? Provide a detailed explanation along
with your answer.
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ANSWERS
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Puzzle #01: Miss Braganza and her Special Grid
Discuss the solution with TestFunda users.
Puzzle #02: Be ready to beat about the bush during CAT
2010
21. D or 22
22. C or 23
23. A or 21
24. B or 24
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Puzzle #03: Phoebe's Phoebia!
4, 10, 14, 40 48, and 49.
Eliminating the prime numbers and the numbers with prime digits leave only
these numbers: 1, 4, 6, 8, 9, 10, 14, 16, 18, 40, 44, 46, 48 and 49.
The number 1 can't be played because:
a. Eliminating the numbers from this set that are 1 more than a prime leaves 1,
9, 10, 16, 40, 46 and 49.
b. But 16 - 9 = 7, 46 - 9 = 37, 16 - 10 = 6, and 46 - 40 = 6.
If the number 4 is played:
a. The numbers that can be in the set are 4, 8, 10, 14, 16, 18, 40, 44, 46, 48, and
49.
If the number 49 is in the set:
a. 8, 18, 44, and 46 can't be played.
b. 14 and 16 cannot both be played.
c. 16 can’t be played because 10 - 4 = 6 and 16 - 10 = 6.
Therefore, the numbers played are 4, 10, 14, 40 48, and 49.
If you try any other combination, you'll see that this is the only solution that
will work.
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Puzzle #04: Good Old Mr. Luis
So, Mr. Luis is 84 years old.
There are 12 months in a year, 52 weeks in a year, and 365 days in a year.
Let m be Mr. Luis's age in years. If s is his son's age in years, then his son is 52s
weeks old. If g is his grand-daughter's age in years, then his grand-daughter is
365g days old. Thus,
365g = 52s.
Since his grand-daughter is 12g months old,
12g = m.
Since his grand-daughter, his son and he together are 140 years,
g + s + m = 140.
The above system of 3 equations in 3 unknowns (g, s and m) can be solved as
follows.
m / 12 + 365 m / (52 × 12) + m = 140 or
52 m + 365 m + 624 m = 624 × 140 or
m = 624 × 140 / 1041 = 84.
So, Mr. Luis is 84 years old.
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Puzzle #05: The Complicated Corporate World
Mona is not the CEO of the 150 employees Firm, since she has more employees
to direct than Howard (clue 8), and neither of them is the CEO of the 310
employees Firm, since the CEO of that firm is Ashley (clue 5). Mona is not the
CEO of the Firm with 190 employees (clue 8). Howard works with Firm (B) as
per clue 6, and so he is not the CEO the 230 employees firm (clue 7). It is
concluded that he can not be the CEO of the 270 employees firm since Mona is
not the CEO of the 310 firm. Howard must be the CEO of the firm with 150
employees. Firm (B) then has 150 employees.
Firm (B) is not owned by Frazer who owns Firm (A) per clue 9, and it is not
owned by Mary per clue 5. Firm (B) is not owned by Alwyn who has 190
employees in his Firm, and it is not owned by Mario who has Esha as the CEO in
his firm as per clue 6. Therefore Firm (B) must be owned by Ross.
Alwyn does not own Firm (A) which is owned by Frazer (clue 5), and he does
not own Firm (B) because he has 190 employees in his Firm (clue 8), while Firm
(B) has 150 employees. He does not own Firm (D) which has 230 employees
(clue 7), and his Firm is not (E) as per clue 8. Therefore his Firm must be (C).
Firm (C) does not have Howard as the CEO (see above), and neither is Esha the
CEO since Esha works for Mario. Ashley, who works with the firm with 310
employees as per clue 5, is also not the CEO and Mona, as per clue 8, isn't the
CEO of Firm (C) either. Therefore the CEO of Firm (C) must be Warren.
Firm (A) has 80 employees more than (C) as per clue 9, and so it must have 270
employees. The CEO of (A) is neither Howard, nor Esha, nor Warren, nor Ashley
because Howard works with Ross (see above), Esha with Mario (clue 6), and
Warren works with Alwyn (see above). Ashley works with the 310 employees
Firm. Therefore Mona must be the CEO of Firm (A).
From the above, Ashley must be working for Mary in firm (E).
