Placement Paper
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1. The teacher is testing a student's
proficiency in arithmetic and poses the following question.
1/3 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
(a)12
(b)18
(c)21
(d) 6
ANS---B
2. Ferrari S.p.A. is an Italian sports
car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as
Scuderia Ferrari, the company sponsored drivers 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 been noted for its continued
participation in racing, especially in Formula One, where it has enjoyed great
success. Rohit once bought a Ferrari. It could go 2 times as fast as Mohit's
old Mercedes. If the speed of Mohit's Mercedes is 32 km/hr and the distance
travelled by the Ferrari is 952 km, find the total time taken for Rohit to
drive that distance.
(a)14.88
(b)476
(c)29.75
(d)15.88
ANS-A
3. A man is standing in front of a
painting of a man, and he tells us the following: Brothers and sisters have I
none, but this man's father is my father's son. Who is on the painting?
(a)He himself
(b)His father
(c)His son
(d)His grandfather
ANS-C
4. One day Rapunzel meets Dwarf and Byte
in the Forest of forgetfulness. She knows that Dwarf lies on Mondays, Tuesdays
and Wednesdays, and tells the truth on the other days of the week. Byte, on the
other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on
the other days of the week. Now they make the following statements to Rapunzel
- Dwarf: Yesterday was one of those days when I lie. Byte: Yesterday was one of
those days when I lie too. What day is it?
(a)Tuesday
(b)Sunday
(c)Thursday
(d)Monday
ANS-C
5. A greengrocer was selling apple 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. What did each child get?
1 apple, 2 chickoos,
1 peanut
1 apple, 1 chickoo, 1
peanut
1 apple, 3 chickoos,
2 peanuts
1 apple, 2 chickoos,
2 peanuts
ANS: 1 apple, 2
chikoos, 1 peanut
ANS-A
6. 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 ans also write code at the same
rate.Suppose 12 such programmers take 12 minutes to write 12 lines of code in
total. How long will it take 72 programmers to write 72 lines of code in total?
12
72
18
6
ANS-A
7. 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
800
500
488
ANS-D
8. There are two boxes, one containing 10
red balls and the other containing 10 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
37/38
1/2
14/19
3/4
ANS-C-14/19
9. 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 1/32 of B's
volume is filled after 3 hours, what is the total duration required to fill it
completely?
7 hours
9 hours
8 hours
10 hours
ANS-C
10. A hare and a tortoise have a race along
a circle of 100 yards diameter. The tortoise goes in one direction and the hare
in the other. The hare starts after the tortoise has covered 1/5 of its
distance and that too leisurely. The hare and tortoise meet when the hare has
covered only 1/8 of the distance. By what factor should the hare increase its
speed so as to tie the race?
8
37.80
40
5
ANS-B
11. Planet fourfi resides in 4-dimensional
space and thus the currency used by its residents are 3-dimensional objects.
The rupee notes are cubical in shape while their coins are spherical. However
the coin minting machinery lays out some stipulations on the size of the coins.
The diameter of the
coins should be at least 64mm and not exceed 512mm.
Given a coin, the
diameter of the next larger coin is at least 50% greater.
The diameter of the
coin must always be an integer.
You are asked to
design a set of coins of different diameters with these requirements and your
goal is to design as many coins as possible. How many coins can you design?
ANS-6
12. The pace length P is the distance
between the rear of two consecutive footprints. For men, the formula, n/P = 144
gives an approximate relationship between n and P where, n = number of steps
per minute and P = pacelength in meters. Bernard knows his pacelength is 164cm.
The formula applies to Bernard's walking. Calculate Bernard's walking speed in
kmph.
ANS-23.238 KMPH
On the planet Oz,
there are 8 days in a week- Sunday to Saturday and another day called Oz day.
There are 36 hours in a day and each hour has 90 min while each minute has 60
sec. As on earth, the hour hand covers the dial twice every day.
Find the approximate
angle between the hands of a clock on Oz when the time is 12:40 am.
ANS-88.88 DEGREE.
13. 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 ans also write code at the same rate.Suppose 12 such
programmers take 12 minutes to write 12 lines of code in total. How many lines
of code can be written by 72 programmers in 72 minutes?
