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$$$Aptitude Questions1.If 2xy=4 then 6x3y=?(a)15(b)12(c)18(d)10Ans. (b)2.If x=y=2z and xyz=256 then what is the value of x?(a)12(b)8(c)16(d)6Ans. (b)3. (1/10)18  (1/10)20 = ?(a) 99/1020(b) 99/10(c) 0.9(d) none of theseAns. (a)4.Pipe A can fill in 20 minutes and Pipe B in 30 minsand Pipe C canempty the same in 40 mins.If all of them worktogether, find the timetaken to fill the tank(a) 17 1/7 mins(b) 20 mins(c) 8 mins(d) none of theseAns. (a)5. Thirty men take 20 days to complete a job working 9hours a day.Howmany hour a day should 40 men work to complete thejob?(a) 8 hrs(b) 7 1/2 hrs(c) 7 hrs(d) 9 hrsAns. (b)6. Find the smallest number in a GP whose sum is 38and product 1728(a) 12(b) 20(c) 8(d) none of theseAns. (c)7. A boat travels 20 kms upstream in 6 hrs and 18 kmsdownstream in 4hrs.Find the speed of the boat in still water and thespeed of thewater current?(a) 1/2 kmph(b) 7/12 kmph(c) 5 kmph(d) none of theseAns. (b)8. A goat is tied to one corner of a square plot ofside 12m by a rope7m long.Find the area it can graze?(a) 38.5 sq.m(b) 155 sq.m(c) 144 sq.m(d) 19.25 sq.mAns. (a)9. Mr. Shah decided to walk down the escalator of atube station. Hefound that if he walks down 26 steps, he requires 30seconds toreach the bottom. However, if he steps down 34 stairshe would onlyrequire 18 seconds to get to the bottom. If the timeis measured fromthe moment the top step begins to descend to thetime he steps offthe last step at the bottom, find out the height ofthe stair way insteps?Ans.46 steps.10. The average age of 10 members of a committee isthe same as it was4 years ago, because an old member has been replacedby a youngmember. Find how much younger is the new member ?Ans.40 years.11. Three containers A, B and C have volumes a, b, andc respectively;and container A is full of water while the other twoare empty. Iffrom container A water is poured into container Bwhich becomes 1/3full, and into container C which becomes 1/2 full, howmuch water isleft in container A?12. ABCE is an isosceles trapezoid and ACDE is arectangle. AB = 10and EC = 20. What is the length of AE?Ans. AE = 10.13. In the given figure, PA and PB are tangents to thecircle at A andB respectively and the chord BC is parallel totangent PA. If AC = 6cm, and length of the tangent AP is 9 cm, then whatis the length ofthe chord BC?Ans. BC = 4 cm.15 Three cards are drawn at random from an ordinarypack of cards.Find the probability that they will consist of a king,a queen and an ace.Ans. 64/2210.16. A number of cats got together and decided to killbetween them999919 mice. Every cat killed an equal number ofmice. Each catkilled more mice than there were cats. How many catsdo you thinkthere were ?Ans. 991.17. If Log2 x  5 Log x + 6 = 0, then what would thevalue / values ofx be?Ans. x = e2 or e3.18. The square of a two digit number is divided byhalf the number.After 36 is added to the quotient, this sum is thendivided by 2.The digits of the resulting number are the same asthose in theoriginal number, but they are in reverse order. Theten's place ofthe original number is equal to twice the differencebetween itsdigits. What is the number?Ans. 4619.Can you tender a one rupee note in such a mannerthat there shallbe total 50 coins but none of them would be 2 paisecoins.?Ans. 45 one paisa coins, 2 five paise coins, 2 tenpaise coins, and 1twentyfive paise coins.20.A monkey starts climbing up a tree 20ft. tall. Eachhour, it hops3ft. and slips back 2ft. How much time would it takethe monkey toreach the top?Ans.18 hours.21. What is the missing number in this series? 8 214 6 11 ? 14 6 18 12Ans. 922. A certain type of mixture is prepared by mixingbrand A at Rs.9 akg. with brand B at Rs.4 a kg. If the mixture is worthRs.7 a kg., howmany kgs. of brand A are needed to make 40kgs. ofthe mixture?Ans. Brand A needed is 24kgs.23. A wizard named Nepo says "I am only three times myson's age. Myfather is 40 years more than twice my age. Togetherthe three of usare a mere 1240 years old." How old is Nepo?Ans. 360 years old.24. One dog tells the other that there are two dogs infront of me.The other one also shouts that he too had two behindhim. How many arethey?Ans. Three.25. A man ate 100 bananas in five days, each dayeating 6 more thanthe previous day. How many bananas did he eat on thefirst day?Ans. Eight.26. If it takes five minutes to boil one egg, how longwill it take toboil four eggs?Ans. Five minutes.27. The minute hand of a clock overtakes the hour handat intervals of64 minutes of correct time. How much a day does theclock gain or lose?Ans. 32 8/11 minutes.28. Solve for x and y: 1/x  1/y = 1/3, 1/x2 + 1/y2= 5/9.Ans. x = 3/2 or 3 and y = 3 or 3/2.29. Daal is now being sold at Rs. 20 a kg. During lastmonth its ratewas Rs. 16 per kg. By how much percent should a familyreduce itsconsumption so as to keep the expenditure