5 TCS MOCK TEST PAPERS with supplement on SHORTCUTS to POPULAR QUESTIONS
1
INDEX
INTRODUCTION
Page 03
MOCK TEST 1
Page 04
MOCK TEST 2
Page 08
MOCK TEST 3
Page 13
MOCK TEST 4
Page 18
MOCK TEST 5
Page 22
ANSWER KEYS
Page 25
POPULAR QUESTIONS SIMPLIFIED
Page 26
DISCLAIMER: Please note that this booklet is intended to be supplementary and cannot substitute thorough preparation. Questions in this booklet are simulated based on TCS Aptitude Test pattern as of August 2011. However, test patterns and questions are likely to change anytime without notice. TCS is in not involved in any way with the development of this booklet and contents thereof.
2
INTRODUCTION
Preparing for your campus placements could be one of the biggest challenges of college life. And being the culmination of all these years of study and effort, it can be quite stressful as well. Understanding the need of the hour, we have put together 5 Mock Test Papers for you to work out, verify and strategize. And that’s not all…Towards the end of the booklet, you will also find plenty of easy-to-remember shortcuts, tips and guidelines to popular TCS Questions which will help you maximize your speed and accuracy. Before you proceed further, here’s a brief on TCS Aptitude Tests as of 2011:
TCS conducts ONLINE TEST. So get comfortable with the mouse and practice before the D-Day.
TCS test has 35 questions with a total duration of 80 minutes.
The test has a single section only.
Watch out for negative marking because negative marking warrants a more careful approach.
All questions involve problem solving and logical thinking to arrive at the answer. But remember that some questions are quite long and cleverly-worded that it also challenges the test-taker’s verbal skills because you first need to understand the question to solve it!
As said earlier, many TCS test questions have a tendency to be long-winding. So while you practice with the Mock Tests that follow, learn to sift through the information mine and quickly spot the relevant data alone. Otherwise, it’s quite easy to get lost with the information overload!
DISCLAIMER: Please note that this booklet is intended to be supplementary and cannot substitute thorough preparation. Questions in this booklet are simulated based on TCS Aptitude Test pattern as of August 2011. However, test patterns and questions are likely to change anytime without notice. TCS is in not involved in any way with the development of this booklet and contents thereof.
3
TCS MOCK TEST 1
1.
The difference between the ages of two of my three grandchildren is 3. My eldest grandchild is three times older than 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) 12 (b) 13 (c) 10 (d) 15
2.
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 7 pennies and got the same amount of each type of fruit for each of his three children. What did each child get? (a) 1 apple, 2 chickoos, 2 peanuts (b) 1 apple, 2 chickoos, 1 peanut (c) 1 apple, 3 chickoos, 2 peanuts (d) 1 apple, 1 chickoo, 1 peanut
3.
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 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) 12 (b) 18 (c) 6 (d) 72
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) Monday (b) Sunday (c) Thursday (d) Saturday
5.
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 (a) 20 (b) 18 (c) 27 (d) 0
6.
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? a) All statements are false. b) The odd numbered statements are true and the even numbered statements are false. c) All statements are true. d) The even numbered statements are true and the odd numbered statements are false.
7.
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. (c) Both A and B (d) Neither A nor B
8.
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) 192 (b) 64 (c) 54 (d) 102
4
9.
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? (a) 8 (b) 12 (c) 16 (d) 24
10.
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) ¼ (b) ½ (c)3/4 (d) 1/3
11.
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) 11/12 (b) 0 (c) 1/12 (d) 1/6
12.
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? (a) 375 (b) 625 (c) 500 (d) 3125
13.
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 (a) 1 (b) 0 (c) 4 (d) 2
14.
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 = pace length in meters. Bernard knows his pace length is 164 cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed in kmph. (a) 236.16 (b) 11.39 (c) 8.78 (d) 23.24
15.
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 coin is the third coin from the top. Then (a) In order to win, Alice’s first move should be a 0-move. (b) In order to win, Alice’s first move should be a 1-move. (c) Alice has no winning strategy. (d) In order to win, Alice’s first move can be a 0-move or a 1-move
16.
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? (a) 5/9 (b) 1/9 (c) 2/3 (d) 1/3
17.
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) 18 (b) 13 (c) 34 (d) 12
5
18.
One 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 minutes while each minute has 60 seconds. As on earth, the hour hand covers the dial twice every day. Find the approximate angle between the hands of clock on Oz when the time is 12.40 am. (a) 89 (b) 251 (c) 111 (d) 79
19.
The IT giant Tirnop has recently crossed a head count of 150000 and earning 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. If 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? (a) 6 (b) 432 (c) 72 (d) 12
20.
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 the 4 faces of the outer surface of the cube are painted totally, how many faces of the smaller cubes remain unpainted? (a) 900 (b) 488 (c) 500 (d) 800
21.
Planet fourfi resides in 4-dimensional space and thus the currency used by its residents are 3dimensional objects. The 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? (a) 5 (b) 8 (c) 9 (d) 6
22.
A hare and a tortoise race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after 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? (a)8 (b) 37.80 (c) 40 (d) 5
23.
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. (a) 1:(2 + 72) (b) 1:(4 + 73) (c) (2 + 72):1 (d) 1:(2 + 62)
24.
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 in1947 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. (a) 15.88 (b) 29.75 (c) 14.88 (d)476
25.
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 is maximized. This maximum probability is (a) 37/38 (b) 1 / 2 (c) 14/19 (d) 3 / 4
26.
Pizza shops make pizzas of same thickness but different diameter. Cost of pizza A with diameter 8 cm is 80 $, cost of the pizza B with diameter 12 cm is 240 $, cost of the pizza B with diameter 24 cm is 720 $. Which of the above mentioned pizzas gives the best value for money? (a) A (b) B (c) C (d) Cannot say
6
27.
Determine the distance between x-intercept and z-intercept of the plane whose equation is 6x+8y-3z=72. (a) 31.92 (b)26.83 (c) 32.66 (d) 25.63
28.
Lucy finds around 25 groups of stars that appear to her as constellations. She draws 7 patterns of the constellations in her notebook and notes down the number of stars in each of them. She counts 5 stars in first constellation and 15 on next. She counts a number the third time and forgets to note it down. The next four constellations she counts 51, 53, 159, 161. Next day her father looks at the notebook and wants to know the number of stars in the third constellation. Lucy only remembers that number of stars counted in each of the constellation followed a pattern 5, 15, x, 51, 53, 159, 161. What is the value of x? (a) 19 (b) 17 (c) 47 (d) 31
29.
6 persons standing in the queue for ROBERT movie are wearing different coloured shirts. All of them belong to different age groups. After two years, their average age will be 43. A seventh person joined with them, hence the current average age has become 45. Find the age of seventh person? (a) 67 (b) 69 (c) 72 (d) 74
30.
X is 6 years younger to Y. X's father is a businessman who invested 10000 at 8% rate of interest and obtained his amount after 10 years. Y's father is a job holder who invested around 20000 at 2% rate and obtained his amount after 20 years. Now compounding, both of them get around Rs. A. After 5 years, the ratio of ages of X and Y is 1:2. Now X's father is 20 years older to Y and Y's father is 30 years more than X. After 20 years, again X's mother asks X's father to purchase a LCD TV which costs around 45000. What is the age of X and Y together? (a) 12 (b) 8 (c) 18 (d) 6
31.
