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 Pattern of Written Test

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Gurunanak
Institute of Technology,Kolkata)
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1. Alok and Bhanu play the following min-max game. Given the expression N=40 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

• 49
• 51
• 31
• 58

2. 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 14 such programmers take 14 minutes to write 14 lines
of code in total. How long will in take 5 programmers to write 5 lines of code in total ?

• 19
• 5
• 14
• 70

3. 14 people meet and shake hands. The maximum number of handshakes possible if there is to be
no ‘cycle’ of handshakes is (A cycle of handshakes is a sequence of people a1, a2,…ak, k>2 such
that the pairs {a1,a2}, {a2,a3},…, {a(k-1), ak}, {ak, a1} shake hands).

• 11
• 12
• 10
• 13

4. 45 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 the suspects are lying. B. The leftmost suspect is guilty. C. The rightmost suspect is
guilty.

• A only
• A and C
• B only
• A and B
5. The Barnes Foundation in Philadelphia has one of the most extra-ordinary and idiosyncratic
collections in French impressionist art. Dr. Barnes who put together this collection has insisted
that the paintings be hung in a particular manner specified by him at a museum designed by
the French architect Paul Philippe Cret who also designed the Rodin Museum. The museum
has, say, seven galleries – Eugene Boudin, Cassatt, Boudin, Forain, Gonzales, Manet and Monet.
Visitors reach the main Eugene Boudin by an elevator, and they can enter and leave the exhibition
only through Eugene Boudin gallery. Once inside, visitors are free to move as they choose.
The following list includes all of the doorways that connect the seven galleries: There is a
doorway between Eugene Boudin and Cassatt, a doorway between Eugene Boudinand Boudin,
and a doorway between Eugene Boudin and Gonzales galleries. There is a doorway between
Cassatt and Boudin galleries. There is a doorway between Gonzales and Forain and a doorway
between Gonzales and Manet galleries. There is a doorway between Manet and Monet galleries.
Which of the following rooms CANNOT be the third gallery that any visitor enters ?

• Monet
• Boudin
• Forain
• Cassatt

6. Mr. Beans visited a magic shop and bought some magical marbles of different colours along with
other magical items. While returning home whenever he saw a coloured light, he took out marbles
of similar colours and counted them. So he counted the pink coloured marbles and found that he has
bought 25 of them. Then he counted 14 green marbles and then 21 yellow marbles. He later
counted 30 purple coloured marbles with him. But when he reached a crossing, he looked at
a red light and started counting red marbles and found that he had bought 23 Red marbles.
As soon as he finished counting, it started raining heavily and by the time he reached home
he was drenched. After reaching home he found that the red, green and yellow marbles had
magically changed colours and became white, while other marbles were unchanged. It will
take 1 day to regain its colours, but he needs to give atleast one pair of marbles to his wife now.
So how many white marbles must be choose and give to his wife so as to ensure that there is
atleast one pair of red, yellow and green marbles ?

• 46;
• 35
• 29
• 48

7. A greengrocer was selling watermelon at a penny each, chickoos at 2 for a penny and peanuts at
3 for a penny. A father spent 7p and got the same amount of each type of fruit for each of his three
children, Jane, Joe and Jill. Jane is three years older than Jill and Joe is exactly half the age of Jane
and Jill together. What did each child get ?

• 1 watermelon, 3 chickoos, 2 peanuts
• 1 watermelon, 1 chickoo, 1 peanus
• 1 watermelon, 2 chickoos, 2 peanuts
• 1 watermelon, 2 chickoos, 1 peanut

8. Given 3 lines in the plane such that the points of intersection from a triangle with sides of length
20, 20 and 20, the number of points equidistant from all the 3 lines is

• 4
• 3
• 0
• 1

9. 33 people {a1, a2,…,a33} meet and shake hands in a circular fashion. In other words, there are totally
33 handshakes involving the pairs, {a1,a2}, {a2,a3},…,{a32, a33}, {a33, a1}. Then the size of the smallest
set of people such that the rest have shaken hands with at least one person in the set is

• 10
• 11
• 16
• 12
10. Consider two vessels, the first containing on litre of water and the second containing one litre of
pepsi. Suppose you take one glass of water out of the first vessel and pour it into the second vessel.
After mixing you take one glass of the mixture from the second vessel and pour it back into the first
vessel. Which one of the following statements holds now?

• None of the statements holds true.
• There is less Pepsi in the first vessel than water in the second vessel.
• There is more Pepsi in the first vessel than water in the second vessel.
• There is as much Pepsi in the first vessel as there is water in the second vessel.

