Infosys Practice Test Quantitative Aptitude II

Transcription

1 Infosys Practice Test Quantitative Aptitude II 1. The number of ways of arranging n students in a row such that no two boys sit together and no two girls sit together is m(m > 100). If one more student is added, then number of ways of arranging as above increases by 200%. The value of n is A. 12 B. 8 C. 9 D How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed? A. 499 B. 500 C. 375 D. 376 E How many five digit positive integers that are divisible by 3 can be formed using the digits 0, 1, 2, 3, 4 and 5, without any of the digits getting repeating A. 15 B. 96 C. 216 D. 120 E There are 10 seats around a circular table. If 8 men and 2 women have to seated around a circular table, such that no two women have to be separated by at least one man. If P and Q denote the respective number of ways of seating these people around a table when seats are numbered and unnumbered, then P : Q equals A. 9 : 1 B. 72 : 1 C. 10 : 1 D. 8 : 1 5. How many factors of are perfect squares? A. 20 B. 24 C. 30 D In how many rearrangements of the word AMAZED, is the letter 'E' positioned in between the 2 'A's (Not necessarily flanked)? A. 24 B. 72 C. 120 D a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets). A. 4

2 B. 5 C. 6 D Bob is about to hang his 8 shirts in the wardrobe. He has four different styles of shirt, two identical ones of each particular style. How many different arrangements are possible if no two identical shirts are next to one another? A. 764 B. 864 C. 964 D Marie is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 5 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90% of the time. When it doesn't rain, he incorrectly forecasts rain 10% of the time. What is the probability that it will rain on the day of Marie's wedding? A B C D Two squares are chosen at random on a chessboard. What is the probability that they have a side in common? A. 1/18 B. 64/4032 C. 63/64 D. 1/9 11. In a game there are 70 people in which 40 are boys and 30 are girls, out of which 10 people are selected at random. One from the total group, thus selected is selected as a leader at random. What is the probability that the person, chosen as the leader is a boy? A. 4/7 B. 4/9 C. 5/7 D. 2/7 12. Sum of digits of a 5 digit number is 41. Find the probability that such a number is divisible by 11? A. 2/15 B. 11/36 C. 3/35 D. 6/ Shiwani thought of a two-digit number and divided the number by the sum of the digits of the number. He found that the remainder is 3. Devesh also thought of a twodigit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Shiwani and Devesh is TRUE? A. 1/15 B. 1/14 C. 1/13 D. 1/ An eight-digit telephone number consists of exactly two zeroes. One of the digits is

3 repeated thrice. Remaining three digits are all distinct. If the first three digits (from left to right) are 987, then find the probability of having only one 9, one 8 and one 7 in the telephone number. A. 1/18 B. 1/20 C. 1/10 D. 5/ The game 'Chunk-a-Luck' is played at carnivals in some parts of Europe. Its rules are as follows: If you pick a number from 1 to 6 and the operator rolls three dice. If the number you picked comes up on all three dice, the operator pays you Rs. 3 ; If it comes up on two dice, you are paid Rs. 2; And it comes up on just one dice, you are paid Rs. 1. Only if the number you picked does not come up at all, you pay the operator Rs. 1. The probability that you will win money playing in this game is: A B C D. None of the above 16. Sun Life Insurance company issues standard, preferred and ultra-preferred policies. Among the company's policy holders of a certain age, 50% are standard with the probability of 0.01 dying in the next year, 30% are preferred with a probability of of dying in the next year and 20% are ultra-preferred with a probability of of dying in the next year. If a policy holder of that age dies in the next year, what is the probability of the decreased being a preferred policy holder? A B C Two friends A and B run around a circular track of length 510 metres, starting from the same point, simultaneously and in the same direction. A who runs faster laps B in the middle of the 5th round. If A and B were to run a 3 km race long race, how much start, in terms of distance, should A give B so that they finish the race in a dead heat? A metres B metres C metres D. Cannot be determined 18. Yana and Gupta leave points x and y towards y and x respectively simultaneously and travel in the same route. After meeting each other on the way, Yana takes 4 hours to reach her destination, while Gupta takes 9 hours to reach his destination. If the speed of Yana is 48 km/hr, what is the speed of Gupta? A. 72 kmph B. 32 mph C. 20 mph 19. Twenty six men - 1,2,3,...25 and 26 participate in 10km running race on a circular track of length 100m. All of them start at the same time, from the same point and run

