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- 1. Question 1Messrs. Siva Constructions, leading agents in Chennai prepared models of their lands in the shape of a rectangle andtriangle. They made models having same area. The length and width of rectangle model are 24 inches and 8 inchesrespectively. The base of the triangle model is 16 inches. What is the altitude of triangle model from the base to the top?a) 24 inches b) 8 inches c) 20 inches d) 32 inchesAnswer : a) 24 inchesSolution :Area of rectangle model -- length x breadth = 24 x 8 = 192 sq. inches.Area of triangle model is also 192 sq.inches.Its base - 16 inchesArea of a triangle - 1/2 x base x height1/2 x 16 x height = 192Height = (192 x 2) / 16 = 24 inches.Question 2Fisher-Price, leading toy manufacturers made a rectangle toy and triangle toy having same area. The length of therectangle was 30 inches. The triangle toy’s height was 36 inches. How will you express the base y of the triangle as afunction of the breadth x of the rectangle ?a. 20x/3 b. 10x/3 c. 16x d. 22xAnswer : b. 10x/3Solution :Base of the triangle = y.Breadth of the rectangle = x.Area of the rectangle = length x breadth = 30xArea of the triangle = 1/2 x base x height = 36y/2 = 18yEquating the areas of triangle and rectangle, we get, 30x = 18y or y = 30x/18 = 10x/3Question 3Ideal Toy company, New York brought out two models – one rectangle and another hexagon in shape. The area of the twoare same. The base and height of the triangle are 48” and √3” respectively. Find the length of each of the sides of thehexagon.a) 2” b) 4” c) 24” d) 8”Answer : b) 4”Solution :Area of triangle = 1/2 x base x height = 1/2 x 48 x √3 = 24√3 sq. inchesSince, the areas of triangle and hexagon are equal , Area of hexagon = 24√3 sq. inches ....(1) 2If the side of hexagon is x inches, then its area = (3√3/2 )r ...(2)Since equations 1 and 2 equal, 224√3 = (3√3/2 )r 216 = rOr r = 4 inchQuestion 4Santosh Iyer had Rs.35 with him and he went for shopping. Vendor was selling one apple for Rs.5, two bananas for Rs.5 andthree guavas for Rs. 5. If Santosh Iyer wants to give equal number of fruits to three of his friends what is the combination(for each of his friends) in which he can buy and give fruits?a) Two apples, two bananas and two guavasb) One apple, two bananas and one guavac) Three apples, two bananas, two guavasd) None of these.Answer : b) One apple, two bananas and one guavaSolution :Cost Observations :Cost of 1 apple = Rs. 5Cost of 2 bananas = Rs. 5. Therefore cost of 1 banana = Rs. 5/2Cost of 3 guavas = Rs. 5. Therefore cost of 1 guava = Rs. 5/3Now its time to inspect option by option, if the total money spent tallies with the amount originally had.i) Consider Option a) 2 Apples, 2 Bananas, 2 GuavasIf a combination 2 apples, 2 bananas and 2 guavas are given to each friend (totally 3 friends), he would have to buy 2 x 3 =
- 2. 6 apples, 2 x 3 = 6 bananas and 2 x 3 = 6 guavasTotal Cost = 6 apples x Cost of 1 apple + 6 bananas x Cost of 1 banana + 6 guavas x Cost of 1 guava= 6 x 5 + 6 x 5/2 + 6 x 5/3 = 30 + 15 + 10 = Rs .55But Rs. 55 is not equal to Rs. 35 which Santosh had initially. Therefore, option a cannot be the right answer.ii) Consider Option b) 1 Apple, 2 Bananas and 1 GuavaIf option b combination is given to each of his friends, in total he would have to buy 3 apples, 6 bananas and 3 guavas.Total Cost = 3 apples x Cost of 1 apple + 6 bananas x Cost of 1 banana + 3 guavas x Cost of 1 guava= 3 x 5 + 6 x 5/2 + 3 x 5/3 = 15 + 15 + 5 = Rs. 35Here, Total cost Rs. 35 tallies perfectly with the amount of Rs. 35 that Santosh had initially. Therefore, option b is correct.Question 5Srinisha went to a leading stationery shop for buying gifts for her four friends—Two pens cost Rs.40, each eraser costsRs.15 and two sharpeners are sold for Rs.12.50. Srinisha had Rs.300 with her. In which combination she can buy theseitems so that she can present her friends equal number of pens, sharpeners and erasers?a) Two pens, one eraser and one sharpenerb) One pen, two erasers and four sharpenersc) One pen, four erasers and two sharpenersd) Two pens, Two erasers and two sharpenersAnswer : b) One pen, two erasers and four sharpenersSolution :This question is very similar to question number 1.Cost Observations :Cost of 1 pen = Rs. 40/2 = Rs. 20Cost of 1 eraser = Rs. 15Cost of 1 sharpener = Rs. 12.5/2Consider option a) 2 pens, 1 eraser, 1 sharpenerIf option a) combination is to be given to each of her 4 friends, she should buy 8 pens, 4 erasers and 4 sharpenersTotal Cost = 8 pens x Cost of 1 pen + 4 erasers x Cost of 1 eraser + 4 sharpeners x Cost of 1 sharpener= 8 x 20 + 4 x 15 + 4 x 12.5/2 = Rs. 465But Rs. 465 is not equal to Rs. 300 which Srinisha had initially. Therefore, option a is not correct.Consider option b) 1 pen, 2 erasers and 4 sharpenersFor 4 friends, she should buy 4 pens, 8 erasers and 16 sharpeners.Total Cost = 4 pens x Cost of 1 pen + 8 erasers x Cost of 1 eraser + 16 sharpeners x Cost of 1 sharpener= 4 x 20 + 8 x 15 + 16 x 12.5/2 = Rs. 300Total cost of Rs. 300 matches perfectly with Rs. 300 that Srinisha had initially. Hence, option b is