Aptitude/Reasoning/Numeric Ability Paper 1 1. What is the number of zeros at the end of the product of the numbers from 1 to 100? Answer : 127 2. A fast typist can type some matter in 2 hours and a slow typist can type the same in 3 hours. If both type combinely, in how much time will they finish? Answer : 1 hr 12 min Explanation : The fast typist's work done in 1 hr = 1/2 The slow typist's work done in 1 hr = 1/3 If they work combinely, work done in 1 hr = 1/2+1/3 = 5/6 So, the work will be completed in 6/5 hours. i.e., 1+1/5 hours = 1hr 12 min 3. Gavaskar's average in his first 50 innings was 50. After the 51st innings, his average was 51. How many runs did he score in his 51st innings. (supposing that he lost his wicket in his 51st innings) Answer : 101 Explanation : Total score after 50 innings = 50*50 = 2500 Total score after 51 innings = 51*51 = 2601 So, runs made in the 51st innings = 2601-2500 = 101 If he had not lost his wicket in his 51st innings, he would have scored an unbeaten 50 in his 51st innings. 4. A rectangular plate with length 8 inches, breadth 11 inches and thickness 2 inches is available. What is the length of the circular rod with diameter 8 inches and equal to the volume of the rectangular plate? Answer : 3.5 inches Explanation : Volume of the circular rod (cylinder) = Volume of the rectangular plate (22/7)*4*4*h = 8*11*2 h = 7/2 = 3.5 5. What is the sum of all numbers between 100 and 1000 which are divisible by 14 ? Answer : 35392 Explanation : The number closest to 100 which is greater than 100 and divisible by 14 is 112, which is the first term of the series which has to be summed. The number closest to 1000 which is less than 1000 and divisible by 14 is 994, which is the last term of the series. 112 + 126 + .... + 994 = 14(8+9+ ... + 71) = 35392 6. If s(a) denotes square root of a, find the value of s(12+s(12+s(12+ ...... upto infinity. Answer : 4 Explanation : Let x = s(12+s(12+s(12+..... We can write x = s(12+x). i.e., x^2 = 12 + x. Solving this quadratic equation, we get x = -3 or x=4. Sum cannot be -ve and hence sum = 4. 7. A cylindrical container has a radius of eight inches with a height of three inches. Compute how many inches should be added to either the radius or height to give the same increase in volume? Answer : 16/3 inches Explanation : Let x be the amount of increase. The volume will increase by the same amount if the radius increased or the height is increased. So, the effect on increasing height is equal to the effect on increasing the radius. i.e., (22/7)*8*8*(3+x) = (22/7)*(8+x)*(8+x)*3 Solving the quadratic equation we get the x = 0 or 16/3. The possible increase would be by 16/3 inches. 8. With just six weights and a balance scale, you can weigh any unit number of kgs from 1 to 364. What could be the six weights? Answer : 1, 3, 9, 27, 81, 243 (All powers of 3) 9. Diophantus passed one sixth of his life in childhood, one twelfth in youth, and one seventh more as a bachelor; five years after his marriage a son was born who died four years before his father at half his final age. How old is Diophantus? Answer : 84 years Explanation : x/6 + x/12 + x/7 + 5 + x/2 + 4 = x 10 . If time at this moment is 9 P.M., what will be the time 23999999992 hours later? Answer : 1 P.M. Explanation : 24 billion hours later, it would be 9 P.M. and 8 hours before that it would be 1 P.M. 11. How big will an angle of one and a half degree look through a glass that magnifies things three times? Answer : 1 1/2 degrees Explanation : The magnifying glass cannot increase the magnitude of an angle. 