11. Amok is attending a workshop ‘How to do more with less’ and today’s theme is Working with fever
digits. The speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as well
as womankind) had only worked with fever digits. The problem posed at the end of the workshop is
‘How many 10 digit numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that are
divisible by 4?’ Can you help Amok find the answer?

• 1953125
• 781250
• 2441407
• 2441406

12. 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 wining. 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 11/12 of winning
the game. What is the probability that Paul with correctly pick the winner of the Ghana-Bolivia game?

• .92
• .01
• .85
• .15

13. There are two boxes, one containing 39 red balls and the other containing 26 green balls. You
are allowed to move the balls between the boxes so that when you choose a box at random and
a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum
probability is

• .60
• .50
• .80
• .30

14. After the typist writes 40 letters and addresses 40 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 improver envelope?

• 1 – 1/40
• 1/40
• 1/401
• 0

15. 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 1/3 of its distance
and that too leisurely. The hare and tortoise meet when the hare has covered only 1/4 of the
distance. By what factor should be hare increase its speed so as the win the race?

• 4
• 3
• 12
• 5.00

16. A sheet of paper has statements numbered from 1 to 20. For each value of n from 1 to 20,
statements n says ‘At least n of the statements on this sheet are true.’ Which statements are
true and which are false?

• The odd numbered statements are true and the even numbered are false.
• The first 13 statements are false and the rest are true.
• The first 6 statements are true and the rest are false.
• The even numbered statements are true and the odd numbered are false.

17. The question is followed by two statements, A and B. Answer the question using the
following instructions: Choose 1: if the question can be answered by using one of the
statements alone but not by using the other statement alone. Choose 2: if the question can
be answered by using either of the statements alone. Choose 3: if the question can be
answered by using both statements together but not by either statement alone.
Choose 4: if the question cannot be answered on the basis of the two statements.
Zaheer spends 30% of his income on his children’s education, 20% on recreation and
10 % on healthcare. The corresponding percentages for Sandeep are 40%, 25% and
13%. Who spends more on children’s education? A” Zaheer spends more on recreation
that Sandeep B: Sandeep spends more on healthcare than Zaheer.

• 3
• 2
• 1
• 4
18. Subha Patel is an olfactory scientist working for International Flavors and Fragrances. She
specializes in finding new scents recorded and reconstituted from nature thanks to Living Flower
Technology. She has extracted fragrance ingredients from different flowering plants into bottles
labeled herbal, sweet, honey, anisic and rose. She has learned that a formula for a perfume is
acceptable if and only if it does not violate any of the rules listed: If the perfume contains herbal,
it must also contain honey and there must be twice as much honey as herbal. If the
perfume contains sweet, it must also contain anisic, and the amount of anisic must
equal the amount of sweet. honey cannot be used in combination with anisic. anisic
cannot be used in combination with rose. If the perfume contains rose, the amount
of rose must be greater than the total amount of the other essence or essences
used. Which of the following could be added to an unacceptable perfume consisting
of two parts honey and one part rose to make it acceptable?

• Two parts rose
• One part herbal
• Two parts honey
• One part sweet

19. The citizens of planet Oz are 6 fingered and thus have developed a number system
in base 6. A certain street in Oz contains 1000 buildings numbered from 1 to 1000.
How many 3’s are used in numbering these buildings? Express your answer in
base 10.

• 144
• 54
• 108
• 36

20. Recent reports have suggested that sportsmen with decreased metabolic rates
perform better in certain sports. After reading one such report, Jordan, a sportsperson
from Arlington decides to undergo a rigorous physical training program for 3 months,
where he performs Yoga for 3 hours, walks for 2 hours and swims for 1 hour each day.
He says: I began my training on a Wednesday in a prime number month of 2008. I lost
1% of my original weight within the first 30 days. In the next two months combined, I
lost 1 Kg. If he walks at 5 mph over a certain journey and walks back over the same
route at 7 mph at an altitude of 200 meters, what is his average speed for the journey?

• 5.83
• 2.92
• 6.00
• 35.00
21. A schoolyard contains only bicycles and 4 wheeled wagons. On Tuesday, the total
number of wheels in the schoolyard was 134. What could be possible number of
bicycles?

• 16
• 15
• 18
• 14

22. A sheet of paper has statements numbered from 1 to 20. For all values of n from
1 to 20, 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.
• All the statements are false.
• The odd numbered statements are true and the even numbered statements are false.
• The second last statement is true and the rest are false.
23. There are two water tanks A and B, A is much smaller than B. While water fills at
the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160 .. in tank
B. (At the end of first hour, B has 10 litres, second hour it has 20, and so on). If tank
B is 1/8 filled after 5 hours, what is the total duration required to fill it completely?

