Model Placement Paper II

Sakshi Education

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?
1. 0.75
2. 1
3. 0.5
4. 0.25
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 * v (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?
1. 24
2. 12
3. 8
4. 16
Alok and Bhanu play the following min-max game. Given the expression N = 9 + 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
1. 27
2. 18
3. 20
4. 0.0
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?
1. 4/9
2. 2/3
3. 1/9
4. 5/9
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.Suppose12 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?
1. 6
2. 18
3. 72
4. 12
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 buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?
1. 256
2. 54
3. 192
4. 64
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
1. 12
2. 13
3. 18
4. 11
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
1. In order to win, Alice’s first move should be a 0-move.
2. In order to win, Alice’s first move should be a 1-move.
3. Alice has no winning strategy.
4. In order to win, Alice’s first move can be a 0-move or a 1-move.
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?
1. The even numbered statements are true and the odd numbered statements are false.
2. The 39th statement is true and the rest are false.
3. The odd numbered statements are true and the even numbered statements are false.
4. All the statements are false.
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).
1. 7
2. 6
3. 9
4. 8
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?
1. 375
2. 625
3. 500
4. 3125
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. 0
2. 12/212
3. 11/12
4. 1/12
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.
1. A only
2. Neither A nor B
3. Both A and B
4. B only
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
2. 3
3. 0
4. 1
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?
1. 40
2. 37.80
3. 8
4. 5
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
1. 3/4
2. 14/19
3. 37/38
4. ½
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?
1. 900
2. 488
3. 500
4. 800
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?
1. 13
2. 10
3. 15
4. 12
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?
1. 72
2. 432
3. 12
4. 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?
1. 18
2. 72
3. 6
4. 12
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.
1. 29.75
2. 15.88
3. 476
4. 14.88
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. 1 apple, 1 chickoo, 1 peanut
2. 1 apple, 2 chickoos, 2 peanuts
3. 1 apple, 2 chickoos, 1 peanut
4. 1 apple, 3 chickoos, 2 peanuts
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?
1. Brown
2. Black
3. Grey
4. White
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?
1. Thursday
2. Tuesday
3. Sunday
4. Monday
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?
1. 7 hours
2. 10 hours
3. 8 hours
4. 9 hours
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?
1. 12
2. 18
3. 6
4. 21
Alok and Bhanu play the following min-max game. Given the expression N = 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
1. 2
2. 4
3. 9
4. -18
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.
1. 29.75
2. 476
3. 14.88
4. 15.88
Rearrange the following letters to make a word and choose the category in which it fits. RAPETEKA
1. Fruit
2. City
3. Bird
4. Vegetable
Question
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?
1. Black
2. White
3. Brown
4. Grey
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?
1. His grandfather
2. His son
3. His father
4. He himself
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?
1. 488
2. 500
3. 800
4. 900
32. Alok is attending a workshop “How to do more with less” and today’s theme is working with fewer digits. The speakers discuss how 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 if
How many 4 digit numbers can be formed using digits 1,2,3,4,5 (but with repetition) that are divisible by 4?
Can you help alok find the answer?
1. 125
2. 82
3. 75
4. 100
The fundamental theorem of arithemtic statesthat every natural number greater than 1 can be written as a uniwue product ofprime numbers. Now hwat is the smallest number by which 3380 must be divided in ordeer to make it into a perfect square?
1. 5
2. 4
3. 8
4. 6
Fermat’s Last Theorem is a statement in number theory which states that it is impossible to separate any power higher than the second into two like power, or more precisely-if an integer n is greater than 2, then the equation a^n b^n = c^n has no solutions in non-zero integers a,b, and c. Now, if the difference of any two numbers is 9 and their product is 17,What is the sum of their squares?
1. 43
2. 115
3. 98
4. 45
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 11 points in the plane is
1. 10
2. 3
3. 5
4. 11
Given a collection of 40 points P in the plane and a point X equidistant from all points in P, which of the following are necessarily true?
A.The points in P lie on a circle.
B.The distance between any pair of points in P is large than the distance between X and a point in P.