ANS-12
14. Given a collection of points P in the
plane, a 1-set is a point in P that can be separated from the rest by a line;
i.e. the point lies on one side of the line while the others lie on the other
side. The number of 1-sets of P is denoted by n1(P). The maximum value of n1(P)
over all configurations P of 10 points in the plane is
ANS--Max= 10 Min= 3
15. Alok and Bhanu play the following
min-max game. Given the expression
N = 12 + 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 plays to their optimal strategies, the value of N at the end of the game
would be
a)12
b)30
c)93
d)-69
ANS-30
16. There are two boxes, one containing 10
red balls and the other containing 10 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
37/38
14/19
3/4
ANS-14/19
17. 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?
ANS-488
18. A sheet of paper has statements numbered
from 1 to 30. For all values of n from 1 to 30, statement n says "At most
n of the statements on this sheet are false". Which statements are true
and which are false?
All statements are
false.
The odd numbered
statements are true and the even numbered are false.
The even numbered
statements are true and the odd numbered are false.
All statements are
true.
ANS-ALL STATEMENTS
TRUE
19. A hare and a tortoise have a race along
a circle of 100 yards diameter. The tortoise goes in one direction and the hare
in the other. The hare starts after the tortoise has covered 1/5 of its
distance and that too leisurely. The hare and tortoise meet when the hare has
covered only 1/8 of the distance. By what factor should the hare increase its
speed so as to tie the race?
ANS-GIVEN ABOVE
20. 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 1/32 of B's
volume is filled after 3 hours, what is the total duration required to fill it
completely?
7 hours
9 hours
10 hours
8 hours
ANS-8 HRS
21. Anoop managed to draw 7 circles of equal
radii with their centres on the diagonal of a square such that the two extreme
circles touch two sides of the square and each middle circle touches two
circles on either side. Find the ratio of the radius of the circles to the side
of the square.
1:(2+ 6
1:(2+ 6√2)
1:(4+ 7
1:(4+ 7√3)
1
1:(2+ 7
1:(2+ 7√2)
(2+ 7√2):1
ANS-1/(2+6SQRT(2))
22. The teacher is testing a student's
proficiency in arithmetic and poses the following question.
1/3 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?
ANS-18
23. 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 ans also write code at the same rate.Suppose 12 such
programmers take 12 minutes to write 12 lines of code in total. How long will
it take 72 programmers to write 72 lines of code in total?
72
6
12
18
ANS-12
24. .Alok and Bhanu play the following
min-max game. Given the expression
N = 12 + 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
-69
93
12
30
ANS-30
25. Given a collection of points P in the
plane, a 1-set is a point in P that can be separated from the rest by a line;
i.e. the point lies on one side of the line while the others lie on the other
side. The number of 1-sets of P is denoted by n1(P). The maximum value of n1(P)
over all configurations P of 10 points in the plane is
5
10
3
ANS-SRY NO IDEA
26. On the planet Oz, there are 8 days in a
week- Sunday to Saturday and another day called Oz day. There are 36 hours in a
day and each hour has 90 min while each minute has 60 sec. As on earth, the
hour hand covers the dial twice every day.
Find the approximate
angle between the hands of a clock on Oz when the time is 12:40 am.
251
111
71
89
ANS-89
27. A hare and a tortoise have a race along
a circle of 100 yards diameter. The tortoise goes in one direction and the hare
in the other. The hare starts after the tortoise has covered 1/5 of its
distance and that too leisurely. The hare and tortoise meet when the hare has
covered only 1/8 of the distance. By what factor should the hare increase its
speed so as to tie the race?
37.80
8
5
40
ANS-37.80
29. Anoop managed to draw 7 circles of equal
radii with their centres on the diagonal of a square such that the two extreme
circles touch two sides of the square and each middle circle touches two
circles on either side. Find the ratio of the radius of the circles to the side
of the square.
1:(2+ 6
1:(2+ 6√2)
(2+ 7√2):1
1:(2+ 7√2)
1:(4+ 7√3)
ANS-1:(2+6SQRT(2))
30. A sheet of paper has statements numbered
from 1 to 30. For all values of n from 1 to 30, statement n says "At most
n of the statements on this sheet are false". Which statements are true
and which are false?
The odd numbered
statements are true and the even numbered are false.
All statements are
false.
All statements are
true.
The even numbered
statements are true and the odd numbered are false.