correct.Question 6Pragathi won Super Singer Contest and wanted to give fruits to her five friends equal number of each fruits. In whatcombination can she purchase and give if she has Rs.1175 with her.? -- 4 Papayas cost Rs. 100, One avocado costs Rs.62.50, ten apples cost Rs.300.a) One papaya, two avocados, 2 applesb) Two papayas, two avocados, 1 applec) Two papayas, 2 avocados, 2 applesd) Three apples, two avocados, 2 apples.Answer : c) Two papayas, 2 avocados, 2 applesSolution :Cost Observations :One papaya costs Rs. 25One avocado costs Rs. 62.50One apple costs Rs. 30Consider option a) 1 papaya, 2 avocado, 2 applesTo give the above combination to each of her 5 friends, she should buy 5 papayas, 10 avocados and 10 applesTotal Cost = 5 papayas x Cost of 1 papaya + 10 avocados x Cost of 1 avocados + 10 apples x Cost of 1 apple= 5 x 25 + 10 x 62.5 + 10 x 30 = Rs. 1050But Rs. 1050 is not equal to Rs. 1175, which she had initially. Hence, option a is not correct.Consider option b) 2 papayas, 2 avocados, 1 appleTo give the above combination to each of her 5 friends, she should buy 10 papayas, 10 avocados and 5 applesTotal Cost = 10 papayas x Cost of 1 papaya + 10 avocados x Cost of 1 avocados + 5 apples x Cost of 1 apple= 10 x 25 + 10 x 62.5 + 5 x 30 = Rs. 1025But Rs. 1025 is not equal to Rs. 1175, which she had initially. Hence, option b is not correct.
- 3. Consider option c) 2 papayas, 2 avocados, 2 applesTo give the above combination to each of her 5 friends, she should buy 10 papayas, 10 avocados and 10 applesTotal Cost = 10 papayas x Cost of 1 papaya + 10 avocados x Cost of 1 avocados + 10 apples x Cost of 1 apple= 10 x 25 + 10 x 62.5 + 10 x 30 = Rs. 1175Total cost is exactly equal to Rs. 1175, which she had initially. Hence, option c is correct.Question 7Four friends namely Rahul, Ravi, Rajesh and Rohan contested for a dairy milk chocolate. To decide which friend will get thechocolate they decided to throw two dice. Every friend was asked to choose a number and if the sum of the numbers ontwo dice equals that number, the concerned person will get the chocolate. Rahuls choice was7, Ravis choice was 9,Rajeshs choice was 10 and Rohans choice was 11. Who has the maximum probability of winning the amount.a) Rahul b) Ravi c) Rajesh d) RohanAnswer : a) RahulSolution :Number 7 will appear more often –(1,6), (2,5), (3,4), (4,3), (6,1), (5,2) --- 6 casesNumber 9 -- (3,6),(6,3), (4,5) (5,4) ---4 casesFor number 10 -- (4,6) ,(6,4) (5,5) ---3 casesFor number 11 -- (5,6),(6,5)...2 cases.Since number 7 has the maximum chance of appearing, it will have the maximum probability as well. Hence, Rahul willmost probably be the winner.Question 8Yegaraj, Zimbo, Kodanda, Ramiah and Kashi were given undescribed measure of gold coins, silver bars etc. Differencesarose among them as to how these are to be distributed. Different strategies/options/methodologies were discussed.Finally it was decided to throw two dice. Every friend was asked to choose a number. Assume Yegaraj chooses 9 and Zimbochooses 10. By how much percentage, probability of Yegaraj winning is more than that of Zimbo.a) 30% b)66.67% c)33.33% d) 25%Answer : c) 33.33%Solution :Possible cases for the sum of the numbers to be 9 -- (3,6),(6,3), (4,5) (5,4) ---4 casesPossible cases for the sum to be 10 -- (4,6) ,(6,4) (5,5) ---3 casesTotal number of combinations when two dice are thrown = 36 (... 6 numbers on first die X 6 numbers on the second die)P1 = probability of Yegaraj winning = Possible cases for the sum to be 9 / Total combinations = 4/36P2 = probability of Zimbo winning = Possible cases for the sum to be 10 / Total combinations = 3/36Percentage by which P1 is more than P2 = (P1 - P2) / P2 x 100% = (4/36 - 3/36) / 3/36 x 100% = 1/3 x 100% = 33.33%Question 9A professor of Statistics posed the following question to his students:“Three dices (six sided) are thrown one after the other. What is the probability of getting a different number on eachdice?”a) 1/12 b) 1/3 c) 5/9 d) 4/9Answer : c) 5/9Solution :Dice rolled first can show any of the six numbers – so there are six possibilities. Second dice shall not have the numberrolled by first dice. So there are 5 possibilities. Similarly for third dice has four possibilities—i.e. it should not show thenumber shown by first dice and/or second dice.Based on the above argument, Number of possibilities for three dice to show different numbers = 6 x 5 x 4 = 120.Also we know that the total possibilities when three dice are thrown = 6 x 6 x 6 = 216Probability of getting a different number on each dice = Number of Possibilities for three dice to show different numbers /Total Possibilities = 120/216 = 5/9Question 10A man raises sheep and chickens. One fine day, his son wants to count the number of sheep and chickens. Farmer gives hitas below :"The average number of legs for each animal is 2 38/57. There are 19 more chickens than that of sheep." Can you help theson by finding the total number of sheep.a) 25 b) 19 c)17 d) 20Answer : b) 19Solution :Let the number of sheep be s and the number of chickens be c.We know every sheep has 4 legs and every chicken has got 2 legs.