12. Divide 45 into four parts such that when 2 is added to the first part, 2 is subtracted from the second part, 2 is multiplied by the third part and the fourth part is divided by two, all result in the same number. Answer: 8, 12, 5, 20 Explanation: a + b + c + d =45; a+2 = b-2 = 2c = d/2; a=b-4; c = (b-2)/2; d = 2(b-2); b-4 + b + (b-2)/2 + 2(b-2) = 45; 13. I drove 60 km at 30 kmph and then an additional 60 km at 50 kmph. Compute my average speed over my 120 km. Answer : 37 1/2 Explanation : Time reqd for the first 60 km = 120 min.; Time reqd for the second 60 km = 72 min.; Total time reqd = 192 min Avg speed = (60*120)/192 = 37 1/2 Questions 14 and 15 are based on the following : Five executives of European Corporation hold a Conference in Rome Mr. A converses in Spanish & Italian Mr. B, a spaniard, knows English also Mr. C knows English and belongs to Italy Mr. D converses in French and Spanish Mr. E , a native of Italy knows French 14. Which of the following can act as interpreter if Mr. C & Mr. D wish to converse a) only Mr. A b) Only Mr. B c) Mr. A & Mr. B d) Any of the other three Answer : d) Any of the other three. Explanation : From the data given, we can infer the following. A knows Spanish, Italian B knows Spanish, English C knows Italian, English D knows Spanish, French E knows Italian, French To act as an interpreter between C and D, a person has to know one of the combinations Italian&Spanish, Italian&French, English&Spanish, English&French A, B, and E know atleast one of the combinations. 15. If a 6th executive is brought in, to be understood by maximum number of original five he should be fluent in a) English & French b) Italian & Spanish c) English & French d) French & Italian Answer : b) Italian & Spanish Explanation : No of executives who know i) English is 2 ii) Spanish is 3 iii) Italian is 3 iv) French is 2 Italian & Spanish are spoken by the maximum no of executives. So, if the 6th executive is fluent in Italian & Spanish, he can communicate with all the original five because everybody knows either Spanish or Italian. 16.What is the sum of the first 25 natural odd numbers? Answer : 625 Explanation : The sum of the first n natural odd nos is square(n). 1+3 = 4 = square(2) 1+3+5 = 9 = square(3) 17. The sum of any seven consecutive numbers is divisible by 2 b) 7 c) 3 d) 11 18. There are seventy clerks working in a company, of which 30 are females. Also, 30 clerks are married; 24 clerks are above 25 years of age; 19 married clerks are above 25 years, of which 7 are males; 12 males are above 25 years of age; and 15 males are married. How many bachelor girls are there and how many of these are above 25? 19.A man sailed off from the North Pole. After covering 2,000 miles in one direction he turned West, sailed 2,000 miles, turned North and sailed ahead another 2,000 miles till he met his friend. How far was he from the North Pole and in what direction? 20.Here is a series of comments on the ages of three persons J, R, S by themselves. S : The difference between R's age and mine is three years. J : R is the youngest. R : Either I am 24 years old or J 25 or S 26. J : All are above 24 years of age. S : I am the eldest if and only if R is not the youngest. R : S is elder to me. J : I am the eldest. R : S is not 27 years old. S : The sum of my age and J's is two more than twice R's age. One of the three had been telling a lie throughout whereas others had spoken the truth. Determine the ages of S,J,R. 21.In a group of five people, what is the probability of finding two persons with the same month of birth? 22.A father and his son go out for a 'walk-and-run' every morning around a track formed by an equilateral triangle. The father's walking speed is 2 mph and his running speed is 5 mph. The son's walking and running speeds are twice that of his father. Both start together from one apex of the triangle, the son going clockwise and the father anti- clockwise. Initially the father runs and the son walks for a certain period of time. Thereafter, as soon as the father starts walking, the son starts running. Both complete the course in 45 minutes. For how long does the father run? Where do the two cross each other? 