The great musician Rahman has organized a live concert. The concert is organized in a big auditorium. Rahman plays both English and Tamil songs on his Yamaha Casio. The audience in the eastern part of the auditorium love listening to Tamil songs and those in the western part of the auditorium love listening to English songs. He plays songs in random. The probability that he plays English songs for 6 consecutive times is 1 in (a) 32 (b) 16 (c) 64 (d) 128
32.
It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same colour? (a) 3 (b) 25 (c) 48 (d) 26
33.
A person was fined for exceeding the speed limit by 10mph. Another person was also fined for exceeding the same speed limit by twice the same. If the second person was traveling at a speed of 35 mph, find the speed limit (a) 35 mph (b) 15 mph (c) 20 mph (d) 30 mph
34.
A person drives with constant speed and after some time he sees a milestone with 2 digits. Then travels for 1 hour and sees the same 2 digits in reverse order. 1 hour later he sees that the milestone has the same 2 digits with a 0 between them. What is the speed of the car? (a) 54 (b) 45 (c) 27 (d) 36
35.
With four fifths of the tank full, a vehicle travels 12 miles. How much distance will the vehicle travel with one-third tank full? (a) 8.05 km (b) 6.05 km (c) 12 km (d) 5 km
7
TCS MOCK TEST 2
1.
If 1/3 of a number is 6 more than 1/6 of that number, then what is the number? (a) 12 (b) 36 (c) 24
(d) 48
2.
The pace length P is the distance between the rear of two consecutive footprints. For men, the formula n/P = 180 gives an approximate relationship between n and P where, n = number of steps per minute and P = pace length in meters. Bernard knows his pace length is 120 cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed in kmph. (a) 236.16 (b) 8.78 (c) 15.56 (d) 23.62
3.
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 24 such programmers take 24 minutes to write 24 lines of code in total. How long will it take 72 programmers to write 72 lines of code in total? (a) 12 (b) 24 (c) 6 (d) 72
4.
A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says “Exactly n of the statements on this sheet are true." Which statements are true and which are false? (a) All statements are false. (b) The odd numbered statements are true and the even numbered statements are false. (c) Second last statement is true and the remaining statements are false. (d) The even numbered statements are true and the odd numbered statements are false.
5.
Alok and Bhanu play the following min-max game. Given the expression N = 25 + 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 (a) 43 (b) 16 (c) 36 (d) 34
6.
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? (a)First half of the statements are true and the rest are false. (b) The odd numbered statements are true and the even numbered statements are false. (c) First half of the statements are false and the rest are true. (d) The even numbered statements are true and the odd numbered statements are false.
7.
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. B) The leftmost suspect is guilty. C) Rightmost suspect is guilty. (a) A only (b) A and B (c) B only (d) B and C
8.
The citizens of planet nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street in nigiet contains 1000 (in base 6) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings? (a) 108 (b) 192 (c) 54 (d) 102
8
9.
One 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 minutes while each minute has 60 seconds. As on earth, hour hand covers the dial twice every day. Find the approximate angle between the hands of clock on Oz when the time is 14.40 a.m. (a) 83 (b) 74 (c) 129 (d) 65
10.
On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny planetoids 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 = 2 * √ (t - 8) for t ≥ 8 where d represents the diameter in mm and t the number of years since the solar blast. Jegan recorded the radius of some echina at a particular spot as 4 mm. How many years back did the solar blast occur? (a) 18 (b) 12 (c) 16 (d) 24
11.
It is dark in my bedroom and I want to get two socks of the same colour from my drawer, which contains 26 red and 24 blue, 34 brown socks. How many socks do I have to take from the drawer to get at least two socks of the each colour? (a) 6 (b) 74 (c) 61 (d) 62
12.
For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumoured 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 rumours to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 5/6 of winning. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game? (a) 0.72 (b) 0.50 (c) 0.64 (d) 0.83
13.
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? (a) 3 red, 3 blue (b) 2 red, 4 blue (c) 6 red, 0 blue (d) 4 red, 2 blue
14.
66 people {a1, a2,..., a66} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {a65, a66}, {a66, a1}. The size of the smallest set of people such that the rest have shaken hands with at least one person in the set is (a) 22 (b) 33 (c) 65 (d) 11
15.
The IT giant Tirnop has recently crossed a head count of 150000 and earning 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 16 such programmers take 16 minutes to write 16 lines of code in total, how many lines of code can be written by 96 programmers in 96 minutes? (a) 16 (c) 432 (d) 96 (b) 576
16.
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 in1947 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 3 times as fast as Mohit’s old Mercedes. If the speed of Mohit’s Mercedes is 33 km/hr and the distance travelled by the Ferrari is 909 km, find the total time taken in hours for Rohit to drive that distance. (a) 9.18 (b) 10.18 (c) 9 (d) 99
17.
Anoop managed to draw 6 circles of equal radii with their centers 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 side of the square to the radius of the circles. Assume 2 is 1.4. (a) 9 : 1 (b) 6.2 : 1 (c) 10.4 : 1 (d) 7.6 : 1
9
18.
A hare and a tortoise race along a circle of 100 yards diameter. The tortoise goes in one direction and the hare in the other. The hare starts after tortoise has covered 1/5 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 the hare increase its speed so as to tie the race? (a) 8 (b) 37 (c) 45 (d) 6.6
19.
There are two boxes, one containing 21 red balls and the other containing 25 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 is maximized. This maximum probability is (a) 0.5 (b) 0.63 (c) 0.72 (d) 0.48
20.
Alok and Bhanu play the following min-max game. Given the expression N = 32 + 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 (a) 113 (b) 32 (c) -49 (d) 50
21.
A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At most n of the statements on this sheet are true." Which statements are true and which are false? (a) All statements are true. (b) The odd numbered statements are true and the even numbered statements are false. (c) The first half of the statements are true and the remaining statements are false. (d) The even numbered statements are true and the odd numbered statements are false.
22.
After a typist writes 25 letters and addresses 25 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) 23/25 (b) 0 (c) 2/25 (d) 1
23.
There are two water tanks A and B, where A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, liters….., in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, and so on) If tank B is 1/64 filled after 17 hours, what is the total duration required to fill it completely? (a) 6 hours (b) 24 hours (c) 22 hours (d) 23 hours
24.
You have a jar containing water absorbing marbles which will take 21 hours to set completely when fixed with white cement. There are 50 red marbles, 52 blue marbles and 63 black marbles. The jar is kept inside a dark room. What is the minimum number of marbles that you need to pick to make sure that you have a pair of marbles in each color? (a) 117 (b) 98 (c) 120 (d) 114
25.
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? (a) 59 (b) 60 (c) 61 (d) 30
26.
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 only 2 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted? (a) 210 (b) 465 (c) 450 (d) 538
10
27.
Planet fourfi resides in 4-dimensional space and thus the currency used by its residents are 3dimensional 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 256 mm and not exceed 4096 mm. - Given a coin, the diameter of the next larger coin is at least 50% greater. - The diameter of a 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? (a) 7 (b) 8 (c) 9 (d) 6
28.
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 7 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? (a) 5000 (b) 15625 (c) 2500 (d) 3179
29.
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 imove 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 (a) In order to win, Alice’s first move should be a 0-move. (b) In order to win, Alice’s first move should be a 1-move. (c) Alice has no winning strategy. (d) In order to win, Alice’s first move can be a 0-move or a 1-move
30.