- 4. Total number of legs = 4s + 2cAverage number of legs = Total number of legs / Total number of all animals= 4s + 2c / (s + c)It is given that the average = 2 38/57 = 152/57Therefore 4s + 2c / (s + c) = 152/57Or 228s + 114c = 152s + 152cOr 76s = 38cOr 2s = cAlso the question states that there are 19 more chickens than that of sheep.Therefore c - s = 19 ...(1)Substituting c = 2s in eq 1 we get2s - s = 19Or s = 19Question 11Ravi had a habit of saving coins given by his mother. He achieved in his objective of saving coins amounting to Rs.50. Hehad ten 1 rupee coins. The ratio of the number of 25 paise coins to that of 50 paise coins was 10/3. Can you find thenumber of 25 paise coins he had.a) 100 b) 105 c) 95 d) 98Answer : a) 100Solution :Let Ravi has X number of 25 paise coins and Y number of 50 paise coins. It is also given that there are ten 1 rupee coins.Total Rupees he has = Rs. 50.His total amount in units of paise = 50 x 100 = 5000 paise ...(1)Amount corresponding to ten 1 rupee coins = 10 x 100 = 1000 paise ...(2)Amount corresponding to X 25 paise coins = X x 25 = 25X paise ...(3)Amount corresponding to Y 50 paise coins = Y x 50 = 50Y paise ...(4)From equations 1,2,3 and 4, Total amount = 1000 + 25X + 50Y = 5000Or 25X + 50Y = 4000X + 2Y = 160 ...(5)Ratio of number of 25 paise coins to that of 50 paise coins = 10/3i.e X/Y = 10/3or Y = 3X/10 ...(6)Substituting eq 6 in eq 5, we getX + 6X/10 = 16016X/10 = 160Or 16X = 1600Or X = 100Therefore there are hundred 25 paise coins.Question 12Sections A and B of class eight had 20 and 40 students respectively. If the average height of first section was 140 cm andthat of the second section was 160 cm, what is the average height of entire class 8 ?a)154 b) 153.35 c)153.33 d)153.25Answer : c)153.33Solution :Average height of students of section A = Total height of all students of section A / Number of students of section A =140cmTotal height of all students of section A / 20 = 140Or Total height of all students of section A = 2800Average height of students of section B = Total height of all students of section B / Number of students of section B =160cmTotal height of all students of section B / 40 = 160Or Total height of all students of section B = 6400Average height of entire class eight= Total height of all students belonging to both the sections / Total number of students in both the sections put together= 2800 + 6400 / 20 + 40 = 9200 / 60 = 153.33 cmQuestion 13There are three brothers x,y and z. If zs age is as much more than ys as ys age is more than xs age, find by how muchpercentage y is older than x. Hints: Age of z is 20 and y is 5 years older than x.
- 5. a. 100% b. 50% c. 25% d. 75%Answer : b. 50%Solution.:Let a,b and c be the ages of x,y and z respectively.It is given that zs age is as much more than ys as ys age is more than xs age.Writing the above statement in the form of an equation, we getc - b = b - a ...(1)It is given that age of z i.e c = 20Substituting c = 20 in eq 1 we get,20 - b = b - a20 = 2b - a ...(2)It is also given that y is 5 years older than x. This implies b - a = 5 or b = a + 5...(3)Substitute b = a + 5 in eq 2 we get,20 = 2a + 10 - a20 = a + 10 or a = 10Substitute a = 10 in eq 3 we getb = 15Percentage by which b is more than a is (b - a)/a x 100% = (15 - 10)/10 x 100 = 50%Question 14John is 100% older than Johan. 20 years hence, John will be 50% older than Johan. Can you find their ages.a. 30,20 b. 40,20 c. 60,40 d. 50,10Answer : b. 40,20Solution :Let age of John be b.Let age of Johan be a.Currently John is 100% older than Johan. This implies b - a/a = 100%Or (b - a)/a = 1 ( this is because, 100% = 100/100 = 1)Or b - a = aOr b = 2a ...(1)20 years later ages of John and Johan will be b + 20 and a + 20 respectivelyAfter 20 years John will be older by 50%i.e (b + 20)-(a+20)/(a+20) = 50% = 1/2(b - a)/ (a + 20) = 1/2Or 2b - 2a = a + 20Or 2b = 3a + 20 ...(2)Substitute 1 in 2 we get4a = 3a + 20 or a = 20.Substitute a = 20 in eq 1 we getb = 40Johns age is 40 and Johans 20.Question 15Let a,b and c be ages of three brothers. bs age is greater than the sum of ages of a and c. After 7 years, by how muchpercentage b will be more than the sum of ages of a and c ?a. (b - a - c - 7) / (a + c + 14) x 100% b. (b - a - c + 7) / (a + c + 14) x 100% c. (b - a - c) / (a + c + 7) x 100% d. (b - a - c - 7) / (a +c + 7) x 100%Answer : a. (b - a - c - 7) / (a + c + 14) x 100%Solution :Percentage by which bs age will be greater than sum of as and cs ages after 7 years= Age of b after 7 years - (sum of ages of a and c after 7 years)------------------------------------------------------------------------------------ x 100%sum of ages of a and c after 7 years= b + 7 - (a + 7 + c + 7)--------------------------------- x 100%a+7+c+7= (b - a - c - 7) / (a + c + 14) x 100%Suresh Raina and Gautam Gambhir after a scintillating IPL match decide to travel by cycle to their respective villages. Bothof them start their journey travelling in opposite directions. Each of their speeds is 6 miles per hour. When they are at a
- 6. distance of 50 miles, a housefly starts flying from Suresh Rainas cycle towards Gautam Gambhir at a relative speed of 17miles per hour with respect to Rainas speed. What will be the time taken by housefly to reach Gambhir?(a)15 hours (b)10 hours (c) 50 hours (d)25 hoursAnswer : b)10 hoursSolution:Since Raina and Gambhir are travelling in opposite directions, Gambhirs Relative speed with respect to Rainas = Speed ofRaina + Speed of Gambhir = 6 + 6 = 12 miles per hour.Now housefly starts from Rainas cycle and travels towards Gambhirs cycle at 17 miles per hour.Relative speed of housefly with respect to Gambhir = Speed of housefly with respect to Raina - Speed of Gambhir withrespect to Raina = 17 - 12 = 5 miles per hourTime taken for housefly to reach Gambhir = Distance to catch up / Relative speed of housefly with respect to Gambhir =50/5 = 10 hours.Question 16Pinky and Ponky decided to have a car race. Initially Pinky was 20 miles behind Ponky’s car. Both of them took the race inthe same direction along the same route. Pinky was travelling at a constant speed of 68 miles per hour, while Ponky wastravelling at a constant speed of 60 miles per hour. How many hours will it take for Pinky to overtake and drive 8 milesahead of Ponky?