23.The Director of Medical Services was on his annual visit to the ENT Hospital. While going through the out patients' records he came across the following data for a particular day : " Ear consultations 45; Nose 50; Throat 70; Ear and Nose 30; Nose and Throat 20; Ear and Throat 30; Ear, Nose and Throat 10; Total patients 100." Then he came to the conclusion that the records were bogus. Was he right? 24.Amongst Ram, Sham and Gobind are a doctor, a lawyer and a police officer. They are married to Radha, Gita and Sita (not in order). Each of the wives have a profession. Gobind's wife is an artist. Ram is not married to Gita. The lawyer's wife is a teacher. Radha is married to the police officer. Sita is an expert cook. Who's who? 25.What should come next? 1, 2, 4, 10, 16, 40, 64, Aptitude/Reasoning/Numeric Ability Paper 2 1. In objective test a correct ans score 4 marks and on a wrong ans 2 marks are ---. a student score 480 marks from 150 question. how many ans were correct? a) 120 b) 130 c) 110 d) 150 Ans130. 2. An artical sold at amount of 50% the net sale price is rs 425 .what is the list price of the artical? a) 500 b) 488 c) 480 d) 510 Ans 500 3. A man leaves office daily at 7pm A driver with car comes from his home to pick him from office and bring back home . One day he gets free at 5:30 and instead of waiting for driver he starts walking towards home. In the way he meets the car and returns home on car He reaches home 20 minutes earlier than usual. In how much time does the man reach home usually?? Ans. 1hr 20min 4. A works thrice as much as B. If A takes 60 days less than B to do a work then find the number of days it would take to complete the work if both work together? Ans. 22½days 5. How many 1's are there in the binary form of 8*1024 + 3*64 + 3 Ans. 4 6. In a digital circuit which was to implement (A B) + (A)XOR(B), the designer implements (A B) (A)XOR(B) What is the probability of error in it ? 6. A boy has Rs 2. He wins or loses Re 1 at a time If he wins he gets Re 1 and if he loses the game he loses Re 1. He can loose only 5 times. He is out of the game if he earns Rs 5. Find the number of ways in which this is possible? Ans. 16 7. If there are 1024*1280 pixels on a screen and each pixel can have around 16 million colors Find the memory required for this? Ans. 4MB 8. On a particular day A and B decide that they would either speak the truth or will lie. C asks A whether he is speaking truth or lying? He answers and B listens to what he said. C then asks B what A has said B says "A says that he is a liar" What is B speaking ? (a) Truth (b) Lie (c) Truth when A lies (d) Cannot be determined Ans. (b) 9. What is the angle between the two hands of a clock when time is 8:30 Ans. 75(approx) 10. A student is ranked 13th from right and 8th from left. How many students are there in totality ? 11. A man walks east and turns right and then from there to his left and then 45degrees to his right.In which direction did he go Ans. North west 12. A student gets 70% in one subject, 80% in the other. To get an overall of 75% how much should get in third subject. 