• 9 hours
• 7 hours
• 3 hours
• 8 hours
24. 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
25. Alice and Bob play the following coins-on-a-stack game. 100 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 (for some I between 0 and 100). 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
coin is the third coin from the top. Then

• In order to win, Alice’s first move should be a 1-move.
• In order to win, Alice’s first move should be a 0-move.
• Alice has no winning strategy.
• In order to win, Alice’s first move can be a 0-move or a 1-move.

26. The teacher is testing a student’s proficiency in arithmetic and poses the
following question: 1/2 of a number is 3 more than 1/6 of the same number.
What is the number?
Can you help the student find the answer?

• 9
• 8
• 10
• 3

27. A circular dashboard of radius 1.0 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?

• 1.00
• .75
• .25
• .50

28. A result of global warming is that the ice of some glaciers is melting. 13
years after the ice disappears, tiny plants, called lichens, start to grow on the
rocks. Each lichen grows approximately in the shape of a circle. The relationship
between the diameter of this circle and the age of the lichen can be approximated
with the formula: d=10*(t – 13) for t > 13, where d represents the diameter of
the lichen in millimeters, and t represents the number of years after the ice has
disappeared. Using the above formula, calculate the diameter of the lichen, 45
years after the ice has disappeared.

• 450
• 437
• 13
• 320
29. A greengrocer was selling orange at a penny each, olives at 2 for a penny
and grapes at 3 for a penny. A father spent 7p and got the same amount of each
type of fruit for each of his three children, Jane, Joe, and Jill. Jane is three years
older than Jill and Joe is exactly half the age of Jane and Jill together. What
did each child get?

• 1 orange, 2 olives, 2 grapes
• 1 orange, 3 olives, 2 grapes
• 1 orange, 1 olive, 1 grape
• 1 orange, 2 olives, 1 grape
30. A sheet of paper has statements numbered from 1 to 20. For each value
of n from 1 to 20, statement n says ‘At least n of the statements on this
sheet are true.’ Which statements are true and which are false?

• The even numbered statements are true and the odd numbered are
false
• The first 13 statements are false and the rest are true.
• The fist 6 statements are true and the rest are false.
• The odd numbered statements are true and the even numbered are false.
31. Ferrari S.p.A. is an Italian sports car manufacturer base in Maranello, Italy.
Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsored
driver and manufactured race cars before moving into production of street –
legal vehicles in 1947 as Ferrari S.p.A..Throughout its history, the company
has bee noted for its continued participation in racing, especially in Formula
One, where it has enjoyed great success. Rohit once brought a Ferrari. It
could go 2 times as fast as Mohit’s old Mercedes. If the speed of Mohit’s
Mercedes is 40 Km/hr and the distance traveled by the Ferrari is 913 Km,
find the total time taken for Rohit to drive the distance.

• 12 Hours
• 22 Hours
• 456 Hours
• 11.41 Hours
32. The result of global warming is the ice of some glaciers is melting.
19 years after the ice disappears, tiny planets, called lichens, start to
grow on the rock. Each lichen grows approximately in the shape of a
circle. The relationship between the diameter of the circle and the age
of the lichen can be approximated with the formula: d =12* (t-19) for
t>19, where d represents the diameter of the lichen in millimeters, and
t represents the number of years after the ice has disappeared. Using
the above formula, calculate the diameter of the lichen, 32 years after
the ice has disappeared.

• 384
• 156
• 19
• 365
33. There are two boxes, one contains 12 red balls and the other containing 47
green balls. You are allowed to move the balls between the boxes so that when
you choose a box at random and a ball at random from the chosen box, the
probability of getting a red ball is maximized. This maximum probability is:

• .59
• .20
• .10
• .50
34. The citizens of planet Oz are fingered and thus have developed a number
system in base 6. A certain street in Oz contains 1000 buildings numbered from
1 to 1000. How many 2’s are used in numbering these buildings? Express your

• 144
• 24
• 108
• 36
35. 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 we as womankind) had only worked
with fewer digits. The problem posed at the end of the workshop is ‘How many
6 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?

• 3906
• 3907
• 3125
• 1250

 TzwSVsOw   subhadeep..If You belong from CS Stream..J2ee is needed otherwise leave it if u have prob. Saturday, October 22, 2011, 11:38 am
 TzwSVsOw   plz send me the solutions on my id i.e,siddharthtrivedi3@gmail.com Friday, August 17, 2012, 7:08 pm