(a)1.7 hours (b)2.0 hours (c)2.5 hours (d)3.0 hours (e) 3.5 hoursAnswer : e) 3.5 hoursSolution:It is to be understood from the problem, that Pinky has to travel 20 miles first to catch up Ponky. Then, he has to travel anadditional 8 miles to be ahead of Ponky. Pinky has to travel a total of 28 extra miles relative to Ponky’s car.Relative Speed of Pinky with respect to Ponky = 68 - 60 = 8 miles per hour.Time taken for Pinky to cover 28 extra miles compared to that of Ponky = Extra Distance / Relative Speed of Pinky withrespect to Ponky = 28/8 = 3.5 hours.Question 17Eveson was working for a multinational company. The pressure of work in the company was too heavy due to seasonalsales. Eveson decided to go weekend trip with his wife for relaxation. Husband and wife decided that the proposed tripshould not exceed 8 hours driving in a day. They decided to maintain the average Speed of forward journey to 40 mph. Dueto traffic on Sundays the return journey average speed can only be at 30 mph. How far the couple can select a picnic spot?(a)142 Miles (b)200 Miles (c)137 Miles (d)220 MilesAnswer : c)137 MilesSolution:If x and y are the speeds corresponding to forward and return journeys, then average speed of the entire journey can befound using the formula : 2xy / x+yIn our case the rate for onward journey is given as 40 mph and rate for return journey is given as 30 mphHence average speed = 2x40x30 / 40+30 = 2400 / 70 = 240 / 7 mphTotal Travel Time is 8 hours. So total distance the couple can plan = Average Speed x Affordable Total Time = 240 / 7 x 8=1920 / 7 = 274 miles (approximately)Since 274 miles should be the total distance that can be covered including forward and return journeys, the picnic spot hasto be at 274 / 2 = 137 miles approximately.Question 18Rambabu is driving a Honda Unicorn Power bike at 80 km per hour. However being sugar patient, Rambabu could nottravel continuously. He takes small breaks each of 2 minutes for every 15 minute of his drive. How much distance Rambabuwill cover in 90 minutes?a)118Km b)89Km c)112Km d) 104kmAnswer : d) 104kmSolution:For every 15 minutes he takes a rest for 2 minute.Hence for 90 minutes of drive he would require 12 minutes of rest. In effect he will be traveling for 90 - 12 = 78 minutes.For 60 minutes he covers 80 Km.For 1 minute he would cover 80/60 Km.For 78 minutes he would cover (80/60)78 = 104 Km
- 7. Q.1. The age of Ram and Sayam are in the ratio 5:6 and after 4 years their ratios are 7:8 then what is the present age ofSayam?Ans. 12years (names and values may change)Q.2. In school there are some bicycles and 4wheeler wagons.one Tuesday there are 190 wheels in the campus. How manybicycles are there?Ans. 15Q.3. Six friends go to pizza corner there are 2 types of pizzas. And six different flavors are there they have to select 4 flavorsfrom 16 flavors. In how many ways we can select?Ans. 16C4Q.4. 3, 15, x, 51, 53,159,161. Find XAns. 17Q.5. 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in someorder IN 7 rounds. A B C AB BC AC ABC. Final round measure is 155 kg then find the average weight of all the 7 rounds?Ans. 4(155)/7=31Q.6. The cost of making robot is divided into cost of material, cost of repairing and cost of painting in the ratio of 5:2:3. Thecost used for material is 200. Find the total cost of making the robot?Ans. 400 (just calculate it).Q.7. A triangle is made from a rope. The sides of the triangle are A cm, B cm and C cm (I do not remember the numericalvalue)What will be the area of the square made from the same rope?Ans. ( (A+B+C)/4)2Q. 8. What is the distance of the z-intercept from the x-intercept in the equation ax+by+cz=d (I do not remember thevalues of a, b, c, d).Ans. sqrt ((d/a) 2+ (d/c) 2)Q.9. A scientist in Antarctic region conducts research on bears came to know that bears changes according to the location.once he moves 1 mile towards north, then he moves 2 miles towards east, then 1 mile towards south. Now the color ofbear he found will be in:Ans. whiteQ.10. Two pipes A and B fill at A certain rate B is filled at 10,20,40,80,. If 1/16 of B if filled in 17 hours what time it will taketo get completely filledAns. 21Q.11. A boy bought a roll A of 56 inches wide and 141 yards long. He also bought B of 77 inches wide of length 333yards.We don’t want any details of B. Some irrelevant matter. Final question is Time taken for cutting A into 1 yard piece is 2seconds. Time taken to cut into 141 pieces of 1 yard each is?Ans. is 2(141) =242
- 8. Q.12. Person buys a horse for 15 ponds, after one year he sells it for 20 pounds. After one year, again he buys the samehorse at 30 pounds and sells it for 40 pounds. What is the profit for that person?Ans. is 15 poundsQ.13. There are 1000 pillars for a temple. 3 friends Linda, Chelsey, Juli visited that temple. (Some unrelated stuff) Linda istaller than Chelsea and taller than 2 of 1000 pillars. Julia is shorter than Linda. Find the correct sentence?(a) Linda is shorter among them(b) Chelsea is taller than Julia(c) Chelsea is shorter than Julia(d) Cannot determine who is taller among Chelsea and JuliaAns. (d)Q.14. In a family there are some boys and girls. All boys told that they are having equal no of brothers and sisters and girlstold that they are having twice the no. of brothers than sisters. How many boys and girls present in a family?Ans. is 4 boys and 3 girlsQ.15. Ram buys a cycle for 31 dollars and given a cheque of amount 35 dollars. Shop Keeper exchanged the cheque with hisneighbor and gave change to Ram. After 2 days, it is known that cheque is bounced. Shop keeper paid the amount to hisneighbor. The cost price of cycle is 19 dollars. What is the profit/loss for shop keeper?Ans. is 23(cost price + change given).Q.16. Metal strip of width ‘x’ cm. 2 metal strips are placed one over the other, then the combine length of 2 strips is ‘y’. If‘z’ strips are placed in that manner. What is the final width of that arrangement?Ans. is (z-1) (y-x) +x.Q.17. A game is played between 2 players and one player is declared as winner. All the winners from first round are playedin second round. All the winners from second round are played in third round and so on. If 8 rounds are played to declareonly one player as winner, how many players are played in first roundAns. is 28.Q.18. There are 3 boys A, B, C and 2 Girls D, E. D always sit right to A. Girls never sit in extreme positions and in the middleposition. C always sits in the extreme positions. Who is sitting immediate right to E?Ans. is B or CQ.19. 