TCS_2011 Questions with Explanation

1. TCS_2011 Questions with Explanation Gradient Training Pvt. Ltd. B-55, Shahid Nagar, Bhubaneswar +91-674-2540254

2. 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? a) 37.80  b)8  c) 40  d) 5 Answer: 37.8 Explanation: (H-1) (H – 1 - H/T) where T = 5 as tortoise has covered 1/5, so take value of T as denominator of the fraction. And H = 8 as Hare has covered 1/8, of the distance before meeting the tortoise, so take value of H as denominator of the fraction. By Substituting the values one can get the answer quite easily. Note: The value of the fraction keeps on changing but only consider the integer in the denominator of each fraction as explained above. The question also comes with data such that H = 4 and T = 3. In that case, answer is 5 times. Gradient Training Pvt. Ltd.

3. Alok and Bhanu play the following min-max game. Given the expressionN = 40 + X + Y – ZWhere 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) 31 b) 50 c) 51 d) 58 Answer: 51 Explanation : Optimal Values in Min-Max game of different expressions are: X+Y-Z= 11; X-Y-Z= 2; X(Y-Z) = 18 Gradient Training Pvt. Ltd.

4. 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)1/9    b)4/9    c)5/9    d)2/3 Ans: 5/9 Explanation: (2/3)*(2/3) --Prediction about Ghana being true + (1/3)*(1/3)----Prediction about Bolivia being true = 5/9 NOTE: Sometime the question comes with probability of Ghana winning as 11/12, in that case the answer is 0.85 Gradient Training Pvt. Ltd.

5. After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?a)1/12    b)0    c)12/212  d)11/12 Ans: 0 Explanation: Impossible Event of exactly one letter going into wrong envelope. Minimum 2 letters are required such that both can go into wrong envelopes. -------------------------------------------------------------------------- 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 Ans: 4 Explanation: There are three Ex-Centres and one in-centre of any triangle, which are all equidistant from the sides of the triangle Gradient Training Pvt. Ltd.

6. 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 isa)1/2    b)14/19      c)37/38 d)3/4     Ans: 14/19 Explanation: Put all red balls except one from the 1st to the 2nd box. So, the probability of drawing a red ball becomes ½*1 + ½*(9/19) = 14/19 ½ is probability of bag selection and 1 & 9/19 are red ball selection probabilities from 2 boxes NOTE: Minimum probability of drawing a red ball is when all the red and green balls are put into the same box. So, the probability will be ½*0 + ½*(10/20) = ¼ Also, this question comes with the data 39 Red and 26 Green balls. In that case the answer is ½ *1 + ½ * {38/(38+26)} = 0.8 Gradient Training Pvt. Ltd.

7. A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the center of the circle than the periphery?a) 0.75    b) 1    c) 0.5    d) 0.25Ans: 0.25 Explanation: Probability =favorable area / Total Area = ∏ (0.5)2 / ∏ (1)2 = 0.25 ----------------------------------------------------------------------------- 14 people meet and shake hands. The maximum number of handshakes possible if there is to be no ‘cycle’ of handshakes is (A cycle of handshakes is a sequence of people a1, a2,…ak, k>2 such that the pairs {a1,a2}, {a2,a3},…, {a(k-1), ak}, {ak, a1} shake hands). a) 11 b) 12 c) 10 d) 13 Answer: 13 Explanation: if n members are there, maximum number of handshakes would be n-1 if the cycle of handshakes is not to be completed. So, for 14 people above, answer is 14-1=13. Gradient Training Pvt. Ltd.

8. 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 and 3 blue faces      b) 2 red and remaining blue c) 6 red and 0 blue d) 4 red and remaining blue Ans: 3 red and 3 blue faces Explanation: Let there be m red and 6-m blue faces on the 2nd die. The probability of A winning should be ½ as both A & B have equal probability of winning. Prob (A wins) = (4/6) * (m/6) + (2/6) * (6-m)/6 = ½; So, m= 3 {both red} {both Blue} So, 3 red faces and 3 blue faces must be there. NOTE: whatever be the number of red and blue faces on the 1st die, the 2nd die will always have 3 red and 3 blue faces for A and B to have equal probability of winning. Gradient Training Pvt. Ltd.