There are 5 pentagonal pyramid shaped bottles whose volumes are in geometric progression and there are 5 materials to make a perfume inside the bottle viz., Lilac, Balsamic, Lemon, Woody and Mimosaic. Also, all the faces of the pyramids are painted in different colours. To make a perfume that is in demand, the following conditions are to be followed: Lilac and Balsamic go together. Woody and Mimosaic go together. Woody and Balsamic never go together. Lemon can be added with any material. All of the following combinations are possible to make a perfume EXCEPT (a) Balsamic and Lilac (b) Woody and Lemon (c) Mimosaic and Woody (d) Mimosaic and Lilac
31.
20 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) (a) 19 (b) 18 (c) 20 (d) 21
32.
There are 45 cans out of which one is poisoned. If a person tastes very little of this, he will die within 14 hours; so they decided to test it with mice. Given that a mouse dies in 24 hours and you have 24 hours in all to find out the poisoned can, how many mice are required to find the poisoned can? (a) 44 (b) 29 (c) 6 (d) 5
33.
Middle-earth is a fictional land inhabited by hobbits, elves, dwarves and men. The hobbits and elves are peaceful creatures who prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows. A tournament is one where out of the two teams that play a match, the one that loses get eliminated. The matches are played in different rounds, where in every round, half of the teams get eliminated from the tournament. If there are 9 rounds played in a knockout tournament, how many matches were played? (a) 511 (b) 512 (c) 256 (d) 255
11
34.
The IT giant Tirnop has recently crossed a head count of 150000 and earning 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 12 such programmers take 12 minutes to write 12 lines of code in total. How many programmers will complete 96 lines in 96 minutes? (a) 12 (b) 96 (c) 1152 (d) 32
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 1sets of P is denoted by n1 (P). The maximum value of n1(P) over all configurations P of 10 points in the plane is (a) 5 (b) 10 (c) 9 (d) 9
12
TCS MOCK TEST 3
1.
If 1/5 of a number is 2 more than 1/6 of that number then what is the number? (a) 24 (b) 30 (c) 60 (d) 10
2.
Alok and Bhanu play the following min-max game. Given the expression N = 25 + 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 (a) 36 (b) 27 (c) 14 (d) 43
3.
A sheet of paper has statements numbered from 1 to N. For each value of N from 1 to 50, statement N says "At least N of the statements on this sheet are false." Which statements are true and which are false? (a) All statements are true. (b) All statements are false. (c) First half of the statements are true and second half of the statements are false. (d) First half of the statements are false and second half of the statements are true.
4.
The IT giant Ozymandias has recently crossed a head count of 450000 and earnings of $10 billion. As one of the forerunners in the technology front, Ozymandias continues to lead the way in products and services in India. At Ozymandias, all programmers are equal in every respect. They receive identical salaries and also write code at the same rate. Suppose 24 such programmers take 24 minutes to write 24 lines of code in total. How many programmers will be required in total to write 72 lines of code in 72 minutes? (a) 18 (b) 36 (c) 72 (d) 24
5.
25 suspects are rounded by the police and questioned about a murder case. 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. B) The leftmost suspect is innocent. C) The rightmost suspect is guilty. (a) A only (b) A and B (c) A or B (d) A and C
6.
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 minutes while each minute has 60 seconds. As on earth, hour hand covers the dial twice every day. Find the approximate angle between the hands of clock on Oz when time is 13.40 am. (a) 109 (b) 89 (c) 74 (d) 65
7.
The citizens of planet nigiet are 4 fingered and have thus developed their decimal system in base 4. A certain street in nigiet contains 100 (in base 4) buildings numbered 1 to 100. How many 3s are used in numbering these buildings? (a) 48 (b) 8 (c) 20 (d) 16
8.
On planet zorba, a solar blast has melted the ice caps on its equator. 8 years after the ice melts, tiny planetoids 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 6 mm. How many years back did the solar blast occur? (a) 12 (b) 15 (c) 11 (d) 17
13
9.
For the FIFA world cup, Paul, the octopus has been predicting the winner of each match with amazing success. It is rumoured 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 rumours to be true and that in a match between Ecuador and Turkey, Ecuador the stronger team has a probability of 5/9 of winning the game. What is the probability that Paul will correctly pick the winner of the Ecuador - Turkey game? (a) 0.49 (b) 0.51 (c) 0.52 (d) 0.46
10.
Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 19, 19 and 19, the number of points equidistant from all the 3 lines is (a) 4 (b) 2 (c) 3 (d) 1
11.
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 in1947 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 4 times as fast as Mohit’s old Mercedes. If the speed of Mohit’s Mercedes is 33 km/hr and the distance travelled by the Ferrari is 954 km, find the total time taken in hours for Rohit to drive that distance. (a) 6.91 (b) 7.23 (c) 8.23 (d) 7.91
12.
A sheet of paper has statements numbered from 1 to N. For each value of n from 1 to 25, statement N says "Exactly N of the statements on this sheet are true." Which statements are true and which are false? (a) All statements are false. (b) The odd numbered statements are true and the even numbered statements are false. (c) Second last statement is true and the remaining statements are false. (d) The even numbered statements are true and the odd numbered statements are false.
13.
There are two boxes, one containing 11 red balls and the other containing 15 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 is maximized. This maximum probability is (a) 0.70 (b) 0.30 (c) 0.25 (d) 0.5
14.
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 (a) 30 (b) 12 (c) 20 (d) 23
15.
A hare and tortoise 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 tortoise has covered ¼ of its distance and that 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? (a) 37 (b) 35.0 (c) 26 (d) 17
16.
Anoop managed to draw 3 circles of equal radii with their centers 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 side of the square to the radius of the circles. Assume 2 is 1.4. (a) 10.8:1 (b) 6.2 : 1 (c) 4.2 : 1 (d) 4.8 : 1
17.
A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At most n of the statements on this sheet are false." Which statements are true and which are false? (a) All statements are false. (b) The odd numbered statements are true and the even numbered statements are false. (c) The first half of the statements are true and the remaining statements are false. (d) The even numbered statements are true and the odd numbered statements are false.
14
18.
There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, liters….., in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, and so on) If tank B is 1/32 filled after 12 hours, what is the total durations required to fill it completely? (a) 16 (b) 20 (c) 17 (d) 21
19.
A circular dartboard of radius 2 foot is at a distance of 40 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 centre of the circle than the periphery? (a) 0 (b) 0.25 (c) 0.5 (d) 0.75
20.
After the typist writes 20 letters and addresses 20 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) 0 (b) 9/10 (c) 1/10 (d) 1
21
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 only 3 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted? (a) 488 (b) 588 (c) 75 (d) 513
22.
Planet fourfi resides in 4-dimensional space and thus the currency used by its residents are 3dimensional objects. The rupees 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 128 mm and not exceed 512 mm. 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? (a) 3 (b) 6 (c) 5 (d) 4
23.
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 9 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? (a) 390625 (b) 198562 (c) 300000 (d) 20124
24.
22 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 such the pairs (a1, a2), (a2, a3), …, (a (k-1), a k) , (ak, a1) shake hands. (a) 22
(b) 7
(c) 21
(d) 11
25.
It is dark in my bedroom and I want to get two socks of the same colour from my drawer, which contains 36 red and 24 blue, 14 brown socks. How many socks do I have to take from the drawer to get at least two socks of the each color? (a) 6 (b) 62 (c) 37 (d) 30
26.