49 members attended the party. In that 22 are males, 17 are females. The shake hands between males, females,male and female. Total 12 people given shake hands. How many such kinds of such shake hands are possible?Ans. is 12C2Q.20. Entry ticket to an exhibition ranges from 1p to 31p. You need to provide exact change at the counter. You have 31pcoin. In how many parts will u divide 31p so that u will provide the exact change required and carry as less coins aspossible?(a) 22(b) 31(c) 6(d) 32Ans. is 6Q.21. There are 2 friends Peter and Paul. Peter age is twice as old as Paul when peter was as old as Paul is now. Sum of thepresent ages of Peter and Paul is 35.What is the present age of Peter?Ans. is 20
- 9. Q.22. A lady took out jacket and gloves, which are available in blue 16, yellow 40 and red 36. Power goes off, she candistinguish between gloves and jacket but not in colors. Whats the possibility their she will pick up pair of gloves of eachcolor.Ans. very easy..Q.23. Two bowls are taken, one contains water and another contains tea. One spoon of water is added to second bowl andmixed well, and a spoon of mixture is taken from second bowl and added to the second bowl. Which statement will holdgood for the above?Ans. second liquid in first bowl is smaller than the first mixture in second bowl)Q.24. Rearrange and categorize the word ‘IGTRE’?Ans. Animal (TIGER)Q.25. One grandfather has three grandchildren, two of their age difference is 3, eldest child age is 3 times youngest child’sage and eldest child’s age is two times of sum of other two children. What is the age of eldest child?Ans. 18Q.26. The ticket for a journey is in the range of 1 to 63 paise. You have 63 paise in your pocket and so on. and the questionis You have to change the money into coins and all denominations are available at final. You have to buy the ticket and youshould have at least one coin? (not same figures)Ans. 64 (Just add 1 to highest i.e. 63+1)Q.27. The sum of two numbers is given and product is also given find the square of difference of two numbers..Ans. (a-b)2=a2+b2+2ab..Q 28. The dog and here are running, dog crosses the roads, rivers and different. Here start running after 2 hours of dogrunning, dog runs 30kmph in 6 hours then what is the average speed of here?(values are not same)Ans. 30*6/4Q.29. There are some chocolates. A woman can eat 3chocolates and a man can eat 1 chocolate and a child can eat halfchocolate. then 20 chocolates is divided in...Ans. Go through the options( 5Woman, 3man, 4children).Q.30. A water tank is filled in the way as 256,128,64,... th parts in every hour, then in how many hours the tank will filled?Ans. 256,128,64,32,16,8,4,2,1 ( 9 hours) values are not same..Q.31. The age of Ram and Sayam are in the ratio 5:6 and after 4 years their ratios are 7:8 then what is the present age ofSayam?Ans. 12years (names and values may change)Q. 32.: There are two water tanks A and B, A is much smaller than B. While water fills at the rate of 1 liter every hour in A, itgets filled up like, 10, 20, 40,80, 160…..in tank B. 1/8 th of the tank B is filled in 22 hours. What is the time to fill the tankfully?a) 26(b) 25(c) 5(d) 27Ans: 22+log 2 base 8=22+4=26
- 10. Q.33.: 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 nof 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.Ans. cNote: For this type of Questions, follow this:--At least- Ist half are true, Last half are false--Exactly- Last second one is true or (N-1)th Statement is true--Almost- All are true.Q 34. : Unnecessary data. A lady has fine gloves and hats in her closet- 18 blue- 32 red , 10 white , 25 yellow, 55 purple, 30orange. The lights are out and it is totally dark in spite of the darkness. She can make out the difference between a hat anda 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 tomake sure she has a pair of each color of blue, red, yellow?(a) 59(b) 8(c) 50(d) 42Ans: a(32+25+2)Note: For this type of questions:Bigger+Middle+1 (Suppose 18, 32, 25 =32+25+1), If you do not find answer in options, choose the one closer those theanswer you got.Q 35. The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunnersin the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers areequal in every respect. They receive identical salaries and also write code at the same rate. Suppose 12 such programmerstake 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?For this type question you should follow d step of basic math that will helpful you get enough time from that.12 prog 12 line 12 min1 prog 12 line 12*121 1 12*12/1272 1 12*12/(12*72)72 72 12*12*72/(12*72)Ans:12Note: This question appears 3 times in our question but app is different please follow basic rule think it it is very very easy.Q.36.: 12 people {a1, a2, …, a12} meet and shake hands in a circular fashion. In other words, there are totally 36handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a11, a12}, {a12, a1}. Then size of the smallest set of people such thatthe rest have shaken hands with at least one person in the set is(a) 12(b) 4(c) 18(d) 11Ans. B (N/3)Q 37.: 10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. Thesuspects are made to stand in a line and each person declares that the person next to him on his right is guilty. Therightmost person is not questioned. Which of the following possibilities are true?A. All suspects are lying.B. leftmost suspect is innocent.C. leftmost suspect is guilty(a) A only