In short,
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1. Frazer owns Firm (A) of which Mona is the CEO and which has 270
employees.
2. Mary owns Firm (E) of which Ashley is the CEO and which has 310
employees.
3. Alwyn owns Firm (C) of which Warren is the CEO and which has 190
employees.
4. Ross owns Firm (B) of which Howard is the CEO and which has 150
employees.
5. Mario owns Firm (D) of which Esha is the CEO and which has 230 employees.
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Puzzle #06: The Mathematician's Stairs
17711. He probably is Leonardo Fibonacci.
Suppose the stairs consists of one step. Then the stairs can be painted in two
ways, see the figure above.
If the stairs have two steps, there are three possibilities.
If the stairs have three steps, there are five possibilities.
The rules for painting are:
After each orange step, there will be a maroon step.
After each maroon step, there will be either a maroon or an orange step.
Let the number of ways in which the mathematician can paint a flight of stairs
of x steps be N(x). Then it is easily seen that the latest step of stairs with x steps
can be painted maroon in N(x-1) ways. The latest step of stairs with x - 1 steps
can be painted maroon in N(x-2) ways.
From this it follows that the latest step of a stairs with x steps can be painted
orange in N(x-2) ways.
So, the mathematician can paint x steps in N(x) = N(x-1) + N(x-2) ways.
From the figure, it follows that N(1) = 2 and N(2) = 3.
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Hence
x
1 2 3 4 5 6 7 8 9 10
N(x) 2 3 5 8 13 21 34 55 89 144
A calculation learns that N(20) = 17711. The mathematician can paint his stairs
in 17711 ways. Such a series is called the Fibonacci series, after an Italian
mathematician. Hence, most probably the mathematician was Leonardo
Fibonacci.
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Puzzle #07: Find the number counting numbers
6210001000
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Puzzle #08: Letters for numbers
1728.
As P - Q = Q, P = Q + Q, which implies P = 2 * Q.
Q * R = P and P = 2 * Q
Hence, R = 2.
R * R = T. Hence, T = 2*2 = 4.
R + T = P. So, 2 + 4 = P and P = 6.
P = 2 * Q. Hence, 6 = 2 * Q. Thus, Q = 3.
S : Q = T so S : 3 = 4, which implies that S = 3 x 4 = 12.
So finally one finds P = 6, Q = 3, R = 2, S = 12 and T = 4. Hence, P*Q*R*S*T =
1728.
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Puzzle #09: Three Mice
Assume A, B & C are the three mice trapped in an equilateral triangular cage of
side 1 meter. Each one of them was at a different corner of the triangle.
Suddenly, each mouse set off running after the mouse in the adjacent corner to
its left, which means A started running towards B, B started running towards C
and C started running towards A.
Let the speed of each of the three mice be V.
Velocity of C towards A = V;
Velocity of A towards C = V* cos(600) = V/2;
Hence, the relative velocity at which C approaches A = V+V/2 = (3/2)*V;
This relative velocity will remain the same till they terminate their movement
at the center O.
Initial distance between C and A = 1 m; Hence the time spent till termination of
movement,
t = 1m /(3V/2) = 2/(3V);
Hence the distance travelled by C, D= V*t = V * [2/(3V)] =2/3 meter.
As all the mice were running at the same speed the distance travelled by each
mouse must be the same. Thus the distance travelled by each mouse is 2/3
meter or 0.6666 meter.
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Puzzle #10: The caselet of the Air-Freight-Carrier planes
Indian
12 condiments
peach
Danish
1 chocolates
magenta Los Angeles
Austrian
3 cheese
auburn
Moscow
Japanese 4 electronic goods
grey
Geneva
Egyptian
gold
La Paz
2 gems
Sydney
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Puzzle #11: Entangled Wires?
16 km.
First, Akhil connects two wires selected randomly from the 120 wires making
60 pairs of wires.
Then, he goes to the far end and randomly labels any wire 1. He then, connects
the battery to it. He, then, connects the bulb to the wires one by one, to find
which wire is tied to "1" at the starting end, and labels that wire 2.
Then he randomly picks another wire other than 1 or 2, labels it as 3, and ties it
to 2. The battery is now connected to 1, 2 and 3.