1. A and B
2. B only
3. A only
4. Neither A nor B
Alchemy is an occult tradition that arose in the ancient Persian empire. Zosimos of panopolis was an early alchemist. Zara, reads bout 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 intothe3 first bucket. Which one of the following statements holds now?
1. There is a much cola in the first bucket as there is ink in the second bucket.
2. None of the statements hold true.
3. There is more cola in the first bucket than ink in the second bucket.
4. There is less cola in the first bucket than ink in the second bucket.
Alok and Bhanu play the following min-max game. Given the expression N= 24 + 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 choose a single digit number and Bhanu substitutes this for a variable f her choice (X, Y or Z) Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alock 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
1. 24
2. 42
3. -57
4. 105
38 suspects are rebounded 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.
1. A only
2. Both A and B
3. B only
A sheet of paper has statements numbered from 1 to 25.For all values of n from 1to 25,statemetnts n says “At most n of the statements on this sheet are false”. Which statements are true and which are false?
1. The odd numbered statements are true and the even numbered are false.
2. All statements are false.
3. The even numbered statements are true and the odd numbered are false.
4. All statements are true.
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 total number o wheels to be 40. What could be the possible number of bicycles?
1. 22
2. 17
3. 19
4. 18
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 horse later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car?
1. 36.00 mph
2. 45.00 mph
3. 27.00 mph
4. 54.00 mph
Alice and Bob play the following chip-off-the-table game. Given a pile of 122 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?
1. In order to win, Alice should pick two chops on her first turn.
2. In order to win, Alice should pick 30 chips on her first turn.
3. Alice has no winning strategy.
4. In order to win, Alice should pick one chip on her fist turn.
A here 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 the win the race?
1. 37.80
2. 5
3. 8
4. 40
34 people attend a party.4 men are single and the rest are there with their wives. There are no children in the party in all 22 women are present. Then the number of married men at the party is
1. 8
2. 34
3. 12
4. 16
Suppose 19 monkeys take 19 minutes to eat 19 bananas. How many minutes would it take 8 monkeys to eat 8 bananas?
1. 152
2. 27
3. 19
4. 8
A and B play a game of dice between them. The dice consist of colors on their faces (instead of number). When the dice are thrown, A wins if both show the same color, otherwise B wins. On 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?
1. 6 red and 0 blue
2. 2 red and remaining blue
3. 3 red and 3 blue faces
4. 4 red and remaining blue
3o teams enter a hockey tournament. A team is out of the tournament if it losses 2 games. What is the maximum number of games to be played to decide one winner?
1. 30
2. 59
3. 60
4. 61
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?
1. Any of the solutions given
2. 5 red and 1 blue faces
3. 3 red and 3 blue faces
4. 1 red and 5 blue faces
Suppose 12 moneys take 12 minutes to eat 12 bananas. How many monkeys would it take to eat 72 bananas in 72 minutes?
1. 72
2. 18
3. 12
4. 6
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 the win the race?
1. 8
2. 5
3. 37.80
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?
1. 25
2. 5
3. 4
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
1. 18
2. 9
3. 3
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?
1. A. All the suspects are lying.
2. B. The leftmost suspect is guilty.
3. B only
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?
1. In order to win, Alice should pick 14 chips on her first turn.
2. In order to win, Alice should pick two chips on her first turn.
3. In order to win, Alice should pick one chip on her first turn.
4. Alice has no winning strategy.
34 people attend a party. 4 men are single and the rest are there with their wives. There are no children in the party. In all 22 women are present. Then the number of married men at the party is
1. 12
2. 8
3. 16
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?
1. 60
2. 59
3. 61
4. 30
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?
1. The odd numbered statements are true and the even numbered are false.
2. The even numbered statements are true and the odd numbered are false.
3. All statements are false.
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?
1. 5 red and 1 blue faces
2. 1 red and 5 blue faces
3. 3 red and 3 blue faces
In a hotel, rooms are numbered from 101 to 550. A room is chosen at random. What is the probability that room number starts with 1, 2 or 3 and ends with 4, 5 or 6?
If there are 30 cans out of them one is poisoned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours, how many mices are required to find the poisoned can?