- 11. (b) A or C(c) A or B(d) B onlyAns. cNote: Remember it I dont know the logicQ.38.: Alok and Bhanu play the following min-max game. Given the expression N = 15 + X*(Y – Z) Where X, Y and Z arevariables representing single digits (0 to 9), Alok would like to maximize N while Bhanu would like to minimize it. Towardsthis end, Alok chooses a single digit number and Bhanu substitutes this for a variable of her choice (X, Y or Z). Alok thenchooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposes the value for the remainingvariable. Assuming both play to their optimal strategies, the value of N at the end of the game would be?Ans. 15+18 =33Note: For this type of questions:x+y-z=11x-y-z=2x*(y+z)=18Q.39. How many four 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) 100(b) 125(c) 75(d) 85Ans:. 5^n-1= 5^4-1=125, n= no of digitsQ.40 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 thepoint 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). Theminimum 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 ona line) is(a) 3(b) 5(c) 2Ans. Will be same as no of points in the plane, IE 5TCS Placement Paper September 2010:-Writen Test:-Q.1. How many four 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) 100(b) 125(c) 75(d) 85Ans. 5^n-1= 5^4-1=125, n= no of digitsQ.2.On planet korba, a solar blast has melted the ice caps on its equator. 9 years after the ice melts, tiny planetoids calledechina start growing on the rocks. Echina grows in the form of circle, and the relationship between the diameter of thiscircle and the age of echina is given by the formula d = 4* (t-9) for t ≥ 9Where 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 12mm. How many years back did the solar blast occur?(a) 17(b) 21.25
- 12. (c) 12(d) 12.06Ans. cQ.3.. Ferrari S.P.A is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 asScuderia Ferrari , the company sponsored drivers and manufactured race cars before moving into production of street-legal vehicles in 1947 as Feraari S.P.A. Throughout its history, the company has been noted for its continued participationin racing, especially in Formula One where it has employed great success. Rohit once bought a Ferrari . It could go 4 timesas fast as Mohans old Mercedes. If the speed of Mohans Mercedes is 46 km/hr and the distance traveled by the Ferrari is953 km, find the total time taken for Rohit to drive that distance.(a) 20.72(b) 5.18(c) 238.25(d) 6.18Ans. bQ.4. 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 nof 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.Ans. cNote: For this type of Questions, follow this:At least- Ist half are true, Last half are falseExactly- Last second one is true or (N-1)th Statement is trueAlmost- All are true.Q.5. 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 1/32 filled after 21 hours, what is the total duration required to fill it completely?(a) 26 hrs(b) 25 hrs(c) 5 hrs(d) 27 hrsAns. aQ.6 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, itgets 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 4 hours, what is the total duration required to fill it completely?(a) 8hrs(b) 25 hrs(c) 5 hrs(d) 27 hrsAns. aQ.7. Unnecessary data. A lady has fine gloves and hats in her closet- 18 blue- 32 red , 10 white , 25 yellow, 55 purple, 30orange. The lights are out and it is totally dark inspite of the darkness. She can make out the difference between a hat anda 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 tomake sure she has a pair of each color of blue, red, yellow?(a) 59(b) 8(c) 50(d) 42Ans. a(32+25+2)Note: For this type of questions:
- 13. Bigger+Middle+1 (Suppose 18, 32, 25 =32+25+1), If you do not find answer in options, choose the one closer tho theanswer you got.Q.8 The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunners inthe technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers areequal in every respect. They receive identical salaries and also write code at the same rate. Suppose 12 such programmerstake 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) 6(b) 18(c) 72(d) 12Ans. dNote: N1T1/W1=N2T2, W=No. of Lines, N=No. of PRGMRS, T=TimeQ.9 The citizens of planet nigiet are 6 fingered and have thus developed their decimal system in base 6. A certain street innigiet contains 1000 (in base 8) buildings numbered 1 to 1000. How many 3s are used in numbering these buildings?(a) 256(b) 54(c) 192(d) 108Ans. dNote: First find no. 3s in 1000 (Decimal only), Definately you will get 300, Now convert 300 into 300 base 6 by this3*6^2+0*6^1+0*6^0Q.10. 12 people {a1, a2, …, a12} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakesinvolving the pairs, {a1, a2}, {a2, a3}, …, {a11, a12}, {a12, a1}. Then size of the smallest set of people such that the rest haveshaken hands with at least one person in the set is(a) 12(b) 4(c) 18(d) 11Ans. B (N/3)Q. 11. Alice and Bob play the following coins-on-a-stack game. 100 coins are stacked one above the other. One of them is aspecial (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top by repeatedly moving thetopmost 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= 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.If the gold coin happens to be on top when it’s a player’s turn then the player wins the game.A. Alice has no winning strategy.B. Initially, the gold coins the third coin from the top. ThenC. In order to win, Alice’s first move should be a 0-move.D. In order to win, Alice’s first move should be a 1-move.Ans. DQ. 12. people meet and shake hands. The maximum number of handshakes possible if there is to be no “cycle” ofhandshakes 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)7(b) 6(c) 9(d) 8Ans. c **(N-1)**Q. 13. After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1