ANS-ALL STATEMENTS
ARE TRUE
31. The pacelength P is the distance between
the rear of two consecutive footprints. For men, the formula, n/P = 144 gives
an approximate relationship between n and P where, n = number of steps per
minute and P = pacelength in meters. Bernard knows his pacelength is 164cm. The
formula applies to Bernard's walking. Calculate Bernard's walking speed in
kmph.
-11.39
23.62
8.78
236.16
ANS-NOT MATCHING
14.16KMPH COMING.SOLVE AND SEE
32. There are two boxes, one containing 10
red balls and the other containing 10 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
14/19
3/4
1/2
37/38
ANS-14/19
33. 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?
500
800
488
900
ANS-488
34. The teacher is testing a student's
proficiency in arithmetic and poses the following question.
1/3 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?
6
18
21
12
ANS-18
35. 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 1/32 of B's
volume is filled after 3 hours, what is the total duration required to fill it
completely?
8 hours
9 hours
10 hours
7 hours
ANS-8
36. Planet fourfi resides in 4-dimensional
space and thus the currency used by its residents are 3-dimensional objects.
The rupee notes are cubical in shape while their coins are spherical. However
the coin minting machinery lays out some stipulations on the size of the coins.
•The diameter of the
coins should be at least 64mm and not exceed 512mm.
•Given a coin, the
diameter of the next larger coin is at least 50% greater.
•The diameter of the
coin must always be an integer.
You are asked to
design a set of coins of different diameters with these requirements and your
goal is to design as many coins as possible. How many coins can you design?
6
9
8
ANS-6
37. Ferrari S.p.A. is an Italian sports car
manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as
Scuderia Ferrari, the company sponsored drivers 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 been noted for its continued
participation in racing, especially in Formula One, where it has enjoyed great
success. Rohit once bought a Ferrari. It could go 2 times as fast as Mohit's
old Mercedes. If the speed of Mohit's Mercedes is 32 km/hr and the distance
travelled by the Ferrari is 952 km, find the total time taken in hours for
Rohit to drive that distance.
15.88
29.75
14.88
476
ANS-15.88
38. For the FIFA world cup, Paul the octopus
has been predicting the winner of each match with amazing success. It is
rumored that in a match between 2 teams A and B, Paul picks A with the same
probability as A's chances of winning.
Let's assume such
rumors to be true and that in a match between Ghana and Bolivia, Ghana the
stronger team has a probability of 2/3 of winning the game. What is the
probability that Paul will correctly pick the winner of the Ghana-Bolivia game?
4/9
5/9
1/9
2/3
ANS-5/9
39. A sheet of paper has statements numbered
from 1 to 40. For each value of n from 1 to 40, statement n says "At least
n of the statements on this sheet are true." Which statements are true and
which are false?
The first 13
statements are true and the rest are false.
The first 26
statements are false and the rest are true.
The odd numbered
statements are true and the even numbered are false.
The even numbered
statements are true and the odd numbered are false
ANS-A)NOT SURE??
40. Alice and Bob play the following
coins-on-a-stack game. 20 coins are stacked one above the other. One of them is
a special (gold) coin and the rest are ordinary coins. The goal is to bring the
gold coin to the top by repeatedly moving the topmost coin to another position
in the stack.
Alice starts and the
players take turns
s. A turn consists of
moving the coin on the top to a position i below the top coin (0 ≤ i ≤ 20). We
will call this an i-move (thus a 0-move implies doing nothing). The proviso is
that an i-move cannot be repeated; for example once a player makes a
2-move on subsequent turns neither
player can make a 2-move.
If the gold coin
happens to be on top when it's a player's turn then the player wins the game.
Initially, the gold coins
the third coin from the top. Then
Alice has no winning
strategy.
In order to win,
Alice's first move should be a 0-move.
In order to win,
Alice's first move can be a 0-move or a 1-move.
In order to win,
Alice's first move should be a 1-move
ANS--?
41. A circular dartboard of radius 1 foot is
at a distance of 20 feet from you. You throw a dart at it and it hits the
dartboard at some point Q in the circle. What is the probability that Q is
closer to the center of the circle than the periphery?
0.5
0.75
0.25
1
ANS-0.25
42. Suspects are rounded by the police and
questioned about a bank robbery. Only one of them is guilty. The suspects are
made to stand in a line and each person declares that the person next to him on
his right is guilty. The rightmost person is not questioned. Which of the
following possibilities are true?
A. All suspects are
lying or the leftmost suspect is innocent.
