TCS Openseesame aptitude questions 2

21.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.His son
b.His grandfather
c.His father
d.He himself

Ans: a


22.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 true.
The even numbered statements are true and the odd numbered are false.
All statements are false.
The odd numbered statements are true and the even numbered are false.


23.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?
5
9
6
8

Ans: c(hint:first coin has length 64 mm,2nd coin diamter length 64+(50/100)*64,3rd coin 2nd coins diameter length+50/100 of 2nd coinds lenght,in that way go till you reach maximum diamter length 512!now think!

24. 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
11.39
8.78
236.16
ans:a


25.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?
800
500
488
900

ans:side of cube = 5 cm
its thichness = 1 cm
so volume of outer cube = 5*5*5
volume of inner cube = 3*3*3
volume of the hollow cube = 5*5*5 - 3*3*3 = 98
so total no of small cubes of the size 1 cm = 98/1*1*1 = 98
we know a cube has 6 faces so total no of face = 98*6 = 588
one surface of outer cube contains a total of 25 surface of smaller cube , so when 4 surface of outer cube is painted total no of surface of small cubes i.e supposed to be painted is 4*25 = 100
so the total no of surfaces of small cube that will be remained unpainted is 588-100 = 488



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26.A person drives with constant speed and after some time he sees a milestone with 2 digits. Then travels for 1 hours and sees the same 2 digits in reverse order. 1 hours later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car?
54.00 mph
45.00 mph
27.00 mph
36.00 mph

27.india with a burgeoning population and a plethora of vehicles (at last count there were more than 20 million of them) has witnessed big traffic jams at all major cities. Children often hone their counting skills by adding the wheels of vehicles in schoolyards or bus depots and guessing the number of vehicles.
Alok, one such child, finds only bicycles and 4 wheeled wagons in his schoolyard. He counts the totalnumber of wheels to be 46. What could be the possible number of bicycles?
25
5
4
ans:5
let y be the number of bycycles,x be number of 4 wheelers
then 2x+4y=46
by trial and error subtitute value of x and give suitable values for y
if x=5 and y=9 then eqn satisfied


28.10 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 .
A only
B only
Neither A nor B
Both A and B



29.. A lady has fine gloves and hats in her closet- 18 blue, 32 red, and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color?
a)50 b)8 c)60 d)42
ans:60
There can be lots of logic for this, but approach the simplest one so that we approach to one of the solutions. Suppose the lady first picks 32 Red gloves, and then 24 Yellow gloves. The next pair she pics will be one Yellow and One Blue which does not make a pair. The next two will be blue gloves. So she make a total of 32+24+1+1+2 = 60 picks.



30. 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]Thursday
b]Tuesday
c]Sunday
d]Monday
ANS::
Thursday
Explanation :
On Thursday, Dwarf says truth. i.e Yesterday(Wednesday) was one of those days when I lies. Its true.
On the other hand, On Thursday, Byte lies. i.e Yesterday(Wednesday) was one of those days when I lie too. Its a lie.... So both satisfied. Hence its Thursday.


31.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]6
d]21
ANS::
x/3=3+x/6
so,x=18

32.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?
a]1 apple, 1 chickoo, 1 peanut
b]1 apple, 2 chickoos, 2 peanuts
c]1 apple, 2 chickoos, 1 peanut
d]1 apple, 3 chickoos, 2 peanuts
ANS::
Go from options
1 apple , 2 chickoos , 1 peanut :::::::::::: 3 children are there so he have to buy 3 apples for dat 3 penny’s. similarly for 2 chickoos each child he have to buy 6 chickoos for dat 3 penny’s and 1 peanut for each child he have to buy 3 peanuts for that 1 penny. So total 7



33.Here 10 programers, type 10 lines with in 10 minutes then 60lines can type within 60 minutes. How many programmers are needed?
a) 16 b) 6 c) 10 d) 60
ANS::
C)10
use the formula man*hour=day
10*10=10
x*60=60
divide eqn 1 by 2 and find x!


34.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?
a) 54 b)64 c) 265 d) 192
ans:d
Consider 3 in one's place. The possible numbers are
3,13,23....,73
103,113...,173
.
.
.
703,713...773
i.e 8*8=64 times.
Similarly consider 10's place
70,71,71...77
170,171,...177
.
.
.
770,771...777
Again 8*8=64
Now to hundred's place
700,701...707
.
.
.
770,771,...777
Again 8*8=64
so total 64+64+64=192!



35.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 minimum value of n1(P) over all configurations P of 5 points in the plane in general position(.i.e no three points in P lie on a line) is
a)3
b)5
c) 2
d)1
ans:b
Arrange the points in a circle

36.Hare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely3. A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and the. 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?

a) 37.80
b)8
c) 40
d) 5
ans:a

37.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. 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 coinis the third coin from the top. Then

a) In order to win, Alice's first move should be a 1-move.
b) In order to win, Alice's first move should be a 0-move.
c) In order to win, Alice's first move can be a 0-move or a 1-move.
d) Alice has no winning strategy.
Consider the situation of a 1-move
---C---
---C---
---G---
C represents the normal coin and G the gold coin. So Alice makes a 1-move, which does not have any effect on the arrangement. Next Bob has to make a 0-move or 2-move. If he makes a 0-move, there is no change and if he make a 2-move, the G goes up by one step. If Bob makes a 2-move, then Alice can do a 0-move and win the game.