- 14. letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?(a) 0(b) 12/212(c) 11/12(d) 1/12Ans. aQ. 14. 10 suspects are rounded by the police and questioned about a bank robbery. Only one of them is guilty. Thesuspects are made to stand in a line and each person declares that the person next to him on his right is guilty. Therightmost person is not questioned. Which of the following possibilities are true?A. All suspects are lying.B. leftmost suspect is innocent.C. leftmost suspect is guilty(a) A only(b) A or C(c) A or B(d) B onlyAns. cQ. 15. Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, thenumber of points equidistant from all the 3 lines is(a) 4(b) 3(c) 0(d) 1Ans. a 3 lines are given so answer is 4 one incenter and 3 excenters. If it is 3 line segments then answer would be 1Q. 16. Alok and Bhanu play the following min-max game. Given the expression N = 15 + 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 tominimize 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 valuefor the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the game would beAns. 15+18 =33Note: For this type of questions:x+y-z=11x-y-z=2x*(y+z)=18Q. 17. A hare and a tortoise have a race along a circle of 100 yards diameter. The tortoise goes in one direction and thehare in the other. The hare starts after the tortoise has covered 1/5 of its distance and that too leisurely. The hare andtortoise meet when the hare has covered only 1/8 of the distance. By what factor should the hare increase its speed so asthe win the race? (for this values are changed)(a) 8(b) 5(c) 37(d) 80Ans. cQ. 18. A sheet of paper has statements numbered from 1 to 45. For all values of n from 1 to 45, statement n says “At mostn of the statements on this sheet are false”. Which statements are true and which are false?A. The odd numbered statements are true and the even numbered are false.B. The even numbered statements are true and the odd numbered are false.
- 15. C. All statements are true.Ans. cQ. 56. 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 1face of theouter surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?(a) 900(b) 488(c) 563(d) 800Ans. cNote: ** 588-(25* No. of painted faces)Q. 19 The IT giant Tirnop has recently crossed a head count of 150000 and earnings of $7 billion. As one of the forerunnersin the technology front, Tirnop continues to lead the way in products and services in India. At Tirnop, all programmers areequal in every respect. They receive identical salaries ans also write code at the same rate. Suppose 12 such programmerstake 12 minutes to write 12 lines of code in total. How many lines of code can be written by 72 programmers in 72minutes?(a) 72(b) 432(c) 12(d) 144Ans. bQ. 20. The teacher is testing a student’s proficiency in arithmetic and poses the following question. 1/3 of a number is 3more than 1/6 of the same number. What is the number? Can you help the student find the answer?(a) 12(b) 18(c) 6(d) 21Ans. bNote: Alok and Bhanu play the following min-max game. Given the expression N = X – Y – ZQ29. Where X, Y and Z are variables representing single digits (0 to 9), Alok would like to maximize N while Bhanu wouldlike to minimize it. Towards this end, Alok chooses a single digit number and Bhanu substitutes this for a variable of herchoice (X, Y or Z). Alok then chooses the next value and Bhanu, the variable to substitute the value. Finally Alok proposesthe value for the remaining variable. Assuming both play to their optimal strategies, the value of N at the end of the gamewould be(a) 2(b) 4(c) 9(d) -18Ans. aQ 21. Horse started to chase dog as it relieved stable two hrs ago. And horse started to ran with average speed 22km/hr,horse crossed 10 mts road and two small pounds with depth 3m, and it crossed two small street with 200 mts length. Aftertraveling 6 hrs, 2hrs after sunset it got dog. compute the speed of dog?Ans. As we have speed and travel time of horse, we can get distance traveled by it.Note: Hence d = 22*6 = 132km,Exactly this 132km was traveled by dog in 8 hours (as it started two hours earlier).Hence speed of dog = 132/8 = 16.5km/hrAns. 16.5km/hr.Q 61. A and B play a game between them. The dice consist of colors on their faces (instead of number). When the dice arethrown, A wins if both show the same color, otherwise B wins. One die has 3 red faces and 3 blue faces. How many red andblue faces should the other die have if the both players have if the both players have the same chances of winning?
- 16. (a) 5 red and 1 blue faces.(b) 1 red and 5 blue faces.(c) 3 red and 3 blue faces.Ans. cQ 22. In planet OZ planet there are 8 days, Sunday to Saturday and 8th day is Oz day. There is 36 hours in a day. What isangle between 12.40?(a) 80(b) 81(c) 87(d) 89Ans. 89Q 23.Ramu & sangeetha went for biological analysis to a island which is 34km from their place. They travelled in a boatwhich went at a speed of 2m/s. when they are in half a distance in the boat sangeetha note there are 7 leg & 8 legoctopuses under the water. Ramu counted the total number of legs of octopuses and got 54. Sangeetha instantly said Iknow how many 7 leged octopuses are there under the water. They both reached the island after 20 min they left . Howmany seven leged octopuses does sangeetha calculate?1. 42. 53. 64. 7Ans : Total number of legs of both 7 & 8 leged octobus = 54. Find number of 7 leged octopusesQ 24 The ratio of current age of X and Y is 5:7. After how many years their age becomes 7:9?Ans : Simple ratioQ 25. by using 1,2,3,4,5,how many 5 digit no. can be formed which is divisible by 4,repetation of no. is allowed??Ans : 2500 (not sure)Q 26. XY=21 and X+Y=13.ans of X & Y will b in points..den x square+y square=??Ans : Solve using quadratic eqn. you get x & yQ 27. Person travels from A- to b in 9km/hr, and B to A in 4 Km/hr. What is the average speed?Ans : 2(9*4)/9+4Q 28. Avg marks of 5 sub is 61. Six sub mark is 89. What is the average after adding 6th?Ans : (61*5) + 89/6Q 29. Find number of 3’s between 1 & 100?Ans : 19Q 30. A pipe can fill a tank at the rate 1 litre/hr, the tank is 1/32 filled in 6 hours. After how many hows the tank is filledcompletelyAns - 1/16, 1/8, ¼, ½, 1. After 5 hours.Q. 31. A man has to get air-mail. He starts to go to airport on his motorbike. Plane comes early and the mail is sent by ahorse-cart. The man meets the cart in the middle after half an hour. He takes the mail and returns back, by doing so, hesaves twenty minutes. How early did the plane arrive?