B. All suspects are
lying and the leftmost suspect is innocent.
B only
Neither A nor B
Both A and B
A only
ANS-NEITHER A NOR B
BCOZ THERE IS NO ONE RIGHT OF THE LEFTMOST(THINK W.R.T PERSON)NOT U.THERE LIES
THE TRICK.
43. A sheet of paper has statements numbered
from 1 to 40. For all values of n from 1 to 40, statement n says: 'Exactly n of
the statements on this sheet are false.' Which statements are true and which
are false?
A.All the statements
are false.
B.Th.e odd numbered
statements are true and the even numbered statements are false.
C.The even numbered
statements are true and the odd numbered statements are false.
D.The 39th statement
is true and the rest are false
ANS-D
44. 36 people {a1, a2, ..., a36} meet and
shake hands in a circular fashion. In other words, there are totally 36
handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}.
Then size of the smallest set of people such that the rest have shaken hands
with at least one person in the set is
11
12
18
13
ANS-12
45. After the typist writes 12 letters and
addresses 12 envelopes, she inserts the letters randomly into the envelopes (1
letter per envelope). What is the probability that exactly 1 letter is inserted
in an improper envelope?
1/12
11/12
12/212
ANS-0
46. Alok is attending a workshop "How
to do more with less" and today's theme is Working with fewer digits . The
speakers discuss how a lot of miraculous mathematics can be achieved if mankind
(as well as womankind) had only worked with fewer digits.
The problem posed at
the end of the workshop is
How many 5 digit
numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that
are divisible by 4?
Can you help Alok
find the answer?
3125
500
375
625
ANS-3125
47. 10 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 k people a1, a2, ......,
ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, ......, {ak-1, ak}, {ak,
a1} shake hands).
9
6
7
8
ANS-9
48. Given 3 lines in the plane such that the
points of intersection form a triangle with sides of length 20, 20 and 30, the
number of points equidistant from all the 3 lines is
1
4
3
ANS-CENTROID
49. The citizens of planet nigiet are 8
fingered and have thus developed their decimal system in base 8. A certain
street in nigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How
many 3s are used in numbering these buildings?
54
192
64
256
ANS-192
50. On planet zorba, a solar blast has
melted the ice caps on its equator. 8 years after the ice melts, tiny plantoids
called echina start growing on the rocks. echina grows in the form of a circle
and the relationship between the diameter of this circle and the age of echina
is given by the formula
d = 4 * √ (t - 8) for
t ≥ 8
where d represents
the diameter in mm and t the number of years since the solar blast.
Jagan recorded the
radius of some echina at a particular spot as 8mm. How many years back did the
solar blast occur?
24
16
ANS-24
52. Planet fourfi resides in 4-dimensional
space and thus the currency used by its residents are 3-dimensional objects.
The rupee notes are cubical in shape while their coins are spherical. However
the coin minting machinery lays out some stipulations on the size of the coins.
The diameter of the
coins should be at least 64mm and not exceed 512mm.
Given a coin, the
diameter of the next larger coin is at least 50% greater.
The diameter of the
coin must always be an integer.
You are asked to
design a set of coins of different diameters with these requirements and your
goal is to design as many coins as possible. How many coins can you design?
ANS-6
53. The pacelength P is the distance between
the rear of two consecutive footprints. For men, the formula, n/P = 144 gives
an approximate relationship between n and P where, n = number of steps per
minute and P = pacelength in meters. Bernard knows his pacelength is 164cm. The
formula applies to Bernard's walking. Calculate Bernard's walking speed in
kmph.
236.16
23.62
11.39
8.78 3
ANS-14.16KMPH
54. Ferrari S.p.A. is an Italian sports car
manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as
Scuderia Ferrari, the company sponsored drivers 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 been noted for its continued
participation in racing, especially in Formula One, where it has enjoyed great
success. Rohit once bought a Ferrari. It could go 2 times as fast as Mohit's
old Mercedes. If the speed of Mohit's Mercedes is 32 km/hr and the distance
travelled by the Ferrari is 952 km, find the total time taken in hours for
Rohit to drive that distance.
15.88
29.75
14.88
ANS-A
55. On the planet Oz, there are 8 days in a
week- Sunday to Saturday and another day called Oz day. There are 36 hours in a
day and each hour has 90 min while each minute has 60 sec. As on earth, the
hour hand covers the dial twice every day.