Wire 3 is tied to some other wire at the other end.
Now, using the bulb again he tests which wire is tied to 3 at the other end, and
labels that as 4. Proceeding in that manner, he will have all 120 wires tied to
each other in a continuous sequence. Then he goes back to the end where he
started at, leaving the battery behind, connected to wire 1.
At the other end, he labels each wire in a pair using letters A, B, C, D … and
then unties the pairs. The labels tell him which wire was paired with which.
Now with all the wires untied at the starting point, he can easily identify which
wire is connected to the battery, and label that as 1. Whichever wire was in the
same pair as 1, must be labelled as 2, and 1 and 2 are tied back together.
Now, he can find 3, because it's tied to 2 on the far end. Once he finds 3, he
must label the wire it was tied to as 4, and proceed further. He will soon
manage to identify all 120 wires without having to rip the ensemble apart.
And since he has only traversed the distance between the 2 exchanges twice,
he will have traversed 16 km.
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Puzzle #12: Transporting a thief
Let the side they were at initially be A and the opposite side be B. Now, the
entire process can be represented as:
A to B : Policeman + Biraj
B to A : Policeman
A to B : Policeman + Girl
B to A : Policeman + Biraj
A to B : Mrs. Pereira + Girl
B to A : Mrs. Pereira
A to B : Mrs. Pereira + Mr. Pereira
B to A : Mr. Pereira
A to B : Policeman + Biraj
B to A : Mrs. Pereira
A to B : Mr. Pereira + Mrs. Pereira
B to A : Mr. Pereira
A to B : Mr. Pereira + Boy
B to A : Policeman + Biraj
A to B : Policeman + Boy
B to A : Policeman
A to B : Policeman + Biraj
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Puzzle #13: The case of the cheating husbands
15 men.
Case 1: One cheating husband
If only one man were cheating, his wife would easily work this out on the first
day as she would have known that no other husbands were cheating and so the
cheating husband must be hers.
Case 2: Two cheating husbands
Consider this from the point of view of Mrs. B, one of the wives (B and A) who
were being cheated on, though all their positions are, in fact, the same. B
would be aware that A's husband was cheating on her and would therefore
expect that she would deduce this on the first day as in the example above. As,
this does not happen B knows that A also is aware of a cheating husband. Since
B was not aware of this, it has to be her husband who is cheating. A will go
through the same thought process and so two men will be thrown out on the
2nd day.
Case 3: Three cheating husbands
C would be aware of A's and B's cheating husbands and expect the process to
be solved as in the example above on the 2nd day. When this didn't happen,
she would know that A and B must also be aware of 2 cheating husbands and
will hence throw her husband out on the third day. A and B would do the
same.
Case 4: N cheating husbands
Any of the wives being cheated on will be aware of N-1 cheating husbands and
expect the process to be solved on the (N-1)th day. When this doesn't happen,
they all become aware that all the other wives that they thought were being
cheated were all under the same impression and hence they must be the Nth
cheated on wife. Hence on the Nth day, N wives throw out N husbands.
Hence, on the 15th day, 15 men are thrown out.
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Puzzle #14: Diwali Chocolates
She received one from Sunila, one from Chandini and 2 from Pooja.
First let's make a grid with what is given, with names at left meaning "Gives"
and names at the top meaning "Receives".