9. Alice starts and the two 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. Thena) In order to win, Alice's first move should be a 1-move.b) In order to win, Alice's first move should be a 0-move.c) In order to win, Alice's first move can be a 0-move or a 1-move.d) Alice has no winning strategy. Answer: In order to win, Alice's first move should be a 1-move. Explanation: In this case, bringing the golden coin to the top results in loosing the game. i= 0 or 1 will keep the golden coin at the 3rd place and i≥2 will take it to the 2nd place. Consider the following moves by A & B in the same sequence. A –0;B - ≥2 (Golden coin now comes at the 2nd place)---A looses whatever he does A -1; B - ≥2; A-0 and then B looses whatever he does A -1; B - 0; A- ≥2 again B looses whatever he does So, Picking a 1-move ensures A’s win Sometimes, instead of 20, there are different no. of coins but the answer won’t change. NOTE:If, however, bringing the golden coin to the top results in winning, A has no winning strategy Gradient Training Pvt. Ltd.

10. Alice and Bob play the following coins-on-a-stack game. 100 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly moving the topmost coin to another position in the stack. Alice starts and the players take turns. A turn consists of moving the coin on the top to a position i below the top coin (for some i between 0 and 100). We will call this an i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated; for example once a player makes a 2-move, on subsequent turns neither player can make a 2-move. Initially, the gold coin is the third coin from the top. Then a) In order to win, Alice’s first move should be a 1-move. b) In order to win, Alice’s first move should be a 0-move. c) Alice has no winning strategy. d) In order to win, Alice’s first move can be a 0-move or a 1-move. Answer: Alice has no winning strategy. Explanation: In this case Alice has no winning strategy. Consider the moves below A–0;B-1; A-≥2 ; B-bringing the coin on top and winning A-1; B-0; A–≥2 ; B-bringing the coin on top and winning A –≥2; B-bringing the coin on top and winning So in all cases B wins and A looses. So, A has no winning strategy. Gradient Training Pvt. Ltd.

11. Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a circle with each coin touching two other coins. Two of the coins are special and the rest are ordinary. Alok starts and the players take turns removing an ordinary coin of their choice from the circle and bringing the other coins closer until they again form a (smaller) circle. The goal is to bring the special coins adjacent to each other and the first player to do so wins the game. Initially the special coins are separated by two ordinary coins O1 and O2. Which of the following is true?a) In order to win, Alok should remove O1 on his first turn.b) In order to win, Alok should remove one of the coins different from O1 and O2 on his first turn.c) In order to win, Alok should remove O2 on his first turn.d) Alok has no winning strategy. Answer: In order to win, Alok should remove one of the coins different from O1 and O2 on his first turn. Explanation: The 1st person to move is always the winner if he is presented with a set up such that there are even number of ordinary coins on one side and odd number of ordinary coins on the other side of the special coins. In order to win, 1st player should always remove the coins from the odd side. Gradient Training Pvt. Ltd.

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 and also write code at the same rate. Suppose 14 such programmers take 14 minutes to write 14 lines of code in total. How long will in take 5 programmers to write 5 lines of code in total ? a)19 b) 5 c) 14 d) 70 Answer: 14minutes Explanation: P1T1/L1 = P2T2/L2 P---Number of Programmers T---Time taken in Minutes L--- Lines of codes to be written Gradient Training Pvt. Ltd.

13. 45 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. The suspects are made to stand in a line and each person declares that the person next to him on his right is guilty. The rightmost person is not questioned. Which of the following possibilities are true? A. All the suspects are lying. B. The leftmost suspect is guilty. C. The rightmost suspect is guilty. Which is the logical combination of statements a) A only b) A and C c) B only d) A and B Answer: A and B Explanation: Each of the suspects is blaming the person on the right (except the rightmost one). The only person who is not blamed by anyone is the leftmost person. So, if we assume that everyone is lying (Statement A) that will lead us to the conclusion that the leftmost person is guilty (Statement B) Gradient Training Pvt. Ltd.

14. The dynamics of crowd behavior are hard to study because usually people are not reliable witnesses of their own behavior. Now consider 4 people standing in the queue of a supermarket. You want to predict their behavior based on their age group. You get to know from the supermarket records that their average age 4 years ago was 43 years. After a while, another person joins the queue and the present average of all the 5 is 40 years. The present age of the last person in the queue is : a) 28 years b) 12 years c) 32 years d) 24 years Answer: 12 years Explanation: Average age of 4 person in the queue four years ago was 43 years. Present average age of 4 of them = 47 years So, sum of the ages of 4 of them = 47*4 = 188 years Average Age of all 5 of them = 40 years So, sum of the ages of all 5 of them = 40*5 = 200 years Hence the age of the 5th person is 200 – 188 = 12 years Gradient Training Pvt. Ltd.