The pace length P is the distance between the rear of two consecutive footprints. For men, the formula, n/P = 150 gives an approximate relationship between n and P where, n = number of steps per minute and P = pace length in meters. Bernard knows his pace length is 152 cm. The formula applies to Bernard’s walking. Calculate Bernard’s walking speed in kmph. (a) 207.936 (b) 7.72 (c) 228 (d) 20.794
15
27.
Alice and Bob play the following coins-on-a-stack game. 50 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 ≤ 50). 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 (a) In order to win, Alice’s first move should be a 0-move. (b) In order to win, Alice’s first move should be a 1-move. (c) Alice has no winning strategy. (d) In order to win, Alice’s first move can be a 0-move or a 1-move.
28.
There are 100 cans out of them one is poisoned. If a person tastes very little of this, he will die within 14 hours; so they decided to test it with mice. Given that a mouse dies in 24 hours and you have 24 hours in all to find out the poisoned can, how many mice are required to find the poisoned can? (a) 10 (b) 99 (c) 7 (d) 6
29.
Middle-earth is a fictional land inhabited by hobbits, elves, dwarves and men. The hobbits and elves are peaceful creatures who prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows. A tournament is one where out of the two teams that play a match, the one that loses get eliminated. The matches are played in different rounds, where in every round; half of the teams get eliminated from the tournament. If there are 6 rounds played in knock out tournament, how many matches were played? (a) 64 (b) 63 (c) 32 (d) 33
30.
The IT giant Tirnop has recently crossed a head count of 150000 and earning 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 10 such programmers take 10 minutes to write 10 lines of code in total. How long will 90 programmers take to write 90 lines of code? (in minutes) (a) 180 (b) 900 (c) 10 (d) 90
31.
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 20 points in the plane is (a) 20 (b) 3 (c) 2 (d) 10
32.
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) 18 (b) 12 (c) 35 (d) 30
33.
There are 5 pentagonal pyramid shaped bottles whose volumes are in geometric progression and there are 5 materials to make a perfume inside the bottle viz. Lilac, Balsalmic, Lemon, Woody and Mimosaic. Also all the faces of the pyramids are painted in different colours. To make a perfume that is in demand, the following conditions are to be followed: Lemon and Balsalmic go together. Woody and Mimosaic go together. Woody and Balsalmic never go together. Lilac can be added with any material. All of the following combinations are possible to make a perfume EXCEPT: (a) Balsalmic and Lemon (b) Woody and Lilac (c) Mimosaic and Woody (d) Mimosaic and Lemon
16
34.
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 30 points in the plane is (a) 3 (b) 30 (c) 2 (d) 1
35.
A research lab in Chennai requires 100 mice and 75 sterilized cages for a certain set of laboratory experiments. To identify the mice, the lab has prepared labels with numbers 1 to 100, by combining tags numbered 0 to 9. The SPCA requires that the tags be made of toxin-free material and that the temperature of the cages be maintained at 27 degrees Celsius. Also, not more than 2 mice can be caged together and each cage must be atleast 2 sq.ft. in area. The 5 experiments to be conducted by lab are to be thoroughly documented and performed only after a round of approval by authorities. The approval procedure takes around 48 hours. How many times is the tag numbered '4' used by the lab in numbering these mice? (a) 9 (b) 19 (c) 20 (d) 21
17
TCS MOCK TEST 4
1.
Middle-earth is a fictional land inhabited by hobbits, elves, dwarves and men. The hobbits and the elves are peaceful creatures who prefer slow, silent lives and appreciate nature and art. The dwarves and the men engage in physical games. The game is as follows. A tournament is one where out of two teams that play a match, the one that loses get eliminated. The matches are played in different rounds where in every round; half of the teams get eliminated from the tournament. If there are 10 rounds played in a knock-out tournament, how many matches were played? (a) 1024 (b) 1023 (c) 1025 (d) 1011
2.
9 years ago, Andromeda’s age was twice Achilles’ age. 9 years hence, Andromeda’s age will be 4/3 times the age of Achilles’. Find Andromeda’s present age in binary numbers. (a) 11011 (b) 11000 (c) 1001 (d) 1010
3.
5 men and 5 women meet and the men dance with the women. Which of the following are always true? A. There are 2 men who have danced with the same number of women. B. There are 2 women who have danced with same number of men. (a) Both A and B (b) A only (c) B only (d) Neither A and B
4.
A number when divided by D leaves a remainder of 8 and when divided by 3D leaves a remainder of 21. What is the remainder left when twice the number is divided by 3D? (a) 13 (b) 42 (c) 3 (d) Cannot be determined
5.
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 powers, 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? (a) 98 (b) 45 (c) 43 (d) 115
6.
The Thousand Pillar Temple of Hyderabad was built by the Kakatiyans of Chalukyan dynasty in the 12th century. Each pillar has carvings made of black monolithic rocks of basalt which are polished to give it a brilliant look. One sunny morning, three tourists visit the temple. Samantha is taller than Lily and taller than two of the thousand pillars and Kelly is shorter than Samantha and three pillars. Which of the following statements would be most accurate? (a) It’s impossible to tell (b) Kelly is as tall as Lily (c) Lily is shorter than Kelly (d) Lily is taller than Kelly
7.
A result of global warming is that the ice of some glaciers is melting. Twelve years after the ice disappears, tiny plants called lichens start to grow on the rocks. Each lichens 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 = 13 * (t-11) for t > 11 where d represents the diameter of the lichen in millimeters, and t represents the number of years after the ice disappeared. Using the above formula, calculate the diameter of the lichen 36 years after the ice has disappeared. (a) 468 mm (b) 457 mm (c) 325 mm (d) 11 mm
8.
A long, thin strip of width 10cm is kept on a flat surface. Another identical strip is kept on it as an overlapping manner such that the combined width of the two is 15cm. What is the width if 22 such strips kept like this? (a) 115 cm (b) 110 cm (c) 200 cm (d) 95 cm
18
9.
The New York Public library is one of the world’s greatest repositories of books and journals. It has a beautiful reading room facing Manhattan’s famous Fifth Avenue. In the reading rooms are 10 reading spots. Each reading spot consists of a round table with 4 chairs placed around it. There are some readers such that in each occupied reading spot there are different numbers of readers. If in all there are 10 readers, how many reading spots are empty? (a) None (b) 6 (c) 5 (d) 4
10.
In the year 2002, Britain was reported to have had 4.3m closed-circuit televisions (CCTV) cameras one for every 14 people in the country. This scrutiny is supposed to deter and detect crime. In one criminal case, the police interrogate two suspects. The ratio between the ages of the suspects is 6:5 and the sum of their ages is 66 years. After how many years will the ratio be 8:7? (a) 11 years (b) 12 years (c) 6 years (d) 7 years
11.
The British mathematician Lewis Caroll also loved to make up fantastic stories in which he embedded a number of clever puzzles and curious riddles. For example, his popular story, Alice in Wonderland, is about young girl called Alice who dreams of a strange world where she meets several unusual characters including the Red Queen and the March hare. In our story, after 2 years of time, Paul will be twice as old as Alice. Presently he is 6 times as old. How old is Paul now? (a) 2 (b) 4 (c) 3 (d) 6
12.