Sunila Krithika Chandini Disha Pooja
Sunila
0
Krithika 4
0
Chandini
0
Disha
3
0
Pooja
0
There are a lot of cells to fill in. First, we can see that Sunila already received
her four, so no other sister gave her any, so we can put zeros in the rest of the
first column, and also in the rest of her row. Moreover, we can notice that one
sister gave one box to each of her sisters. That sister had to be Sunila, because
none of the other other sisters could give Sunila a box because she had
received her four already. Thus we can fill in the first row too:
Sunila Krithika Chandini Disha Pooja
Sunila
0
1
1
1
1
Krithika 4
0
0
0
0
Chandini 0
Disha
0
Pooja
0
0
3
0
0
Now we look at the total in the last row and see that it is already 4. So the last
cell in the last row must be zero:
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Sunila Krithika Chandini Disha Pooja
Sunila
0
1
1
1
1
Krithika 4
0
0
0
0
Chandini 0
Disha
0
Pooja
0
0
3
0
0
0
Now we come to the problem that we don't know if Chandini gave her fourth
box to Krithika or Disha, and we need to know that to solve the problem. But
there is a way to keep filling in the table other ways. Look at Disha's boxes
received. She only has one so far and needs to get four and has only two sisters
left to give them to her. Thus, she must get one box from one sister and two
from the other. But Disha cannot receive two from Chandini, who only has one
left to give. So Disha must receive one from Chandini and two from Pooja:
Sunila Krithika Chandini Disha Pooja
Sunila
0
1
1
1
1
Krithika 4
0
0
0
0
0
1
3
Chandini 0
Disha
0
0
0
Pooja
0
2
0
Technically we are done at this point because we can say that Disha received
one box from Sunila and Chandini, and two from Pooja. But how can we resist
filling in the rest of the table? Clearly Disha must be the one giving away two
boxes to each of two sisters because there are only two left to give them to.
And so Pooja must the be sister who split up the boxes 2-1-1. Thus we can fill in
the entire table. Note that each gives four boxes and each receives four:
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Sunila Krithika Chandini Disha Pooja
Sunila
0
1
1
1
1
Krithika 4
0
0
0
0
Chandini 0
0
0
1
3
Disha
0
2
2
0
0
Pooja
0
1
1
2
0
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Puzzle #15: Sentencing the Thief
He can ask for all the pills be put in one cup except one blue pill in the other.
There was a 1/2 chance of getting the cup with the blue pill, and 100% chance
of getting a blue pill in that case. Even if he got the other one, he still had a
49/99 chance of saving himself, which is nearly 1/2. Thus, the total odds are
about 1/2 (if right cup) + 1/4 (half the time if wrong cup) = 3/4.
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Puzzle #16: A Tale from the South
Vimble and Jincy are the parents of Thomas and Mariam.
We'll start with each pair of statements and test to see whether if two are true,
are the others necessarily false. First let's assume the first two statements are
true. Statement 1 means that Vimble and Mariam are not both parents,
Statement 2 means that Thomas is the father. Now we need the last two
statements to be false. Statement 3 could be false only if Jincy is the mother,
so that would mean Thomas and Jincy are the parents. But then Statement 4
would also be true, so this is not the solution because that would be 3 true
statements.
So, now let's suppose Statement 1 is false. Then Vimble and Mariam are the
parents. This would mean that Statement 2 is also false because Vimble would
be older than his son Thomas. Statement 3 could be true because Jincy could
be Thomas's younger sister. But, Statement 4 would be false, which is too many
false statements. Thus we have deduced that Statement 1 must be true and
Statement 2 must be false.
Statement 2 being false means that Vimble is the father, and Statement 1 true
then means that Jincy is the mother. Statement 3 must then be false because
Jincy must be older than her son Thomas. That means Statement 4 needs to be
true, and it is: Jincy would be older than her daughter Mariam. So there is
exactly one solution: Vimble and Jincy are the parents of Thomas and Mariam.
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Puzzle #17: Hoping for Sunny Weather
11/243.
The probability of a clear sky on at least 4 out of 5 days is 11/243.
The probability of 5 sunny days is (1/3)^5 = 1/243.
The probability of 1 cloudy day and 4 sunny days is (2/3)*(1/3)^4 = 2/243.
There are 5 ways in which this can occur.
The probability of sun on at least 4 out of 5 days is, thus, 1/243 + 5(2/243) =
11/243.
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Puzzle #18: Shuchi's Birthday Party
The total amount of money possessed by all 50 players is 50X and this is
constant throughout the games.
Suppose the 13th player has Y amount of money at the start.
After 12 games, he will have (2^12)Y money.
The total amount of money of the other players is 50X-(2^12)Y.
Thus, after the 13th game, the 13th player gives this amount of money in total
to the other players, and he is left with (2^12)Y-(50X-(2^12)Y) = (2^13)Y-50X in
his pocket. The remaining 37 games are then played, after which the 13th
player has 2^37((2^13)Y-50X)=(2^50)Y-(2^38)*25X.