15. One day Snow-white meets Pal and Unicorn in the Fairyland. She knows the Pal lies on Mondays, Tuesdays and Wednesdays, and tells the truth on the other days of the week. Unicorn, 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 Snow-white – Pal: Yesterday was one of those days when I lie. Unicorn: Yesterday was one of those days when I lie too. What day is it? a) Tuesday b) Monday c) Thursday d) Sunday Answer: Thursday Explanation: Go Through Options. If you check for Thursday, It is a ‘TRUTH DAY’ for Pal and a ‘LIE DAY’ for Unicorn. So, pal should tell the truth and Unicorn should lie on Thursday, which they are doing when they mention that statement. Gradient Training Pvt. Ltd.

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

17. Mr. Beans visited a magic shop and bought some magical marbles of different colors along with other magical items. While returning home whenever he saw a colored light, he took out marbles of similar colors and counted them. So he counted the pink colored marbles and found that he has bought 25 of them. Then he counted 14 green marbles and then 21 yellow marbles. He later counted 30 purple colored marbles with him. But when he reached a crossing, he looked at a red light and started counting red marbles and found that he had bought 23 Red marbles. As soon as he finished counting, it started raining heavily and by the time he reached home he was drenched. After reaching home he found that the red, green and yellow marbles had magically changed colors and became white, while other marbles were unchanged. It will take 1 day to regain its colors, but he needs to give at least one pair of marbles to his wife now. So how many white marbles must be choose and give to his wife so as to ensure that there is at least one pair of red, yellow and green marbles? a) 46 b) 35 c) 29 d) 48 Answer: 46 Explanation: There are 23 red, 21 yellow and 14 green marbles. These are marbles which are changing colors to white. We will take the ‘worst case scenario’, i.e. despite picking a certain number of marbles, Mr Beans is not sure of picking at least 2 of each color. So, for that we add the two bigger numbers 23 and 21 and then add 2 more to it. So worst case scenario is 23 red + 21 yellow + 2 Green = 46 marbles. Minimum that is the number which he has to pick in order to be sure of having at least one of each color Gradient Training Pvt. Ltd.

18. In the reading room of a library, there are 23 reading spots. Each reading spot consists of a round table with 9 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 36 readers, how many reading spots do not have even a single reader? a)8 b) none c) 16 d) 15 Answer: 15 Explanation: start with 1 reader on 1st reading spot 2 readers on 2nd reading spot 3 readers on 3rd reading spot and so on… 36 readers in this manner will occupy 8 reading spot as 1+2+3…8 = 36. So, 23-8=15 reading spots would be vacant NOTE: Sometime this question comes with 10 reading spots and 4 chairs on each spot. Answer in that case is 6 spots would remain vacant. Gradient Training Pvt. Ltd.

19. Susan used small cubes of 8 cubic cm volume to make a block, 3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized 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 make the block? a)114 b) 135 c) 21 d) 71 Answer: 114 Explanation: Total number of small cubes = 3X9X5 = 135 Total number of small cubes to be removed to make a hollow block = 1X7X3 = 21 So, number of small cubes required would be 135-21 = 114 cubes NOTE: If there are is a cuboid of p X q X r small cubes, number of small cubes in the core (beneath the outer surface) would be (p-2) X (q-2) X (r-2). Gradient Training Pvt. Ltd.

20. A toy train produces 10 different sounds when it moves around a circular toy track of radius 5 m at 10 m per min. However, the toy train is defective and it now produces only 2 different tunes at random. What are the odds that the train produces four consecutive music tones of the same type?a) 1 in 16 b) 1 in 4 c) 1 in 8 d) 1 in 32 Answer: 1 in 8 Explanation: for four consecutive times the probability of a particular musical tune is (½)4. But there are 2 tunes so either of them can be played 4 consecutive times would be 2X (½)4 = (½)3 = 1/8 Note: If the music tune has to be played n consecutive times, answer would be 1/2n-1 or 1 in 2n-1. ------------------------------------------------------------------------- Out of 7 children the youngest is boy then find the probability that all the remaining children are boysa) 1/64 b) 1/32 c) 1/128 d) 1/256Answer: (½)6 = 1/64. Here only one choice is there that of boy. So, the probability would be 1/2n Gradient Training Pvt. Ltd.