The great Indian mathematician Bhaskaracharya formulated this problem in the twelfth century for his teenage prime number aged daughter Lilavati. He also authored the eponymous Lilavati, a compendium of mathematical puzzles, in which the number of problems that use this formula is the sum of two prime numbers. The product of the two prime numbers is smaller than the total number of problems in the Lilavati. Now, if the difference of any two numbers is 4 and their product is 18, what is the sum of their squares? (a) 34 (b) 40 (c) 52 (d) 42
13.
The Thanksgiving banquet at No.2, Richter Street, had 49 guests which consisted of 6 statesmen, 26 relatives and their families. At the end of a banquet, 19 people shake hands with one other, some of which were between the statesmen alone, some between relatives alone and some between the statesmen and relatives. How many handshakes will there be in total? (a) 342 (b) 171 (c) 180 (d) 162
14.
Two blocks of copper with density of 100 kg/m^3 are twisted into wires of length 100 km and thickness 0.1mm. Copper is a very ductile material. Its ductility is measured in terms of percentage elongation upon application of tensile forces. The conductivity of the copper wire is extremely high rendering it useful in the construction of many electronic circuits. If the voltage through one such circuit is 18 V and the current flowing in the circuit is 190 mA. What is the resistance of the wire? (a) 208.00 K Ohms (b) 3420.00 K Ohms (c) 0.09 k Ohms (d) 10.56 K Ohms
15.
If you rearrange the letters – RAPATEKA – to form a meaningful word, what do you get? (a) A vegetable (b) A fruit (c) A city (d) A bird
16.
There is a pie to be divided among 20 people. A man eats 3 pieces, a women eats two pieces and a child eats half a piece of pie. Find the number of men, women and children so that they are 20 people in total and everyone gets some pie. There are 20 pieces of pie in all. (a) 7 women, 1 men and 12 children (b) 5 women, 1 men and 14 children (c) 6 women, 2 men and 12 children (d) 4 women, 2 men and 14 children
17.
A sheet of paper has statements numbered from 1 to 10. For all values of n from 1 to 10, statement n says At most n of the statement on this sheet are false. Which statements are true and which are false? (a) All the statements are true. (b) The odd numbered statements are true and the even numbered statements are false. (c) The first half of the statements are true and the rest are false. (d) The even numbered statements are true and the odd numbered statements are false.
19
18.
In a pizza restaurant, you get a basic pizza with two toppings, cheese and tomato. You can also make up your own pizza with extra toppings. You can also choose from 10 different toppings, e.g. olives, ham, mushroom, salami etc. Ross wants to order a pizza with 2 different extra toppings. How many different combinations are possible? (a) 100 (b) 1024 (c) 90 (d) 45
19.
There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter 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 liters, second hour it has 20, and so on) If tank B is 1/16 filled after 17 hours, what is the total duration required to fill it completely? (a) 4 hours (b) 20 hours (c) 21 hours (d) 24 hours
20.
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 1sets 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) 7
21.
Peter is twice as old as Paul was when Peter was as old as Paul is now. The combined age of Peter and Paul is 42 years. How old is Peter now? (a) 21 (b) 18 (c) 24 (d) 26
22.
There are 7 children. You are told that the youngest child is a boy. The probability that all of them are boys is 1 in (a) 64 (b) 21 (c) 2 (d) 128
23.
Determine the distance between the x-intercept and the z-intercept of the plane whose equation is 2x+9y-3z=18. (a) 6.32 (b) 10.82 (c) 3.00 (d) 5.00
24.
A toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters, at 10 meters per minute. However, the toy train is defective and it now produces only two different tunes at random. What are the odds that the toy train produces three music tunes of the same type (1 in _____)? (a) 3 (b) 9 (c) 8 (d) 4
25.
A taxi driver commenced his journey from a point, and drove 10 km towards north, and turned to his left and drove another 20 km. After waiting to meet a friend here he turned to his right and continued to drive another 50 km. In which direction is he now? (a) North (b) South (c) West (d) East
26.
Three boys John, Tom and Oliver and two girls Rachel and Kim are to be seated in a row. Rachel always sits to the left of John. No girl sits at the extreme positions and at the middle positions. Tom always sits at the extreme positions. Who sits to the right of Kim? (a) Oliver (b) Tom (c) Tom or Oliver (d) John
27.
The ticket to Disneyland will cost anywhere from 1p to 63p. You need to produce the exact change as the ticket counter and have with you a 63p coin. So you decide to break this into change but you want to carry with you as few coins as possible. Assuming that coins of all denominations are available, how many coins (denominations) would you split the 63p into? (a) 33 (b) 63 (c) 6 (d) 64
28.
Franchois Pachet, a researcher at Sony Computer Science Laboratories, is also a jazz musician. He decided to build a robot able to improvise like a pro. Named Continuator, the robot can duet with a live musician in real-time. It listens to a musical phrase and then computes a complementary phrase with the same playing style. If the cost of making the robot is divided between materials, labour and overheads, it is the ratio of 4:5:2. If the materials costs $ 84.0, the cost of the robot is (a) 184.80 $ (b) 189.00 $ (c) 231.00 $ (d) 462.00 $
20
29.
Fill dirt or fill soil is usually the sub-soil removed from an excavation side and is used to level a place or create artificial mounds. If the average density of sub-soil removed from a site is 3gm/cu cm weighing 400 kg, how many hemispherical pits each of volume 240 cubic cm can this sub-soil fill? (a) 555 (b) 277 (c) 556 (d) 554
30.
A schoolyard contains only bicycles and 4 wheeled wagons. On Tuesday, the total number of wheels in the schoolyard was 166. What could the possible number of bicycles? (a) 14 (b) 10 (c) 12 (d) 11
31.
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 participations in racing, especially in Formula One, where it has enjoyed great success Rohit once bought a Ferraris. It could go 4 times as fast Mohit’s old Mercedes. If the speed of Mohit’s Mercedes is 35 km/hr and the distance travelled by the Ferrari is 986 km, find the total time taken for Rohit to drive that distance. (a) 242 hours (b) 27 hours (c) 7 hours (d) 6.91 hours
32.
Paul the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous accuracy has now been invited to predict ICC world cup matches in 2011. We will assume that the world cup contenders have been divided into 2 groups of 9 teams each. Each team in a group plays the other teams in the group. The top two teams from each group enter the semi finals (after which the winner is decided by knockout). However, Paul has a soft spot for India and when India plays any team, Paul always backs India. Alas, his predictions on matches involving India are right only 2 out of 3 times. In order to qualify for the semi finals, it is sufficient for India to win 7 of its group matches. What is the probability that India will win the ICC world cup? (a) (2/3)^10 (b) (2/3)^9 + 8/3 * (2/3)^9 (c) 8/3 * (2/3)^9 (d) (2/3)^10 + 8/3*(2/3)^9
33.
Three boys Bob, Peter and Oliver and two girls Samantha and Kristie are to be seated in a row. Samantha always sits to the left of Bob. No girl sits at the extreme positions and at the middle positions. Peter always sits at the extreme positions. Who sits to the right of Kristie? (a) Peter or Oliver (b) Bob (c) Peter (d) Oliver
34.
A group of friends Tom, Tim, Dick, Diana, Harry, and Harriet go out to a fair three hundred meters from the McDonalds which is five KMs away. They see a weighing machine and decide to have some fun. However the girls refuse to step on the weighting machine. So Tom, Dick and harry, weigh themselves in a particular order. First Tom, Dick, and Harry weigh themselves individually and then tom and Dick, Dick and Harry, Tom and Harry and then Tom, Dick and harry together respectively. The recorded weight for the last measure is 158 kg. The average of all the 7 measures is (a) 112.86 (b) 52.67 (c) 90.29 (d) 67.71
35.