4 in the same direction. Their speeds, taken in the order, are in increasing AP. The time taken by 26 to meet 1, for the first time after they start is 20 sec and the time taken by 13 to complete the race is 52 minutes and 5 seconds. Find the time taken (in seconds), for all the twenty six men to meet for the first time at the starting point. A B. 500 C. 625 D A man driving his bike at 24 kmph reaches his office 5 minutes late. Had he driven 25% faster on an average he would have reached 4 minutes earlier than the scheduled time. How far is his office? A. 24 km B. 72 km C. 18 km D. Data Insufficient 21. Two motorists Anil and Sunil are practicing with two different sports car; Ferrari and Maclarun, on the circular racing track, for the car racing tournament to be held next month. Both Anil and Sunil start from the same point on the circular track. Anil completes one round of the track in 1 min and Sunil takes 2 min to complete a round. While Anil maintains speed for all the rounds, Sunil halves his speed after the completion of each round. How many times Anil and Sunil will meet between 6th round and 9th round of Sunil (6th and 9th round is excluded)? Assume that the speed of Sunil remains steady throughout each round and changes only after the completion of that round. A. 382 B. 347 C The XYZ river flows at 12 km/hr. A boy who can row at 2518 m/s in still water had to cross it in the least possible time. The distance covered by the boy is how many times the width of the river XYZ? A. 2.1 B. 2.3 C. 2.6 D In a 3600 m race around a circular track of length 400m, the faster runner and the slowest runner meet at the end of the fourth minute, for the first time after the start of the race. All the runners maintain uniform speed throughout the race. If the faster runner runs at thrice the speed of the slowest runner. Find the time taken by the faster runner to finish the race. A. 36 minute B. 24 minute C. 16 minute D. 12 minute 24. In an industry, the raw materials and the finished goods are transported on the conveyor belt. There are two conveyor belt, one for carrying parts from P to point Q and another for carrying parts from R to point Q. P, Q and R in that order are in a straight line. Sometimes, the belt serves to transport cart, which can themselves move with respect to the belts. The two belts move at a speed of 0.5 m/s and the cart move at a uniform speed of 2m/s with respect to the belts. A cart goes from point P

5 to R and back to P taking a total of 64s. Find the distance PR in meters. Assume that the time taken by the cart to turn back at R is negligible? A. 48 B. 54 C. 60 D Three pipes A,B and C are connected to a tank. These pipes can fill the tank separately in 5hr, 10 hr and 15hr respectively. When all the three pipes were opened simultaneously, it was observed that pipes A and B were supplying water at (34)th of their normal rates for the 1st hour after which they supplied water at normal rate. Pipe C supplied water at (23)rd of its normal rate for 1st 2 hour, after which it supplied at its normal rate. In how much time, tank would be filled? A hr B hr C hr 26. If A and B work together, they will complete a job in 7.5 days. However, if A works alone and completes half the job and then B takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will B alone take to do the job if A is more efficient than B? A. 20 days B. 40 days C. 36 days D. 30 days 27. Abhishek starts to paint a fence on one day. On the second day, two more friend of Abhishek join him. On the third day 3 more friends of him join him and so on. If the fence is completely painted this way in exactly 20 days, then find the number of days in which 10 girls painting together can paint the fence completely, given that every girl can paint twice as fast as Abhishek and his friends(boys)?(assume that the friends of Abhishek are all boys). A. 20 B. 40 C. 45 D A and B undertake to do a piece of work for Rs 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they can finish it in 3 days, Find the share of C? A. 70 B. 75 C. 80 D There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes? A. 6 B. 8 C. 7 D. 5

6 30. Among four persons Prince, Queen, Raj and Sashi. Prince takes thrice as much time as Queen to complete a piece of work. Queen takes thrice as much time as Raj and Raj takes thrice as much time as Sashi to complete the same work. One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days. Which is the group that takes 13 days? A. Prince, Queen, Raj B. Prince, Queen, Sashi C. Queen, Raj, Sashi D. Prince, Raj, Sashi 31. Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe B fills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow? A. 42 minutes B. 14 minutes C. 39 minutes 32. A man takes 20 days to reach the point B under normal circumstances. But, due to the increasingly hostile weather conditions the distance they travel every day reduces by 20%. In how many days would the man reach the point B, taking into consideration weather conditions? A. 25 B. 50 C The largest number amongst the following that will perfectly divide is: A. 100 B. 10,000 C D. 100, Let n be the number of different 5 digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n? A. 144 B. 168 C Three gold coins of weight 780gm, 840gm and 960gm are cut into small pieces, all of which have the equal weight. Each piece must be heavy as possible. If one such piece is shared by two persons, then how many persons are needed to give all the pieces of gold coins? A. 86 B. 70 C. 43 D Each of X alarm tolls at regular intervals. All of them tolls together twelve times a day. No two alarm at equal intervals of time. If each alarm tolls after a whole number of minutes, what is the maximum possible value of X? A. 14