21. A car manufacturer produces only red and blue models which come out of the final testing area completely at random. What are the odds that 5 consecutive cars of the same color will come through the test area at any one time? a)  1 in 16      b) 1 in 12     c) 1 in 32     d)1 in 25 Answer: 1 in 16 Explanation: for five consecutive times the probability of a particular color car coming out is (½)5. But there are 2 colors, so either of them coming out 5 consecutive times would be 2 X (½)5 = (½)4 = 1/16 Note: If there are n cars of the same color, answer would be 1/2n-1 or 1 in 2n-1. ------------------------------------------------------------------------------------- A scientist was researching on animal behavior in his lab. He was very interested in analyzing the behavior of bear. For some reason he travelled 1mile in north direction & reached at North Pole. There he saw a bear. He then followed the bear around 1 hr with a speed of 2km/hr in east direction. After that he travelled in south direction & reached at his lab in2 hrs. Then what is the color of the bear? a) White b) Black c) Gray d) Brown Answer: White Explanation: Polar bears come only in one color i.e. white, unless they are wearing black jackets due to the cold weather! Gradient Training Pvt. Ltd.

22. A person has to make 146 pieces of a long bar. He takes 4 seconds to cut a piece. What is the total time taken by him in seconds to make 146 pieces?a) 584 b) 580 c) 730 d) 725 Answer: 580 Explanation: 146 pieces would require 145 cuts. So total time would be 145* 4 = 580 seconds --------------------------------------------------------------------------- A Person buys a horse for 15 pounds, after one year he sells it for 20 pounds. After one year, again he buys the same horse at 30 pounds and sells it for 40 pounds. What is the profit for that person? Answer: 15 pounds Explanation: In the 1st transaction there is a profit of 5 pounds and in the 2nd one, 10 pounds. Total profit = 15 pounds Gradient Training Pvt. Ltd.

23. A lady has fine gloves and hats in her closet- 13 blue, 27 red, and 40 yellow gloves are there. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that if it is a glove. How many gloves must she take out to make sure she has a pair of each color? Answer: 69 gloves Explanation: Two largest values + 2 more. 40+ 27 + 2 = 69 NOTE: Just like Mr. beans this problem would be solved by the same logic Gradient Training Pvt. Ltd.

24. If there are 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the possible number of 2 wheelers parked there if there were 58 wheels parked there. a)10 b) 23 c) 22 d) none Answer: 23 Explanation: 2a + 4 b = 58. a and b are no. of 2 & 4 wheelers respectively So, a + 2b = 29 or 2b = 29 – a. In the above equation, a has to be odd for b to be an integer. NOTE: the above question comes with numerous variations and data. In all the cases choose the odd value from the options. ------------------------------------------------------------------------------------ One grandfather has three grandchildren, two of their age difference is 3, eldest child age is 3 times the 2nd child’s age and eldest child’s age is two times of sum of other two children. What is the age of eldest child? Answer: 18 Explanation: Take the ages of 3 grandchildren as a, a+3 and 3(a + 3) It is given that eldest child’s age is twice the sum of other two children. So, 3(a+3) = 2 (2a + 3). From here a = 3 and eldest child’s age is 18 years. Gradient Training Pvt. Ltd.

25. Consider two vessels, the first containing one liter of water and the second containing one liter of Pepsi. Suppose you take one glass of water out of the first vessel and pour it into the second vessel. After mixing you take one glass of the mixture from the second vessel and pour it back into the first vessel. Which one of the following statements holds now? None of the statements holds true. There is less Pepsi in the first vessel than water in the second vessel. There is more Pepsi in the first vessel than water in the second vessel. There is as much Pepsi in the 1st vessel as there is water in the 2nd one Answer: There is as much Pepsi in the 1st vessel as there is water in the 2nd one Explanation: The process explained above will always lead to the same ratio of Pepsi and water in the 1st as that of water and Pepsi in the 2nd vessel. In other words, Vessel 1–Water : Pepsi = a:b Vessel 2– Pepsi : Water = a:b NOTE: Even if the above process is repeated several times, the result explained above will not change i.e. there will be as much Pepsi in the 1st vessel as there is water in the 2nd one and vice-versa. Gradient Training Pvt. Ltd.