Find the approximate
angle between the hands of a clock on Oz when the time is 12:40 am.
ANS-89DEGREE
56. Given a collection of points P in the
plane, a 1-set is a point in P that can be separated from the rest by a line;
i.e. the point lies on one side of the line while the others lie on the other
side. The number of 1-sets of P is denoted by n1(P). The maximum value of n1(P)
over all configurations P of 10 points in the plane is
57. Alok and Bhanu play the following
min-max game. Given the expression
N = 12 + 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
58. There are two boxes, one containing 10
red balls and the other containing 10 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
37/38
14/19
3/4
59. 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?
60. A sheet of paper has statements numbered
from 1 to 30. For all values of n from 1 to 30, statement n says "At most
n of the statements on this sheet are false". Which statements are true
and which are false?
All statements are
false.
The odd numbered
statements are true and the even numbered are false.
The even numbered
statements are true and the odd numbered are false.
All statements are
true.
61. A hare and a tortoise have a race along
a circle of 100 yards diameter. The tortoise goes in one direction and the hare
in the other. The hare starts after the tortoise has covered 1/5 of its
distance and that too leisurely. The hare and tortoise meet when the hare has
covered only 1/8 of the distance. By what factor should the hare increase its
speed so as to tie the race?
62. 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 1/32 of B's
volume is filled after 3 hours, what is the total duration required to fill it
completely?
7 hours
9 hours
10 hours
8 hours
63. The teacher is testing a student's
proficiency in arithmetic and poses the following question.
1/3 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?
64. A greengrocer was selling apple 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. What did each child get?
1 apple, 3 chickoos,
2 peanuts
1 apple, 2 chickoos, 2
peanuts
1 apple, 2 chickoos,
1 peanut
1 apple, 1 chickoo, 1
peanut
65. A hare and a tortoise have a race along
a circle of 100 yards diameter. The tortoise goes in one direction and the hare
in the other. The hare starts after the tortoise has covered 1/5 of its
distance and that too leisurely. The hare and tortoise meet when the hare has
covered only 1/8 of the distance. By what factor should the hare increase its
speed so as to tie the race?
66. A man is standing in front of a painting
of a man, and he tells us the following: Brothers and sisters have I none, but
this man's father is my father's son. Who is on the painting?
His son
He himself
His grandfather
His father
67. A man is standing in front of a painting
of a man, and he tells us the following: Brothers and sisters have I none, but
this man's father is my father's son. Who is on the painting?
His son
He himself
His grandfather
His father
68. A hunter leaves his cabin early in the
morning and walks one mile due south. Here he sees a bear and starts chasing it
for one mile due east before he is able to shoot the bear. After shooting the
bear, he drags it one mile due north back to his cabin where he started that
morning. What color is the bear?
White
Black
ANS-POLAR BEAR(WHITE)
69. 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?
70. One day Rapunzel meets Dwarf and Byte in
the Forest of forgetfulness. She knows that Dwarf lies on Mondays, Tuesdays and
Wednesdays, and tells the truth on the other days of the week. Byte, on the
other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on
the other days of the week. Now they make the following statements to Rapunzel
- Dwarf Yesterday was one of those days when I lie. Byte: Yesterday was one of
those days when I lie too. What day is it?
Monday
Thursday
Tuesday
Sunday
71. Rearrange the following letters to make
a word and choose the category in which it fits. RAPETEKA
Vegetable
City
ANS-PARAKEET(BIRD)
72. Ferrari S.p.A. is an Italian sports car
manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as
Scuderia Ferrari, the company sponsored drivers 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 been noted for its continued
participation in racing, especially in Formula One, where it has enjoyed great
success. Rohit once bought a Ferrari. It could go 2 times as fast as Mohit's
old Mercedes. If the speed of Mohit's Mercedes is 32 km/hr and the distance
travelled by the Ferrari is 952 km, find the total time taken for Rohit to
drive that distance.
14.88
29.75
73. There are two boxes, one containing 10
red balls and the other containing 10 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
74. 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 1/32 of B's
volume is filled after 3 hours, what is the total duration required to fill it
completely?
9 hours
10 hours
8 hours
7 hours
75. The difference between the ages of two
of my three grandchildren is 3. My eldest grandchild is three times older than
the age of my youngest grandchild and my eldest grandchild's age is two years
more than the ages of my two youngest grandchildren added together. How old is
my eldest grandchild?