Hence, 2^50Y - (2^38)*25X = X
Thus, Y =(1+(2^38)*25)X/2^500)
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Puzzle #19 : Shuchi's Birthday Party 2
Let's call Shuchi and Kasturi 'S' and 'K'. The trick is to start at the end and work
backwards.
S wins if she says 50, she can say this if...
K says any number in the range 40 - 49 and will have to say one of these if...
S says 39, she can say this if...
K says any number in the range 29 - 38 and will have to say one of these if...
S says 28, she can say this if...
K says any number in the range 18 -27 and will have to say one of these if...
S says 17, she can say this if...
K says any number in the range 7 - 16 and will have to say one of these if...
S starts on 6.
Thus, it is pretty much clear that Shuchi will win if she starts on 6 and then
simply follows the sequence 6, 17, 28, 39, 50.
Another way of thinking about this is that Shuchi forces each pair of numbers
to go up in 11's regardless of what Kasturi says, hence she starts on 6 which is
50 - 4x11.
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Puzzle #20 : The Lazy Ant
Consider the ant at point E and the grain of sugar at point C in the folowing
diagram.
We have to get from point E to point C only moving along the walls.
The shortest route is shown it is E-I-C where I is the mid point of DH.
Assume the cube has sides of length 1 unit. The distance EI is the hypotenuse of
a triangle. Using Pythagoras' theorem, we get that EI = sqrt(5/4). Similarly, IC
has the same length. Hence the total length = 2 x sqrt(5/4) = sqrt(5) = 2.236.
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Puzzle #21 : LINKing your rent
Only two links need to be cut.
She can cut link number 4 and link number 11, counting from the same
beginning link.
She will then haves 2 pieces of length 1 (the cut links), and one each of 3, 6, and
12 links. She can thuse can then pay the rent as follows:
One each of the first two days, she can give a cut link.
On Day 3, she can give the chain with 3 links and get the two cut links back.
Then, she can use them on days 4 and 5, and then trade all the links given so
far and give the 6-link chain on Day 6.
She repeats the first steps for days 7-11. On day 12, she gets back all those links
and gives the 12-link chain. She then repeats the actions of the first 11 days to
go all the way though day 23.
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Puzzle #22 : The case of the blue bandanas
Everyone can see that each man could be thinking that his bandana might be
blue or black because the other two men could be raising their hands because
of each other. Again, this is the point where most people stop, and indeed,
where the men stopped while all three hands were up. The trick to solving this
problem is to REALLY put yourself into the smart man's shoes. If you REALLY
were he, you'd say, either I have a blue or a black bandana. Suppose you had a
black bandana. The other two men would be looking at one black bandana and
one blue. They would each quickly figure out that that only reason the other's
hand was up was because of their own blue bandana. The fact that neither of
them figured it out was the tip off to the first that he must also have a blue
bandana. Most people put themselves in the place of the first person, but to
solve this one, you must then also put yourself in the place of a second man.
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Puzzle #23 : At which table have you been seated?
Manish - 128
Rohit - 140.
All one needs to do is take the sum of the values of the letters and then double
it. Put A = 1, B = 2 and so on.
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Puzzle #24 : Use all your devices
Don't believe all that you see. What you see isn't always what you get.
The message can be easily decoded using a QWERTY keyboard. Each latternumber pair represents a letter/symbol. The first character of a letter is always
Q, A or Z, specifying which row on a QWERTY keyboard the letter is on. The
number succeeding the letter is the position of the letter on a QWERTY
keyboard from left to right along the row. For example, A1 is 'A', A2 is 'S', A3 is
'D' and so on.
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Puzzle #25 : Another Taj Mahal
17,760 Newtons.
If there are x men, then there are (3552 - x) women.
Thus, one ninth of the men (= x / 9) received 45 N and one twelfth of the
women (= (3552 - x) / 12) received 60 N.
So, the total amount received is (45 * (x / 9)) + (60 * (3552 - x) / 12).
x cancels out, leaving 5 * 3552 = 17,760.
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Puzzle #26 : The Engineer and the Marketing Manager
The 2 women aren't blood relatives. So, from (2), if the engineer is a woman,
the marketing manager is a man. Then from (3), the engineer is a man. Because
a contradiction arises from assuming the engineer is a woman, the engineer
must be a man.