26. 33 people {a1, a2,…,a33} meet and shake hands in a circular fashion. In other words, there are totally 33 handshakes involving the pairs, {a1,a2}, {a2,a3},…,{a32, a33}, {a33, a1}. Then the size of the smallest set of people such that the rest have shaken hands with at least one person in the set is a)10 b)11 c)16 d)12 Answer: 11 Explanation: Always 1/3rd of the persons present will be taken out. Consider the set {a2, a5, a8,…..a32}. If we separate out these people from the original group, people who would be left in that group would have shaken hands with at least one person in the new set. a2 with a1 and a3; a5 with a4 and a6 and so on. So the smallest set possible is n/3 whereas n is the total number of people present. NOTE: If n is not divisible by 3 then go to the next number which is divisible by 3 and find 1/3rd of that number. For ex- if n=80, answer is 27 (81/3). Gradient Training Pvt. Ltd.

27. A greengrocer was selling watermelon at a penny each, chickoos at 2 for a penny and peanuts at 3 for a penny. A father spent 7p and got the same amount of each type of fruit for each of his three children, Jane, Joe and Jill. Jane is three years older than Jill and Joe is exactly half the age of Jane and Jill together. What did each child get? a) 1 watermelon, 3 chickoos, 2 peanuts b) 1 watermelon, 1 chickoo, 1 peanuts c) 1 watermelon, 2 chickoos, 2 peanuts d) 1 watermelon, 2 chickoos, 1 peanut Answer: 1 watermelon, 2 chickoos, 1 peanut Explanation: The share of each of the children would be 7/3 p. The only option which would ensure 7/3 p for each child is option (d). 1 watermelon----1p 2 chickoos ------1p 1 Peanut---------1/3 p 7/3 P Gradient Training Pvt. Ltd.

28. Leena cut small cubes of 10 cm dimension each. She joined it to make a cuboid of length 100 cm, width 50 cm and depth 50 cm. How many more cubes does she need to make a perfect cube? Answer: 750 Explanation: There are 10 small cubes on length, 5 on breadth and 5 on depth side. So total number of cubes she has is 10X5X5 = 250. In order to make a perfect cube she has to make a cube of 10X10X10 dimension which requires 1000 small cubes. No. of additional small cubes she needs is 1000-250 = 750 ------------------------------------------------------------------------- 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? a) 900 b) 488 c) 500 d) 800 Answer: 488 Explanation: Total number of small cubes would be 5X5X5–3X3X3=98 Total faces of these 98 cubes = 98X6= 588 Total faces of small cubes on each face of bigger cube = 5X5 = 25 Total faces of Big cube painted = 4 Total faces of small cube painted = 4X25 = 100 Total faces of small cubes unpainted = 588-100 = 488 Gradient Training Pvt. Ltd.

29. The citizens of planet Oz are 6 fingered and thus have developed a number system in base 6. A certain street in Oz contains 1000 buildings numbered from 1 to 1000. How many 3’s are used in numbering these buildings? Express your answer in base 10. a) 144 b) 54 c) 108 d) 36 Answer: 108 Explanation: In each of the Unit’s 10’s and hundred’s place 3 would come 36 times. For ex- In _ _ 3, 10’s place can be filled in 6 ways (0-5 as the base is 6) and so can be 100’s place in 6 ways. So total number of numbers in which 3 is at the unit’s place = 6X6 = 36 In 10s place, 3 would come in the same manner 36 times In 100s place, 3 would come in the same manner 36 times Total number of occurrence of 6 would be = 36X3 = 108 NOTE: use the expression nbn-1 where n is the power of 10 up to which the houses are numbered. b is the base that is used by citizens of planet Oz. In the above question n =3 as 1000 = 103and b = 6. So any digit (including 0 ) will appear that many number of times Gradient Training Pvt. Ltd.

30. Subha Patel is an olfactory scientist working for International Flavors and Fragrances. She specializes in finding new scents recorded and reconstituted from nature thanks to Living Flower Technology. She has extracted fragrance ingredients from different flowering plants into bottles labeled herbal, sweet, honey, anisic and rose. She has learned that a formula for a perfume is acceptable if and only if it does not violate any of the rules listed: If the perfume contains herbal, it must also contain honey and there must be twice as much honey as herbal. If the perfume contains sweet, it must also contain anisic, and the amount of anisic must equal the amount of sweet. Honey cannot be used in combination with anisic. anisic cannot be used in combination with rose. If the perfume contains rose, the amount of rose must be greater than the total amount of the other essence or essences used. Which of the following could be added to an unacceptable perfume consisting of two parts honey and one part rose to make it acceptable? a) Two parts rose b) One part herbal c) Two parts honey d) One part sweet Answer: two parts rose Explanation: Read the italics part of the question above. Rose has to be greater than the total amount of other essences mixed. Presently, it is one part and in order to be acceptable it has to be at least three parts as there are two parts honey. So, option (a) is correct. NOTE: sometimes rose is replaced by cedar, but answer will remain the same if conditions remain unchanged. Gradient Training Pvt. Ltd.