ANS-15
76. One day Rapunzel meets Dwarf and Byte in
the Forest of forgetfulness. She knows that Dwarf lies on Mondays, Tuesdays and
Wednesdays, and tells the truth on the other days of the week. Byte, on the
other hand, lies on Thursdays, Fridays and Saturdays, but tells the truth on
the other days of the week. Now they make the following statements to Rapunzel
- Dwarf: Yesterday was one of those days when I lie. Byte: Yesterday was one of
those days when I lie too. What day is it?
Thursday
Tuesday
Sunday
Monday
77. A greengrocer was selling apple 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. What did each child get?
1 apple, 2 chickoos,
1 peanut
1 apple, 3 chickoos
1 apple, 2 chickoos,
2 peanuts
1 apple, 1 chickoo, 1
peanut
78. Ferrari S.p.A. is an Italian sports car
manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as
Scuderia Ferrari, the company sponsored drivers 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 been noted for its continued
participation in racing, especially in Formula One, where it has enjoyed great
success. Rohit once bought a Ferrari. It could go 2 times as fast as Mohit's
old Mercedes. If the speed of Mohit's Mercedes is 32 km/hr and the distance
travelled by the Ferrari is 952 km, find the total time taken for Rohit to
drive that distance.
14.88
29.75
15.88
79. 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?
80. There are two boxes, one containing 10
red balls and the other containing 10 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
37/38
14/19
81. 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 1/32 of B's volume
is filled after 3 hours, what is the total duration required to fill it
completely?
7 hours
9 hours
8 hours
10 hours
82. Rearrange the following letters to make
a word and choose the category in which it fits. RAPETEKA
Vegetable
Fruit
83. A hunter leaves his cabin early in the
morning and walks one mile due south. Here he sees a bear and starts chasing it
for one mile due east before he is able to shoot the bear. After shooting the
bear, he drags it one mile due north back to his cabin where he started that
morning. What color is the bear?
Black
Brown
White
84. A sheet of paper has statements numbered
from 1 to 40. For each value of n from 1 to 40, statement 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 true and the rest are false.
The even numbered
statements are true and the odd numbered are false.
The first 26
statements are false and the rest are true.
ANS: All the
statements are true but there is not such an option.
85. Alok is attending a workshop "How
to do more with less" and today's theme is Working with fewer digits . The
speakers discuss how a lot of miraculous mathematics can be achieved if mankind
(as well as womankind) had only worked with fewer digits.
The problem posed at
the end of the workshop is
How many 5 digit
numbers can be formed using the digits 1, 2, 3, 4, 5 (but with repetition) that
are divisible by 4?
Can you help Alok
find the answer?
86. 36 people {a1, a2, ..., a36} meet and
shake hands in a circular fashion. In other words, there are totally 36
handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a35, a36}, {a36, a1}.
Then size of the smallest set of people such that the rest have shaken hands
with at least one person in the set is
11
87. 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?
500 800
488 900
88. A sheet of paper has statements numbered
from 1 to 30. For all values of n from 1
to 30, statement n
says "At most 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 are false.
The odd numbered statements are true and the even numbered are
false.
All statements are
true.
All statements are
false.
ANS: All statements
are true.
89. Planet fourfi resides in 4-dimensional
space and thus the currency used by its
residents are
3-dimensional objects. The rupee notes are cubical in shape while their coins
are spherical. However the coin minting machinery lays out some stipulations on
the size oft he coins.The diameter of the coins should be at least 64mm and not
exceed 512mm. Given a coin, the diameter of the next larger coin is at least
50% greater.
The diameter of the
coin must always be an integer.You are asked to design a set of coins of
different diameters with these requirements and your goal is to design as many
coins as possible. How many coins can you design?
8 5 6 9
90. On the planet Oz, there are 8 days in a
week- Sunday to Saturday and another day
called Oz day. There
are 36 hours in a day and each hour has 90 min while each minute has 60 sec. As
on earth, the hour hand covers the dial twice every day.
Find the approximate
angle between the hands of a clock on Oz when the time is 12:40 am.
91. Given a collection of points P in the
plane, a 1-set is a point in P that can be
separated from the
rest by a line; i.e. the point lies on one side of the line while the
others lie on the
other side. The number of 1-sets of P is denoted by n1(P). The maximum value of
n1(P) over all configurations P of 10 points in the plane is
9 10
3 5
92. There are two boxes, one containing 10
red balls and the other containing 10 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:
3/4 1/2
14/19 37/38
93. 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 1/32 of
B's volume is filled
after 3 hours, what is the total duration required to fill it completely?