13. A man shows his friend a woman sitting in a park and says that she the daughter of my grandmother's only son. What is the relation between the two Ans. Daughter 14. How many squares with sides 1/2 inch long are needed to cover a rectangle that is 4 ft long and 6 ft wide (a) 24 (b) 96 (c) 3456 (d) 13824 (e) 14266 15. If a=2/3b , b=2/3c, and c=2/3d what part of d is b/ (a) 8/27 (b) 4/9 (c) 2/3 (d) 75% (e) 4/3 Ans. (b) 16. Successive discounts of 20% and 15% are equal to a single discount of (a) 30% (b) 32% (c) 34% (d) 35% (e) 36 Ans. (b) 17. The petrol tank of an automobile can hold g liters.If a liters was removed when the tank was full, what part of the full tank was removed? (a)g-a (b)g/a (c) a/g (d) (g-a)/a (e) (g-a)/g Ans. (c) 18. If x/y=4 and y is not '0' what % of x is 2x-y (a)150% (b)175% (c)200% (d)250% Ans. (b) 19.Find the odd man out 3,5,7,12,13,17,19 Answer : 12 20. Find the odd man out 2,5,10,17,26,37,50,64 Answer : 64 Explanation : 2+3=5; 5+5=10; 10+7=17; 17+9=26; 26+11=37; 37+13=50; 50+15=65; 21. For the following, find the next term in the series 6, 24, 60,120, 210 a) 336 b) 366 c) 330 d) 660 Answer : a) 336 Explanation : The series is 1.2.3, 2.3.4, 3.4.5, 4.5.6, 5.6.7, ..... ( '.' means product) 22. For the following, find the next term in the series 1, 5, 13, 25 Answer : 41 Explanation : The series is of the form 0^2+1^2, 1^2+2^2,... 23. Out of 80 coins, one is counterfeit. What is the minimum number of weighings needed to find out the counterfeit coin? Answer : 4 24. What can you conclude from the statement : All green are blue, all blue are red. ? some blue are green some red are green some green are not red all red are blue (a) i or ii but not both (b) i & ii only (c) iii or iv but not both (d) iii & iv Answer : (b) 25. Find the odd one out 105,85,60,30,0,-45,-90 Answer : 0 Explanation : 105-20=85; 85-25=60; 60-30=30; 30-35=-5; -5-40=-45; -45-45=-90; Aptitude/ Reasoning/ Numeric Ability Paper 3 1. A car travels a certain distance taking 7 hrs in forward journey, during the return journey increased speed 12km/hr takes the times 5 hrs.What is the distance travelled (a) 210 kms (b) 30 kms (c) 20 kms (c) none of these Ans. B 2. Instead of multiplying a number by 7, the number is divided by 7. What is the percentage of error obtained ? 57. Find (7x + 4y ) / (x-2y) if x/2y = 3/2 ? (a) 6 (b) 8 (c) 7 (d) data insufficient Ans. C 3. A man buys 12 lts of liquid which contains 20% of the liquid and the rest is water. He then mixes it with 10 lts of another mixture with 30% of liquid.What is the % of water in the new mixture? 4. If a man buys 1 lt of milk for Rs.12 and mixes it with 20% water and sells it for Rs.15, then what is the percentage of gain? 5. Pipe A can fill a tank in 30 mins and Pipe B can fill it in 28 mins.If 3/4th of the tank is filled by Pipe B alone and both are opened, how much time is required by both the pipes to fill the tank completely ? 6. If on an item a company gives 25% discount, they earn 25% profit. If they now give 10% discount then what is the profit percentage. (a) 40% (b) 55% (c) 35% (d) 30% Ans. D 7. A certain number of men can finish a piece of work in 10 days. If however there were 10 men less it will take 10 days more for the work to be finished. How many men were there originally? (a) 110 men (b) 130 men (c) 100 men (d) none of these Ans. A 8. In simple interest what sum amounts of Rs.1120/- in 4 years and Rs.1200/- in 5 years ? (a) Rs. 500 (b) Rs. 600 (c) Rs. 800 (d) Rs. 900 Ans. C 9. If a sum of money compound annually amounts of thrice itself in 3 years. In how many years will it become 9 times itself. (a) 6 (b) 8 (c) 10 (d) 12 Ans A 10. Two trains move in the same direction at 50 kmph and 32 kmph respectively. A man in the slower train observes the 15 seconds elapse before the faster train completely passes by him. What is the length of faster train ? (a) 100m (b) 75m (c) 120m (d) 50m Ans B 11. How many mashes are there in 1 squrare meter of wire gauge if each mesh is 8mm long and 5mm wide ? (a) 2500 (b) 25000 (c) 250 (d) 250000 Ans B 12. x% of y is y% of ? (a) x/y (b) 2y (c) x (d) can't be determined Ans. C 13. The price of sugar increases by 20%, by what % should a housewife reduce the consumption of sugar so that expenditure on sugar can be same as before ? (a) 15% (b) 16.66% (c) 12% (d) 9% Ans B