31. The question is followed by two statements, A and B. Answer the question using the following instructions: Choose1: if the question can be answered by using one of the statements alone but not by using the other statement alone. Choose2: if the question can be answered by using either of the statements alone. Choose3: if the question can be answered by using both statements together but not by either statement alone. Choose4: if the question cannot be answered on the basis of the two statements. Zayed spends 30% of his income on his children’s education, 20% on recreation and 10% on healthcare. The corresponding percentage for Sandeep are 40%, 25% and 13%. Who spends more on children’s education? A: Zayed spends more on recreation than Sandeep B: Sandeep spends more on healthcare than Zayed. a) 4 b) 3 c) 2 d) 1 Answer: 1 Explanation: In order to answer the question, we have to find out if 30Z > 40S or not. Statement A means: 20Z > 25S. So 30Z > 37.5S. From this we cannot ascertain the above expression. Statement B means: 13S > 10Z. From this 39S > 30Z. So it also means that 40S > 30Z. So we can answer the main question with statement B alone but not by A Gradient Training Pvt. Ltd.

32. The question is followed by two statements, A and B. Answer the question using the following instructions: Choose1: if the question can be answered by using one of the statements alone but not by using the other statement alone. Choose2: if the question can be answered by using either of the statements alone. Choose3: if the question can be answered by using both statements together but not by either statement alone. Choose4: if the question cannot be answered on the basis of two statements. Tarun is standing 2 steps to the left of a green mark and 3 steps to the right of a black mark. He tosses a coin. If it comes up heads, he moved one step to the right, otherwise he moves one step to the left. He keeps doing this until he reaches one of the two marks, and then he stops. At which mark does he stops? A: he stops at 21 coin tosses. B: he obtains three more tails than heads. a) 1 b) 3 c) 4 d) 2 Answer: 2 i.e. the question can be answered by using either of the statements alone Explanation: If H – T =2, then Tarun will stop at Black mark. If T – H = 3, then Tarun will stop at Green mark. Statement A: He stops at 21 tosses => H + T = 21. It means, out of H & T, one is even and the other one is an odd number. In that case their difference would also be odd. The only possible case of an odd difference is T – H = 3, in which case he stops at Green mark. Statement B: Here it is directly given that T – H = 3, which again takes us to the conclusion that Tarun stops at Green mark Gradient Training Pvt. Ltd.

33. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. (At the end of first hour, B has 10 litres, second hour it has 20, and so on). If tank B is 1/8 filled after 5 hours, what is the total duration required to fill it completely?(a) 9 hours (b) 7 hours (c) 3 hours (d) 8 hours Answer: 8 hours Explanation: If 1/8th is filled in 5 hours, then the volume filled in 5 hours = 310 Ltrs. So, total volume of the tank = 310 X 8 = 2480 Ltrs. In the 6th , 7th & 8th hour volumes filled would be 320, 640 & 1280 Ltrs. So, total volume filled at the end of 8th hour = 2550 Ltrs. Hence It will take 8 hours to fill the tank. NOTE: Consider the statement, If tank B is 1/8 filled after 5 hours, given in the question. In that 1/8 = 1/23. Take the exponent of 2 in the denominator i.e. 3 and add it to 5 hours. The answer will be the sum i.e. 8 hours So, if 1/2n of B is filled after ‘t’ hours, total time taken would be n+t hours Gradient Training Pvt. Ltd.

34. A result of global warming is that the ice of some glaciers is melting. 13 years after the ice disappears, tiny plants, called lichens, start to grow on the rocks. Each lichen grows approximately in the shape of a circle. The relationship between the diameter of this circle and the age of the lichen can be approximated with the formula: d=10*(t – 13) for t > 13, where d represents the diameter of the lichen in millimeters, and t represents the number of years after the ice has disappeared. Using the above formula, calculate the diameter of the lichen, 45 years after the ice has disappeared.(a) 450 (b) 437 (c) 13 (d) 320 Answer: 320 Explanation: Just substitute 45 in place of t in the formula given. NOTE: Sometimes the expression for d = 4 √(t – 8) for t > 8 and value to t is given as 24. The answer is 16 mm ----------------------------------------------- Rearrange the following letters to make a word and choose the category in which it fits RAPETEKA a) Bird   b) Vegetable    c) City     d) Fruit Answer: Bird Explanation: Re-arranging the above letters results in PARAKEET which is a Bird. Gradient Training Pvt. Ltd.