38.36 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

a)12
b)11
c)13
d)18
ans:a
Understand the question, we have to find the minimum set, so that all other people shake hand to the selected set of people. Let me take an example of 6 people. {a1,a2,a3,a4,a5,a6} Now if we include a minimum set {a2,a5} all other people are shaking hands with them. So if its 2 for 6(1/3rd) then its 36/3=12


39.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?

a)1/12
b)0
c)12/212
d)11/12

ANS:::
b)
Becoz atleast two letter will be inserted in the improper envelop number



40.There is a toy train that can make 10 musical sounds. It makes 2 musical sounds after being defective. What is the probability that same musical sound would be produced 5 times consecutively?


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41.By using 1,2,3,4,5, how many 12 digit no. can be formed which is divisible by 4, repetation of no. is allowed?


42.Alchemy is an occult tradition that arose in the ancient Persian empire. Zosimos of Panopolis was an early alchemist. Zara, reads about Zosimos and decides to try some experiments. One day, she collects two buckets, the first containing one litre of ink and the second containing one litre of cola. Suppose she takes one cup of ink out of the first bucket and pours it into the second bucket. After mixing she takes one cup of the mixture from the second bucket and pours it back into the first bucket. Which one of the following statements holds now?

A.There is more cola in the first bucket than ink in the second bucket.
B.There is as much cola in the first bucket as there is ink in the second bucket.
C.There is less cola in the first bucket than ink in the second bucket

43.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 19 points in the plane is
18
9
3

44.15 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.

B only


45,Alchemy is an occult tradition that arose in the ancient Persian empire. Zosimos of Panopolis was an early alchemist. Zara, reads about Zosimos and decides to try some experiments. One day, she collects two buckets, the first containing one litre of ink and the second containing one litre of cola. Suppose she takes one cup of ink out of the first bucket and pours it into the second bucket. After mixing she takes one cup of the mixture from the second bucket and pours it back into the first bucket. Which one of the following statements holds now?

A.There is more cola in the first bucket than ink in the second bucket.
B.There is as much cola in the first bucket as there is ink in the second bucket.
C.There is less cola in the first bucket than ink in the second bucket.

46.Both A and B Alice and Bob play the following chip-off-the-table game. Given a pile of 58 chips, Alice first picks at least one chip but not all the chips. In subsequent turns, a player picks at least one chip but no more than the number picked on the previous turn by the opponent. The player to pick the last chip wins. Which of the following is true?
In order to win, Alice should pick 14 chips on her first turn.
In order to win, Alice should pick two chips on her first turn.
In order to win, Alice should pick one chip on her first turn.


47.Both A and B Alice and Bob play the following chip-off-the-table game. Given a pile of 58 chips, Alice first picks at least one chip but not all the chips. In subsequent turns, a player picks at least one chip but no more than the number picked on the previous turn by the opponent. The player to pick the last chip wins. Which of the following is true?

In order to win, Alice should pick 14 chips on her first turn.

In order to win, Alice should pick two chips on her first turn.

In order to win, Alice should pick one chip on her first turn.

48.30 teams enter a hockey tournament. A team is out of the tournament if it loses 2 games. What is the maximum number of games to be played to decide one winner?
60
59
61
30
34



49.Suppose 12 monkeys take 12 minutes to eat 12 bananas. How many monkeys would it take to eat 72 bananas in 72 minutes?
6
72
12



50.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?
625
375
230
500


51.A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 4 red face and 2 blue faces. How many red and blue faces should the other die have if the both players have the same chances of winning?
3 red and 3 blue faces
2 red and remaining blue
6 red and 0 blue
4 red and remaining blue


52.A sheet of paper has statements numbered from 1 to 45. For all values of n from 1 to 45, 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.
The even numbered statements are true and the odd numbered are false.
All statements are false.

53.There are two containers A and B. A is half filled with wine whereas B which is 3 times the size of A contains one quarter portion wine. If both containers are filled with water and the contents are poured into container C, what portion of container C is wine?
.30
.31
.42
.25
nts are true.

54.A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One die has 3 red faces and 3 blue faces. How many red and blue faces should the other die have if the both players have the same chances of winning?
5 red and 1 blue faces
1 red and 5 blue faces
3 red and 3 blue faces


55.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?

a]0.75

b]1

c]0.5

d]0.25

Ans:.25
Here the data about the distance is of no use.
For radius of 1 m if dart is inside the circle of 1/2 m radius the dart is closer to center than periphery
so area of 1/2 m circle is pie/4
area of board is pie
So probability = 0.25


56.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?
a]6
b]18
c]72
d]12
ans:12


57.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?
a]13
b]10
c]15
d]12
Ans::
15



58.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?

a]Brown
b]Black
c]Grey
d]White


Ans::
From North Pole, there are an infinite number of points about 1 mile away , where you can walk 1 mile south, walk one mile east (all the way around the earth back to the same spot), and then back north again,
This is only possible if the cabin of man is at North Pole.

He can walk one mile due south, then one mile due east and finally one mile due north where he finds his cabin again. This means that his cabin can only be at the north pole, and for that reason the bear will be white.