7 B. 16 C. 18 D A person uses the base x for his number system, where x 10. A student had to add two-digit numbers. None of the digits was 0. By oversight, he reversed the digits of both the numbers and added them. He later found that the difference between his answer and the correct answer was $(84)_10. If this value is the maximum possible for x, then what is the value of x. A. 6 B. 7 C. 8 D N is the smallest number that has 5 factors. How many factors does (N - 1) have?? A. 2 B. 3 C. 4 D Ram and Shyam take a vacation at their grandparents' house. During the vacation, they do any activity together. They either played tennis in the evening or practiced Yoga in the morning, ensuring that they do not undertake both the activities on any single day. There were some days when they did nothing. Out of the days that they stayed at their grandparents' house, they involved in one of the two activities on 22 days. However, their grandmother while sending an end of vacation report to their parents stated that they did not do anything on 24 mornings and they did nothing on 12 evenings. How long was their vacation? A. 36 days B. 14 days C. 29 days D. Cannot be determined 40. A set of S consists of i). All odd numbers from 1 to 55. ii). All even numbers from 56 to 150. What is the index of the highest power of 3 in the product of all the elements of the set S? A. 35 B. 48 C. 6 D The three words "TATA Assets Rock" are flashed such that the words individually are switched on at regular intervals of 4,7 and 9 seconds respectively and after they are switched on, the words are switched off after 2 sec, 4 sec and 5 sec respectively. If at time 't' all the words happened to switch off simultaneously, find the least time 't' which all three words will switch on simultaneously. A. 252 sec B. 126 sec C. 94 sec D. 38 sec 42. How many factors of are odd numbers? A. 20 B. 24

8 C. 30 D Dexter was born between October 6th and 10th (6th and 10th excluding). His year of birth is also known. What is the probability of Dexter being born on a Saturday? A. 0 or 1/3 B. 1/7 or 3/7 C. 1/3 or 1/7 D. Cannot be determined 44. Laila drives to the station each day to pick up her husband Majnu, who usually arrives on a train at 6o clock. Last Monday, Majnu finished work earlier, caught an earlier train and arrived at the station at 5 o clock. He started to walk home and eventually met Laila who drove him the rest of the way, getting home 20 minutes earlier than usual. On Tuesday, he again finished early and found himself at the station at 5:30. Again he began to walk home, again he met Laila on the way, and she drove him home the rest of the way, Assume constant speed throughout with no wasted time for waiting, backing of the car etc. How earlier than the usual time were they home on Tuesday? A. 6 min B. 8 min C. 10 min D. 12 min 45. Ramesh has two examinations on Wednesday - Engineering mathematics in the morning and Engineering Drawing in the afternoon. He has a fixed amount of time to read the textbooks of both these subjects on Tuesday. During this time he can read 80 pages of Engineering Mathematics and 100 pages of Engineering drawing. Alternatively, he can also read 50 pages of Engineering Mathematics and 250 pages of Engineering drawing. Assume that the amount of time it takes to read one page of the textbook of either subject is constant. Ramesh is confident about Engineering Drawing and wants to devote full time to reading Engineering Mathematics. The number of Engineering Mathematics text book pages he can read on Tuesday is : A. 500 B. 300 C. 100 D N O G U N + N O H U N T A.U=0,H=1,T=2,O=7,N=8,G=9 B.U=0,H=1,T=2,O=6,N=8,G=9 C.U=0,H=1,T=3,O=7,N=8,G=9 D.U=0,H=1,T=2,O=5,N=8,G=9

9 47. NINA + SING AGAIN A.I=0,A=1,G=4,N=5,S=8 B.I=0,A=1,G=4,N=5,S=9 CI=0,A=1,G=4,N=6,S=9 DI=0,A=2,G=4,N=5,S=8 48. THY + HAY MYTH A.M=1,Y=4,T=5,A=7,H=8 B.M=1,Y=4,T=5,A=6,H=8 C.M=1,Y=4,T=4,A=7,H=8 D.M=1,Y=3,T=5,A=7,H=8 49. TAKE + A + CAKE KATE A.E=1,C=2,T=3,K=6,A=8 B.E=1,C=2,T=3,K=6,A=9 C.E=1,C=2,T=4,K=6,A=9 D.E=1,C=2,T=3,K=5,A=9 50. STARS + RATE TREAT A.E=1,A=4,R=6,S=8,T=9 B.E=1,A=5,R=7,S=8,T=9 C.E=1,A=5,R=6,S=8,T=9 D.E=1,A=5,R=6,S=7,T=9