Mr. Singhania's son is the youngest of the four and is a blood relative of the
other 3. So, from (1), the engineer is not Mr. Singhania's son. Then you know
the occupation of Mr. Singhania. He is the engineer.
From (1), then, the marketing manager cannot be Mr. Singhania's mother. So,
the marketing manager is either his wife or son. (The engineer may be older
then the marketing manager.) So, we don't know the occupation of anyone
else.
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Puzzle #27 : Q21. of CAT 2012
As each letter represents a different digit and AxBxC, BxGxE and DxExF are
equal, no letter can be 0, 5 or 7. The product for each row is a multiple of 1, 2,
3, 4, 6, 8 and 9. So, the smallest possible product is 9x8 = 72 and the product is
a multiple of 72. But the product cannot be any of 72x2, 72x3 etc. as it is not
possible to get a product larger than 72 three times. Hence, the product is 72.
Then, 72 = 1x8x9 = 2x36
= 2X4X9 = 3X24
= 3x4x6
Because 4 & 9 are used twice, B or E is 4 and the other is 9. Hence, G is 2.
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Puzzle #28 : Q42. of CAT 2012
[A, B, C] = [17, 8, -8]
If we take the sums and differences of the equations involving A and B, we find
that 2A is the sum of two squares in two different ways, 2C is the difference of
two
squares in two different ways, and 2B is both the sum of two squares and the
difference of two squares.
Thus, we know that the squared integers in the equations for 2A, 2B, and 2C
must be either both even or both odd.
As we are looking for the minimum solution for A + B + C, we take cases in
which the integers that are squared are small, perhaps 0 through 10. Working
through those values yields the answer given above.
Discuss the solution with TestFunda users.
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Puzzle #29 : Of Dads and Sons
If Statement 3 is false, statement 1 and statement 2 are both false. But from a,
b and c, if 1 is false, 2 or 3 is true, as a false statement 1 implies one dad always
lies while the other always tells the truth. So, statement 3 cannot be false and
must be true.
As Statement 3 is true, at least 1 or 2 is true. But, from a and b, if statement 2 is
true, statement 1 or 3 is false. So, If statement 2 is true, statement 1 is false.
In short:
Case 1 Case 2
Statement 1 True
False
Statement 2 False True
Statement 3 True
True
If case 1 were the correct one, from statement 1 & b, the speakers of 1 and 3
would be fathers; and from statement 2 and from b and c, the speakers of 1
and 3 will both be sons (because a false statement B implies both sons always
tell the truth or both always lie). This situation is impossible from a as only
Tarun is both a father and a son; so case 1 isn't a valid case.
Thus, Case 2 is the correct one. Hence, from statement 1, b and c, the speaker
of statement 1 is a father and from statements 2 and b, the speaer of
statement 1 is a son. So, from a, Tarun made statement 1.
Discuss the solution with TestFunda users.
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The LEADER in Online Test Prep
Puzzle #30 : To which party do I belong?
Bhavika's party - ABC party.
From the given statement,
Case 1: If Akanksha's statement is true, all three cannot be members of the XYZ
party and Chitra cannot be the only one of the three who is a member of the
ABC party.
So, if Akanksha's statement is true, either: Akanksha is the only one of the
three who is a member of the XYZ party or Bhavika is the only member of the
three who is a member of the XYZ party.
Case 2: If Akanksha's statement is false, Akanksha cannot be the only member
of the 3 who is a member of the ABC party and Bhavika cannot be the only one
of the three who is a member of the XYZ party. So, if Akanksha's statement is
false, either: Chitra is the only one of the three who is a member of the XYZ
party or all three are members of the XYZ party.
Then: Akanksha is a member of the XYZ party in case 1 and Akanksha is a
member of the ABC party in case 2. Bhavika is a member of the ABC party in
case 1 and Bhavikais a member of the XYZ party in case 2. Chitra may be a
member of either party in case 1 and Chitra might be member of either family
in case 2.
So, you only know the political party to which Bhavika belonged - ABC party.
Discuss the solution with TestFunda users.
Book 2 of TestFunda Puzzles
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The LEADER in Online Test Prep
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