35. Ferrari S.P.A. is an Italian sports car manufacturer base in Maranello , Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari, the company sponsored driver and manufactured race cars before moving into production of street – legal vehicles in 1947 as Ferrari S.p.A. Throughout its history, the company has bee noted for its continued participation in racing, especially in Formula One, where it has enjoyed great success. Rohit once brought a Ferrari. It could go 2 times as fast as Mohit’s old Mercedes. If the speed of Mohit’s Mercedes is 40 Km/hr and the distance traveled by the Ferrari is 913 Km, find the total time taken for Rohit to drive the distance.(a) 12 Hours (b) 22 Hours (c) 456 Hours (d) 11.41 Hours Answer: 11.41 Hours Explanation: Read the italics part of the question. Ferrari is twice the speed of Mercedes. Speed of Mercedes is 40 km/hr so, speed of Ferrari would be 80 Km/hr. So time taken to cover 913 Km would be Time = distance /speed Time = 913Km / 80Kmph = 11.41 Hours Gradient Training Pvt. Ltd.

36. A sheet of paper has statements numbered from 1 to 20. For all values of n from 1 to 20, statement n says: ‘Exactly n of the statements on this sheet are true.’ Which statements are true and which are false? a) Only the 1st statement is true and the rest are false b) 1st 6 statements are true and rest are false c) 1st 11 statements are true and rest are false d) The second last statement is true and the rest are false. Answer: Only the 1st statement is true and rest are false. Explanation: In case of Exactly….True combination, there are 2 valid logic Logic 1: Only the 1st statement is true and rest are false Logic 2: None of the statements are true and all are false Both are valid. Most likely a candidate would find an option related to Logic 1 among the given options and hence has to mark that as the answer. Gradient Training Pvt. Ltd.

37. A sheet of paper has statements numbered from 1 to 20. For all values of n from 1 to 20, statement n says: ‘Exactly n of the statements on this sheet are false.’ Which statements are true and which are false? a) The even numbered statements are true and the odd numbered statements are false. b) All the statements are false. c) The odd numbered statements are true and the even numbered statements are false. d) The second last statement is true and the rest are false. Answer: The second last statement is true and the rest are false. Explanation: In case of Exactly….False combination, 2nd last statement is the only statement to be true, rest are false. Gradient Training Pvt. Ltd.

38. A sheet of paper has statements numbered from 1 to 20. For each value of n from 1 to 20, statements n says ‘At least n of the statements on this sheet are true’. Which statements are true and which are false? a) The odd numbered statements are true and the even numbered are false. b) The first 13 statements are false and the rest are true. c) The first 6 statements are true and the rest are false. d) The even numbered statements are true and the odd numbered are false. Answer: The first 6 statements are true and the rest are false. Explanation: In case of At Least….True combination, 1st any number of statements can be true and the rest would be false. NOTE: Instead of 1st 6 statements, there can be other answers like 1st 8, 1st 15, or all 20 statements are true. Look for the answer which is of the form 1st m statements are true and rest are false. 0≤m≤n Gradient Training Pvt. Ltd.

39. A sheet of paper has statements numbered from 1 to 70. For all values of n from 1 to 70. Statement n says ' At least n of the statements on this sheet are false. ‘Which statements are true and which are false?a) The even numbered statements are true and the odd numbered are false.b) The odd numbered statements are true and the even numbered are false.c) The first 35 statements are true and the last 35 are false.d) The first 35 statements are false and the last 35 are false. Answer: The first 35 statements are true and the last 35 are false. Explanation: In case of At Least….False combination, 1st n/2 statements are true rest are false. NOTE: At Least….False combination is only valid for even number of statements. Gradient Training Pvt. Ltd.

40. A sheet of paper has statements numbered from 1 to 55. For all values of n from 1 to 55. Statement n says ‘At most n of the statements on this sheet are True’ Which statements are true and which are false?a) All the statements on the sheet are true b) All the statements on the sheet are false c) The first 27 statements are true and the rest are false.d) The first 27 statements are false and the rest are true. Answer: The first 27 statements are false and the rest are true Explanation: In case of At Most….True combination, 1st (n-1)/2 statements are false rest are true. For n = 55, (n-1)/2 = 27 NOTE:At Most….True combination is only valid for odd number of statements. Gradient Training Pvt. Ltd.