A schoolyard contains only bicycles and 4 wheeled wagons. On Tuesday, the total number of wheels in the schoolyard was 90. What could the possible number of bicycles? (a) 12 (b) 14 (c) 10 (d) 11
21
TCS MOCK TEST 5
1.
Rahul buys an article at Rs.15850 from the retailer who sells it at a profit of 15%. The retailer bought it from a wholesaler who sold it at a profit of 20%. The manufacture sold it at a profit of 30% to the retailer. Find the cost price of manufacturing the article (approximately)? (a) Rs. 8835 (b) Rs.15000 (c) Rs. 12192 (d) Cannot say
2.
Find the maximum possible value of x-y+33 if x, y are any two single digit integers, not necessarily the same. (a) 41 (b) 33 (c) 42 (d) 43
3.
Arun was all bent on building a new house. He carefully got the blue print of his house designed by his friend Ashwin, a civil engineer. He wanted to build a room of dimension 27 by 48 ft and lay tiles in this room. Each tile was of dimension 2 by 3 ft. How many such tiles should Arun buy? (a) 184 (b) 224 (c) 318 (d) 216
4.
Find the value of (a) 191
213 x 213 x 213 - 31 x 31 x 31 . 213 x 213 + 213 x 31 + 31 x 31
(b) 182
(c) 178
(d) 210
5.
5 Neptuninas can destroy 5 small plutos in 5 solar years. How long will 7 Neptunians take to destroy 7 small plutos (in solar years)? (a) 7 (b) 5 (c) 10 (d) 12
6.
Jenny makes a block with small cubes of 9 cubic cm volume. To make the block, she uses 4 small cubes long, 8 small cubes wide and 16 small cubes deep. She realizes that she has used more small cubes than she really needed. She realizes that she could have glued a fewer number of cubes together to look like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to take out so that the bigger cube is hollow? (a) 168 (b) 512 (c) 344 (d) 342
7.
In a group there are 5 singers, 3 dancers, 2 artists, 1 musician, 1 guitarist and 1 teacher. The average height of the above mentioned people reduces by 2cm if I replace the guitarist with a joker. Find the height of the joker if the height of the guitarist is 184 cm. (a) 154 cm (b) 171 cm (c) 158 cm (d) 160 cm
8.
How many 3-digit numbers have even number of factors? (a) 22 (b) 879 (c) 21
(d) 878
9.
Seven years ago, the combined ages of Amir and Akshay was twice that of Saif. If the sum of the ages of Akshay and Amir, fifteen years hence, is 98 years, what is the present age of Saif? (a) 27 yrs (b) 35 yrs (c) 34 yrs (d) 49 yrs
10.
If there are 30 cans out of them one is poisoned. If a person tastes very little of this he will die within 14 hours so they decided to test it with mice. Given that a mouse dies in 24 hours and you have 24 hours in all to find out the poisoned can, how many mice are required to find the poisoned can? (a) 29 (b) 15 (c) 6 (d) 5
11.
Cadbury manufactures a chocolate box which contains “x” number of chocolates. There are three houses A, B and C in the neighbourhood of Cadbury. Since it is a new variety of chocolate, the marketing manager of Cadbury decided to distribute free chocolates to the children in the neighbouring houses A, B and C. In House A there are 3 children, in B there are 5 children, and in C there are 7 children. After distributing the chocolates, he was left with one chocolate in each case. How many chocolates did he have in the beginning for distribution? (a) 204 (b) 211 (c) 214 (d) 217
22
12.
Vodafone has come up with a new scheme called “Pay Easy”. They have decided to charge the first 100 calls of a Pay Easy customer @Rs.1/-call, the next 100 calls @Rs.1.25/-call and the next 100 calls @Rs.1.75/-call. Raj is a Pay Easy customer. He paid Rs.286.25/- as his mobile bill that month. How many calls did Raj make? (a) 243 (b) 241 (c) 242 (d) 235
13.
Pointing to a photograph, a man tells his friend, “She is the daughter of the only son of my father’s wife”. How is the girl in photograph related to the man? (a) Niece (b) Daughter (c) Mother (d) None of these
14.
Arvind, a mason, decided to build a small house. For constructing the house he had to mix gravel, sand and cement in the ratio 7:5:3. The cement costs Rs.250 a bag which contains 10 kg of cement. He has spent Rs.4500 to buy cement. How much will he have to spend for sand which costs Rs.70 for a 20 kg bag? (a) Rs.1050 (b) Rs.2050 (c) Rs.1075 (d) Rs.2000
15.
Find the missing term in the sequence 2, 6, 22, 86, 342, ___. (a) 728 (b) 1366 (c) 912
(d) 1648
16.
If 29th February 2004 was a Sunday, which month starts with a Sunday in that year? (a) September (b) October (c) August (d) December
17.
Kailash faces North. Turning to his right, he walks 25 m. He then turns to his left and walks 30 m. Next, he moves 25 m to his right. He then turns to his right again and walks 55 m. Finally, he turns to the right and moves 40 m. In which direction is he now from his starting point? (a) South-West (b) South (c) North-West (d) South-East
18.
Eight years ago, the average age of a family of three members was 25 years. A baby was born after a few years and the present average age of the family is the same as it was eight years ago. What is the present age of the baby? (a) 2 yrs (b) 3 yrs (c) 4 yrs (d) 1 yr
19.
A family consists of a father, a mother, their two sons and the youngest daughter. The age of the first son and daughter are in the ratio 3:1. The mother is 3.5 times as old as the second son. The age of the second son is 2/3 of the age of the first son. The age of the youngest daughter is 5 years. What is the age of the mother? (a) 40 (b) 35 (c) 15 (d) 25
20.
When 5% of the total wheat is lost in grinding, a country can export 9 million tons of wheat, but when 6% of the total wheat is lost in grinding it needs to import 2 million tonnes of wheat. What is the total production of wheat in the country? (in million tonnes) (a) 1000 (b) 900 (c) 1100 (d) 1150
21.
Mr.Govind was a building contractor. He was doing reasonably well in his business but was always on an expansion mode. Mr.Govind won a contract with the Corporation and his business began to boom. So he decided to deploy more people in his projects. If he were to increase his labour force by 33.33%, what will be percentage reduction in the work load of each employee? (a) 75 (b) 50 (c) 25 (d) 33.33
22.
5-digit numbers are formed using the digits 1, 2, 3, 4 and 5 without repetition. The probability that a numbers so formed is divisible by 6 is (a) 1/5 (b) 2/5 (c) 3/5 (d) 4/5
23.
A pipe can fill a tank in 3 hrs. Due to a leakage in the tank, it takes 3.5 hrs to fill the same tank. Then how many hours will the leakage can empty the tank. (a) 3.5hrs (b) 30hrs (c) 0.5 hrs (d) 21hrs
23
24.
Joe counts 48 heads and 134 legs among the chickens and dogs on his farm. How many dogs does he have? (a) 29 (b) 21 (c) 18 (d) 19
25.
A father with eight children takes three at a time to the zoological garden, as often as he can, without taking the same three children together more than once. How often will he go and how often will each child go? (a) 56, 35 (b) 92, 42 (c) 56, 21 (d) 56, 42
26.