- 17. Ans:10min:::assume he started at 1:00,so at 1:30 he met cart. He returned home at 2:00.so it took him 1 hour for the totaljorney.by doing this he saved 20 min.so the actual time if the plane is not late is 1 hour and 20 min.so the actual time ofplane is at 1:40.The cart travelled a time of 10 min before it met him.so the plane is 10 min early.Q. 32. 2 trees are there. One grows at 3/5 of the other. In 4 years total growth of the trees is 8 ft. what growth will smallertree have in 2 years.Sol) THE BIG TREE GROWS 8FT IN 4 YEARS=>THE BIG TREE GROWS 4FT IN 2 YEARS.WHEN WE DIVIDE 4FT/5=.8*3=>2.4ans: 1.5 mt 4 (x+(3/5)x)=88x/5=2x=5/4 after 2 years x=(3/5)*(5/4)*2 =1.5Q. 33. There is a six digit code. Its first two digits, multiplied by 3 gives all ones. And the next two digits multiplied by 6 giveall twos. Remaining two digits multiplied by 9 gives all threes. Then what is the code?sol) Assume the digit xx xx xx (six digits)First Two digit xx * 3=111 xx=111/3=37( first two digits of 1 is not divisible by 3 so we can use 111)Second Two digit xx*6=222 xx=222/6=37( first two digits of 2 is not divisible by 6 so we can use 222)Thrid Two digit xx*9=333 xx=333/9=37( first two digits of 3 is not divisible by 9 so we can use 333)Q. 34. There are 4 balls and 4 boxes of colours yellow, pink, red and green. Red ball is in a box whose colour is same as thatof the ball in a yellow box. Red box has green ball. In which box you find the yellow ball?Ans is green...Sol) Yellow box can have either of pink/yellow balls.if we put a yellow ball in "yellow" box then it wud imply that "yellow" is also the colour of the box which has the redball(becoz acordin 2 d question,d box of the red ball n the ball in the yellow box have same colour)thus this possibility is ruled out...therefore the ball in yellow box must be pink,hence the colour of box containin red ball is also pink....=>the box colour left out is "green",,,which is alloted to the only box left,,,the one which has yellow ball..Q. 35. A bag contains 20 yellow balls, 10 green balls, 5 white balls, 8 black balls, and 1 red ball. How many minimum ballsone should pick out so that to make sure the he gets at least 2 balls of same color.Ans:he should pick 6 ball totally.Sol) Suppose he picks 5 balls of all different colours then when he picks up the sixth one, it must match any on of thepreviously drawn ball colour.thus he must pick 6 ballsQ. 36. What is the number of zeros at the end of the product of the numbers from 1 to 100Sol) For every 5 in unit palce one zero is added Ch eta naSso between 1 to 100 there are 10 nos like 5,15,25,..,95 which has 5 in unit place.Similarly for every no divisible by 10 one zero is added in the answer so between 1 to 100 11 zeros are addedfor 25,50,75 3 extra zeros are addedso total no of zeros are 10+11+3=24Q. 37. 10 Digit number has its first digit equals to the numbers of 1s, second digit equals to the numbers of 2s, 3rd digitequals to the numbers of 3s .4th equals number of 4s..till 9th digit equals to the numbers of 9s and 10th digit equals tothe number of 0s. what is the number?.(6marks)Ans:21000100062---shows that two 1s in the ans1---shows that one 2 in ans
- 18. 0---shows no 3 in the ans0---shows no 4 in the ans0---shows no 5 in the ans1---shows one 6 in the ans0---shows no 7 in the ans0---shows no 8 in the ans0---shows no 9 in the ans6---shows six 0s in the ansQ. 38 A and B are shooters and having their exam. A and B fall short of 10 and 2 shots respectively to the qualifying mark. Ifeach of them fired atleast one shot and even by adding their total score together, they fall short of the qualifying mark,what is the qualifying mark?Ans is 11coz each had atleast 1 shot done so 10 + 1 = 11n 9 + 2 = 11so d ans is 11Q. 39 Gavaskar average in first 50 innings was 50. After the 51st innings his average was 51 how many runs he made in the51st inningsAns) first 50 ings.- run= 50*50=250051st ings.- avg 51. so total run =51*51=2601.so run scored in that ings=2601-2500=101 runs.Q. 40. Anand finishes a work in 7 days, Bittu finishes the same job in 8 days and Chandu in 6 days. They take turns to finishthe work. Anand on the first day, Bittu on the second and Chandu on the third day and then Anand again and so on. Onwhich day will the work get over?a) 3rdb) 6thc) 9thd) 7thAns is d) 7th daySol) In d 1st day Anand does 1/7th of total worksimilarly,Bithu does 1/8th work in d 2nd dayhence at d end of 3 days, work done = 1/7+1/8+1/6=73/168remaining work = (168-73)/168 = 95/168again after 6 days of work, remaining work is = (95-73)/168 = 22/168and hence Anand completes the work on 7th day.(hope u understood.)

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