41. A sheet of paper has statements numbered from 1 to 40. For all values 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 the statements on the sheet are true b) All the statements on the sheet are false c) The first 20 statements are true and the rest are false.d) The first 20 statements are false and the rest are true. Answer: All the statements on the sheet are true Explanation: In case of At Most….False combination, all statements are true is the only valid logic Gradient Training Pvt. Ltd.

42. 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) cannot be determined c) 3 d) 42Answer: 3 Explanation: Let N be that number. So, according the question, N = D X Q1 + 8 -------------(A) Also, N = 3D X Q2 + 21 -----------(B) Subtracting (A) – (B) we get, 0= D (Q1 – 3Q2) – 13 or 13 = D (Q1 – 3Q2). From this we get that D = 13 as if (Q1 – 3Q2) = 13 then D = 1, which is not possible. Putting D = 13 in (B), we get N = 39Q2 + 21, so twice of N is 2N = 78Q2 + 42. Dividing 2N by 3D i.e. 39, we get remainder as 3 (Remainder of 42/39) Gradient Training Pvt. Ltd.

43. A triangle is made from a rope. The sides of the triangle are 21 cm, 24 cm and 28 cm. What will be the area of the square made from the same rope? a) 280.5625 b) 333.0625 c) 245.0125 d) 400 Answer: 245.0125 Explanation: Use Hero’s formula √s(s-a)(s-b)(s-c) S = (a+b+c)/2 = 73/2 = 36.5. So, the value is 245.1 ----------------------------------------------------------------------------------- a, b & c measured their weights in the following manner. 1st a, b, c weighed themselves separately then a& b, b & c and c & a weighed themselves in pairs. At last a, b & c weighed themselves together. The last weight was 167,then what will be the average weight of the 7 reading? Answer: 95.2 Explanation: There are 7 weighing in total. Sum of 1st three is a+b+c; Sum of next three is 2(a+b+c) Last one is a+b+c So, Sum of all 7 weighing is 4(a+b+c) and average = 4(a+b+c)/7 Substitute a+b+c = 167 NOTE: Instead of 167 there can be other data. Just multiply that with 4/7 in order ot get the average. Gradient Training Pvt. Ltd.

44. Spores of a fungus, called late blight, grow and spread infection rapidly. These pathogens were responsible for the Irish potato famine of the mid-19th century. These seem to have attacked the tomato crops in England this year. The tomato crops have reduced and the price of the crop has risen up. The price has already gone up to $45 a box from $27 a box a month ago. How much more would a vegetable vendor need to pay to buy 27 boxes this month over what he would have paid last month? a) $276 b) $418 c) $456 d) $486 Answer: $486 Explanation: Difference between old and new price is $45 - $27 = $18 Total difference in payment is $18/box X 27 boxes = $486 ---------------------------------------------------------------------------------------- What is the distance between the z-intercept from the x-intercept in the equation ax+by+cz+d=0 Answer: d (1/a2 + 1/c2)1/2 Explanation: For finding the X intercept, put y=z=0. x= -d/a. Similarly, for Z intercept , put x=y=0. So z=-d/c. Now by using distance formula, find the distance between (-d/a,0,0) and (0,0,-d/c) The distance is d (1/a2 + 1/c2)1/2 NOTE: In test, there would be constant values used instead of a, b, c & d. Use the above result accordingly. Gradient Training Pvt. Ltd.

45. John buys a cycle for 31 dollars and given a cheque of amount 35 dollars. Shop Keeper exchanged the cheque with his neighbor and gave change to John. After 2 days, it is known that cheque is bounced. Shop keeper paid the amount to his neighbor. The cost price of cycle is 19 dollars. What is the profit/loss for shop keeper? a) loss 23 b) gain 23 c) gain 54 d) Loss 54 Answer: Loss 23 Explanation: There are 3 parties involved- John, the cycle shopkeeper and his neighbor. The transaction between the shopkeeper and his neighbor is clear. Shopkeeper gives the cheque to his neighbor, receives cash and then take the bounced check back from him and gives him the same amount of cash. The transaction between John and the shopkeeper resulted in loss of the total value that John ran away with. He ran away with $19 worth of cycle and $4 cash. So, a total of $23 was the loss to the shopkeeper. Gradient Training Pvt. Ltd.

46. End of Part -1THANK YOU Gradient Training Pvt. Ltd.