John buys a cycle for 31 dollars and gives a cheque for 35 dollars. The shopkeeper exchanges the cheque with his neighbour and gives the change to John. After 2 days, the cheque is bounces and the shopkeeper is forced to pay the cheque amount to his neighbour. The cost price of the cycle is 19 dollars. What is the loss incurred by the shopkeeper? (a) 23 (b) 35 (c) 19 (d) 31
27.
A person buys a brand new Honda bicycle for Rs.800. He uses it for a year and then sells it. He makes a profit of 10% in this transaction. Then, again, he buys a new cycle but finds that the price has gone up by 20%. He uses the new cycle for a year and then sells it for a profit of 30%. Find the average annual profit of the person through these transactions. (a) 160 (b) 184 (c) 168 (d) 172
28.
A cuboid of length 4 cm, breadth 6 cm and height 8 cm is formed using unit cubes. All the faces of the cuboid are painted using different colours. Now the cubes are separated and the cubes with no face painted are used to form a new cuboid. Find the volume of the newly formed cuboid. (a) 48 (b) 72 (c) 96 (d) 36
29.
Eight coins are tossed together. The probability that all of them show the same face is 1 in (a) 256 (b) 128 (c) 4096 (d) 64
30.
The Tatas have decided to launch their new brand “Aria” in the SUV segment. Mr.Mehra decided to take a test drive before choosing Aria. During the test drive, he found that Aria could cover 500m in 20seconds. Aria is known for its uniform acceleration. Can you find out the acceleration? (a) 3.2 (b) 2.5 (c) 1.8 (d) 2
31.
The points A (-5,4), B (-7,6) and C (5,2) are the coordinates of a right angled triangle. Which of the following angle is a right angle? (a) A (b) B (c) C (d) None of these
32.
If Tarun buys only pens costing Rs.13 each or only pencils costing Rs. 5 each, he is left with Rs. 2 in each case. Which of the following cannot be the amount available with him? (a) Rs. 457 (b) Rs. 782 (c) Rs. 577 (d) Rs. 1042
33.
A man, a woman and a boy can do a work in 20 days, 30 days and 60 days respectively. How many boys must assist 2 men and 8 women to do the work in 2 days? (a) 4 (b) 5 (c) 6 (d) 8
34.
We all know that Aryabhatta is a greatest mathematician from India. When his daughter Mayabati was a teenager, he discovered a problem. At that time, Mayabati’s age was x, a prime number. After some years, her age became y. At this time, Aryabhatta was able to solve that problem with the help of his daughter Mayabati. If x + y = 15 and the product of x and y is 26 then what is the sum of the squares of the two numbers x and y? (a) 212 (b) 173 (c) 128 (d) 132
35.
A bag contains 20 yellow balls, 23 green balls, 27 white balls. What is the minimum number of balls one should pick out so that to make sure that one gets at least 2 balls of all colours? (a) 48 (b) 52 (c) 60 (d) 68
24
ANSWER KEYS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
MOCK TEST 1 d 21 b 22 a 23 c 24 a 25 a 26 a 27 a 28 d 29 a 30 b 31 b 32 c 33 d 34 b 35 a d a b b
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
MOCK TEST 3 c 21 b 22 d 23 d 24 c 25 a 26 b 27 d 28 b 29 a 30 b 31 c 32 a 33 a 34 b 35 d a c b a
1 2 3 4 5 6 7
a d d b b a c
8 9 10 11 12 13 14
d b d c c d b b b b c a b b d
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
d d a c b d b c b c a b d a c
d a d b d b b
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 MOCK TEST 5 15 b 16 c 17 d 18 d 19 b 20 c 21 c
22 23 24 25 26 27 28
MOCK TEST 2 b 21 c 22 b 23 c 24 c 25 a 26 b 27 a 28 c 29 d 30 d 31 a 32 a 33 a 34 b 35 a a d c d MOCK TEST 4 b 21 a 22 d 23 c 24 d 25 a 26 c 27 a 28 b 29 b 30 c 31 c 32 b 33 c 34 d 35 b a d c a
b d d c a b a
29 30 31 32 33 34 35
a b d a a d a b b d a c a a b
c a b d a c c c a d d d a c d
b b d c d b b
25
POPULAR TCS QUESTIONS SIMPLIFIED!
SHORTCUTS and TRICKS make life…and tests simple… For this very reason, after extensive research, our experts have come up with simple formulae, tips and guidelines for popular TCS Questions. But please remember, SHORTCUTS are not failsafe. Aptitude Test patterns and questions are subject to change anytime and there’s no better strategy than thorough reading, concept strengthening and consistent practice. And then of course – if you get lucky – apply shortcuts to save time!
POPULAR QUESTION #1 Lines and Programmers (No of workers )∗Time Amount of work
= constant
(No of programmer )∗(Time ) No . of lines codes
= constant
FORMULA 1: If asked to find lines of codes n1 lines, n1 programmers, n1 min Let x lines, n2 programmers, n2 min ( n1 programmers )∗(n1 min ) ( n2 programmers )∗(n2 min ) = n1 lines x lines
Lines of codes = x =
𝒏𝟐∗𝒏𝟐 𝒏𝟏
FORMULA 2: If asked to find no. of programmers n1 lines, n1 programmers, n1 min Let n2 lines, x programmers, n2 min ( n1 programmers )∗(n1 min ) ( x programmers )∗(n2 min ) = n1 lines n2 lines
No. of Programmers = x = n1 FORMULA 3: If asked for time taken (in min) n1 lines, n1 programmers, n1 min Let n2 lines, n2 programmers, x min ( n1 programmers )∗(n1 min ) ( n2 programmers )∗(x min ) = n1 lines n2 lines
Time taken = x= n1
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POPULAR QUESTION #2: Points on a Plane n1(P) n points:
For Maximum number of lines, place the points on a circle. Then number of lines = Number of points = n Maximum n lines E.g.: For 5 points, lines are as shown in right-hand figure: Similarly for Minimum no. of lines, take points inside a triangle. If no condition 2 lines With condition 3 lines
POPULAR QUESTION #3 Handshakes n people TYPE 1: Let n people {a1, a2 ... an} meet and shake hands in a circular fashion. In other words, there are totally n handshakes involving the pairs, {a1, a2}, {a2, a3}, ..., {an-1, an}, {an, a1} For no cycle, we have to exclude the pair ( an-1, an). So, when no cycle, the MAXIMUM no. of handshakes = (n-1) handshakes. TYPE 2: For minimum people in a set we can consider handshakes as {a1, a2, a3}, {a4, a5, a6}, {a7, a8, a9},…….{ an-2,an-1,an} For minimum people, we can consider the set {a2, a5, a8… an-1}. 𝒏
So, MINIMUM people in a set = 𝟑
POPULAR QUESTION #4 Statements TYPE 1: Question states “At most n are true” All true / 1st half false TYPE 2: Question states “At least n are true” 1st half true, 2nd half false TYPE 3: Question states “Exactly n true” One statement true / Second last statement true * In case the question is asked with “false”, then replace wherever “true” is there in the previous answers with “false” and vice versa in all types. E.g.: Question states “At most n are false” All false / 1st half true
27
POPULAR QUESTION #5 Dart Board Probability (Q is close to centre) =
Area of Inner Circle Area of the Bigger Circle
=
𝑟 2
𝜋( )2 𝜋(𝑟)2
=
1 4
1
Probability (Q is close to centre) = 4 = 0.25 1 4
Probability (Q is close to periphery) = 1- =
3 4
= 0.75
POPULAR QUESTION #6 Ghana Bolivia – Football Match – Octopus Probability (Paul will correctly pick the winner) = Probability (Paul picks Ghana and Ghana wins) + Probability (Paul picks Bolivia and Bolivia wins) = Probability (Paul picks Ghana)* Probability (Ghana wins/ Paul picks Ghana) + Probability (Paul picks Bolivia)* Probability (Bolivia wins /Paul picks Bolivia) For Q.16 of Mock Test 1, 2
Required Probability = ( 3 *
2 3
1
)+(3 *
1 3
5
) = 9 = .55
For Q.12 of Mock Test 2, 5
5 6
5
5 9
Required Probability= ( 6 *
1
)+(6 *
1 6
26
) = 36 = .72
For Q.9 of Mock Test 3, Required Probability= ( 9 *
4
)+(9 *
4 9
41
) = 81 = .51
POPULAR QUESTION #7 Red Ball Maximize out of 2 Boxes 1
1
No of red balls − 1 No of balls − 1
Required Probability = ( 2 ) + 2 (Total
)
POPULAR QUESTION #8 Unpainted Faces of a Hollow Cube n cm cube Answer = (( 𝑛3 − (𝑛 − 2)3 ) * 6) – (No of faces painted *n2) Suppose 5 cm cube with 4 faces painted (( 53 − (5 − 2)3 ) * 6) – (4 * 52 )
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POPULAR QUESTION #9 Planet – Finger B No. of fingers 1 - 100 2B 1 - 1000 3 B2 1 - 10000 4 B3
POPULAR QUESTION #10 Triangle – Equidistant points If 3 lines in a plane are such that the points of intersection form a triangle of any kind, then the number of points equidistant from all the 3 lines is 4, consisting of 1 in-centre and 3 ex-centres. (as shown in right-hand side figure)
POPULAR QUESTION #11 Poison Cans – Mice n cans Convert (n-1) to binary Answer is the number of digits in the binary number E.g.: In Q.32 of Mock Test 2, there are 45 cans. 45 - 1 = 44; Binary value of 44 is 101100 which has 6 digits. Therefore, answer is 6.