7 hours 8 hours
9 hours 10 hours
94. A
hare and a tortoise have a race along a circle of 100 yards diameter. The
tortoise goes in one direction and the hare in the other. The hare starts after
the tortoise
has covered 1/5 of
its distance and that too leisurely. The hare and tortoise meet when the
hare has covered only
1/8 of the distance. By what factor should the hare increase its speed so as to
tie the race?
37.80 5
40 8
95. Anoop managed to draw 7 circles of equal
radii with their centres on the diagonal
of a square such that
the two extreme circles touch two sides of the square and each middle circle
touches two circles on either side. Find the ratio of the radius of the circles
to the side of the square.
1:(2+ 7√2) 1:(4+ 7√3)
1:(2+ 6√2) (2+ 7√2):1
95. The pacelength P is the distance between
the rear of two consecutive footprints.
For men, the formula,
n/P = 144 gives an approximate relationship between n and P where, n = number
of steps per minute and P = pacelength in meters. Bernard knows his pacelength
is 164cm. The formula applies to Bernard's walking. Calculate Bernard's walking
speed in kmph.
23.62 236.16
8.78 11.39
96. The teacher is testing a student's
proficiency in arithmetic and poses the
following question.
1/3 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?
18 6
21 12
97. 10 suspects are rounded by the police
and questioned about a bank robbery. Only one of them is guilty. The suspects
are made to stand in a line and each person declares that the person next to
him on his right is guilty. The rightmost person is not questioned. Which of
the following possibilities are true?
A. All suspects are
lying or the leftmost suspect is innocent.
B. All suspects are
lying and the leftmost suspect is innocent .
Neither A nor B
B only
A only
Both A and B
98. After the typist writes 12 letters and
addresses 12 envelopes, she inserts the letters randomly into the envelopes (1
letter per envelope). What is the probability that exactly 1 letter is inserted
in an improper envelope?
11/12
12/2^12
1/12
99. A circular dartboard of radius 1 foot is
at a distance of 20 feet from you. You throw a dart at it and it hits the
dartboard at some point Q in the circle. What is the probability that Q is
closer to the center of the circle than the periphery?
0.75
0.25
0.5
1
100. On planet zorba, a solar blast has melted
the ice caps on its equator. 8 years after the ice melts, tiny plantoids called
echina start growing on the rocks. echina grows in the form of a circle and the
relationship between the diameter of this circle and the age of echina is given
by the formula
d = 4 *
d = 4 * √ (t - 8) for
t ≥ 8
where d represents
the diameter in mm and t the number of years since the solar blast.
Jagan recorded the
radius of some echina at a particular spot as 8mm. How many years back did the
solar blast occur?
24
12
8
16
101. A hare and a tortoise have a race along a
circle of 100 yards diameter. The tortoise goes in one direction and the hare
in the other. The hare starts after the tortoise has covered 1/5 of its
distance and that too leisurely. The hare and tortoise meet when the hare has
covered only 1/8 of the distance. By what factor should the hare increase its
speed so as to tie the race?
5
37.80
40
8
102. 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
800
488
500
103. A hunter leaves his cabin early in the
morning and walks one mile due south. Here he sees a bear and starts chasing it
for one mile due east before he is able to shoot the bear. After shooting the
bear, he drags it one mile due north back to his cabin where he started that
morning. What color is the bear?
Brown
Black
Grey
White
104. The difference between the ages of two of
my three grandchildren is 3. My eldest grandchild is three times older than the
age of my youngest grandchild and my eldest grandchild's age is two years more
than the ages of my two youngest grandchildren added together. How old is my
eldest grandchild?
12
15
10
13
105. There are two boxes, one containing 10 red
balls and the other containing 10 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
3/4
37/38
14/19
½
106. A hare and a tortoise have a race along a
circle of 100 yards diameter. The tortoise goes in one direction and the hare
in the other. The hare starts after the tortoise has covered 1/5 of its
distance and that too leisurely. The hare and tortoise meet when the hare has
covered only 1/8 of the distance. By what factor should the hare increase its
speed so as to tie the race?
8
37.80
5
40
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