POPULAR QUESTION #12 Red Green Yellow socks /Gloves/Marbles (Maximum of Red, Green, Yellow) + (2nd maximum of Red, Green, Yellow) + 2
POPULAR QUESTION #13 Suspects TYPE 1: A All lying B Left most culprit/ guilty Answer A and B TYPE 2: A All lying B Left most innocent Answer A or B
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POPULAR QUESTION #14 Clocks – Planet Oz 360°
2
Speed of the hour hand = 18×90 minutes = ( 9 ) ° per minute. 360°
Speed of the minute hand = 90 minutes = 4° per minute. 2
Relative speed of the two hands of clock = (4 - 9 ) ° per minute =
34° per minute. 9
Suppose we have to find angle at H hr and M minutes. Then 360° of the number of hours in a day on the Planet
Angle = (half
360° 34° )H±( 9 )M 18
×M(
) × H ± (relative speed of the two hands of the clock)
34° )M 9
= (20°) H ± (
E.g. 1 for 12: 40 am 34° ) 40 9
Angle = (20°) 12 ± (
= 240° ± 151.11° = 89° (or) 391.11° E.g. 2 for 11: 40 am 34° ) 40 9
Angle = (20°) 11 ± (
= 220° ± 151.11° = 69° (or) 371.11° E.g. 3 for 9: 40 am Angle = (20°) 9 ± (
34° ) 40 9
= 180° ± 151.11° = 29° (or) 391.11° For this type of question, we have found that most frequently asked are 12: 40 am 89° / 11: 40 am 69° / 9: 40 am 29°
POPULAR QUESTION #15 Number of matches – n rounds Answer 𝟐𝐧 − 𝟏
30
POPULAR QUESTION #16 Alok and Bhanu – Maximize Value for Equation If equation in the question is N= (X+Y-Z) + K Answer = K+ 11 N= (X-Y-Z) + K Answer = K+ 2 N= (X*(Y-Z)) + K Answer = K+ 18
POPULAR QUESTION #17 Envelopes Reasoning: Placing exactly one letter in a wrong envelope and remaining letters in proper envelopes is not possible because if remaining letters are properly placed, then that one particular letter has to be placed into its own envelope. So given event is an impossible event. Probability (exactly 1 letter in improper envelope) = 0 POPULAR QUESTION #18 Divisible by 4, digits 1, 2, 3, 4, 5 form n digit number when repetition of digits is allowed Number of values = 𝟓𝐧−𝟏
POPULAR QUESTION #19 Alice Bob – Coin Stack Answer Alice moves 1 move
POPULAR QUESTION #20 Hare Tortoise Race
By fluke, we found that the answer to this question always had a decimal point while all other options did not! So look for the option with decimal point. Now, to be safe, also learn the quick application formula: X first distance Y meeting point distance Answer =
𝟏−𝒚 (𝟏− 𝒙+𝒚 ) 𝒚𝟐
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POPULAR QUESTION #21 Distance ∗ Speed
Time taken by Ferrari n times
POPULAR QUESTION #22 Circles – Anoop – x circles Let a = side of the square, n = no of circles and r = radius of the circle
Then a 2 = 2 2 r + (2n-2) r a 2 = 2[ 2 + n − 1]r
So
a r
= 2[
or
𝐚 𝐫
=
and
r a
2+n −1] 2
𝟐[ 𝟐+𝐧−𝟏] 𝟏
=
=
(𝐧−𝟏) 𝟐 +𝟐 𝟏
1 (𝐧−𝟏) 𝟐 +𝟐
Side of square: radius of circle = [(n-1) 𝟐 + 2]: 1 = [(n-1)1.4 + 2]: 1 E.g.: In Q.22 of Mock Test 1, 𝑟 𝑎
=
1 (𝟕−𝟏) 𝟐 +𝟐
=
1 𝟔 𝟐 +𝟐
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POPULAR QUESTION #23 Diameter of coins 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟
1.5𝑛 should be less than 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 Answer = n+1
POPULAR QUESTION #24 Pace length n = P(cm )
x
Answer =
𝐱 ∗ 𝟔𝟎 ∗ 𝐏 𝟐 𝟏𝟎𝟕
POPULAR QUESTION #25 Number 𝑛 2
𝑛
=3+6
Number divisible by 2 and 3 is the answer.
POPULAR QUESTION #26 Water Tank Amount of water in the tank B after any hour is twice the amount of water in it, previous hour. 1 So if 2n is the part of the tank B filled in x hours then, 1 1 ×2 = n −1 part 2n 2 1 1 water in tank = 2n −1 ×2 = 2n −2 . 1 1 water in tank = 2n −2 ×2 = 2n −3 .
After 1 hour water in tank = After 2 hours After 3 hours
1
1
Continuing this way water in tank after n hours (n hours after x hours) =2n −n = 20 = 1 part. So total time = (x + n) hours. In short, 1 if 2n is the part of Tank B filled in x hours, then time taken to fill the remaining part is n hour. 𝟏
If 𝟐𝒏 is filled in x hours, then Answer (x + n) hours E.g.: In Q.23 of Mock Test 2, 1 64
1
= 26 is filled in 17 hours. Here, n=6 and x = 17 hours. Therefore, answer = 17 + 6 = 23 hours.
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