fixed?Ans. 20 %.30. Find the least value of 3x + 4y if x2y3 = 6.Ans. 10.31. Can you find out what day of the week was January12, 1979?Ans. Friday.32. A garrison of 3300 men has provisions for 32 days,when given at arate of 850 grams per head. At the end of 7 days areinforcementarrives and it was found that now the provisions willlast 8 daysless, when given at the rate of 825 grams per head.How, many more mencan it feed?Ans. 1700 men.33. From 5 different green balls, four different blueballs and threedifferent red balls, how many combinations of ballscan be chosentaking at least one green and one blue ball?Ans. 3720.34. Three pipes, A, B, & C are attached to a tank. A &B can fill itin 20 & 30 minutes respectively while C can empty itin 15 minutes.If A, B & C are kept open successively for 1 minuteeach, how soonwill the tank be filled?Ans. 167 minutes.35. A person walking 5/6 of his usual rate is 40minutes late. What ishis usual time? Ans. 3 hours 20 minutes.36.For a motorist there are three ways going from CityA to City C. Byway of bridge the distance is 20 miles and toll is$0.75. A tunnelbetween the two cities is a distance of 10 miles andtoll is $1.00 forthe vehicle and driver and $0.10 for each passenger. Atwolanehighway without toll goes east for 30 miles to city Band then 20miles in a northwest direction to City C.1. Which is the shortest route from B to C(a) Directly on toll free highway to City C(b) The bridge(c) The Tunnel(d) The bridge or the tunnel(e) The bridge only if traffic is heavy on the tollfree highwayAns. (a)2. The most economical way of going from City A toCity B, in terms oftoll and distance is to use the(a) tunnel(b) bridge(c) bridge or tunnel(d) toll free highway(e) bridge and highwayAns. (a)3. Jim usually drives alone from City C to City Aevery working day.His firm deducts a percentage of employee pay forlateness. Whichfactor would most influence his choice of the bridgeor the tunnel ?(a) Whether his wife goes with him(b) scenic beauty on the route(c) Traffic conditions on the road, bridge and tunnel(d) saving $0.25 in tolls(e) price of gasoline consumed in covering additional10 miles on thebridgeAns. (a)4. In choosing between the use of the bridge and thetunnel the chieffactor(s) would be:I. Traffic and road conditionsII. Number of passengers in the carIII. Location of one's homes in the center oroutskirts of one of thecitiesIV. Desire to save $0.25(a) I only(b) II only(c) II and III only(d) III and IV only(e) I and II onlyAns. (a)37.The letters A, B, C, D, E, F and G, not necessarilyin that order,stand for seven consecutive integers from 1 to 10D is 3 less than AB is the middle termF is as much less than B as C is greater than DG is greater than F1. The fifth integer is(a) A(b) C(c) D(d) E(e) FAns. (a)2. A is as much greater than F as which integer isless than G(a) A(b) B(c) C(d) D(e) EAns. (a)3. If A = 7, the sum of E and G is(a) 8(b) 10(c) 12(d) 14(e) 16Ans. (a)4. A  F = ?(a) 1(b) 2(c) 3(d) 4(e) Cannot be determinedAns. (a)5. An integer T is as much greater than C as C isgreater than E. Tcan be written as A + E. What is D?(a) 2(b) 3(c) 4(d) 5(e) Cannot be determinedAns. (a)6. The greatest possible value of C is how muchgreater than thesmallest possible value of D?(a) 2(b) 3(c) 4(d) 5(e) 6Ans. (a)38.1. All G's are H's2. All G's are J's or K's3. All J's and K's are G's4. All L's are K's5. All N's are M's6. No M's are G's1. If no P's are K's, which of the following must betrue?(a) All P's are J's(b) No P is a G(c) No P is an H(d) If any P is an H it is a G(e) If any P is a G it is a JAns. (a)2. Which of the following can be logically deducedfrom the conditionsstated?(a) No M's are H's(b) No M's that are not N's are H's(c) No H's are M's(d) Some M's are H's(e) All M's are H'sAns. (a)3. Which of the following is inconsistent with one ormore of theconditions?(a) All H's are G's(b) All H's that are not G's are M's(c) Some H's are both M's and G's(d) No M's are H's(e) All M's are H'sAns. (a)4. The statement "No L's are J's" isI. Logically deducible from the conditions statedII. Consistent with but not deducible from theconditions statedIII. Deducible from the stated conditions togetherwith the additionalstatement "No J's are K's"(a) I only(b) II only(c) III only(d) II and III only(e) Neither I, II nor IIIAns. (a)39.In country X, democratic, conservative and justiceparties havefought three civil wars in twenty years. TO restorestability anagreement is reached to rotate the top officesPresident, PrimeMinister and Army Chief among the parties so that eachparty controlsone and only one office at all times. The three topoffice holdersmust each have two deputies, one from each of theother parties. Eachdeputy must choose a staff composed of equally membersof his or herchiefs party and member of the third party.1. When Justice party holds one of the top offices,which of thefollowing cannot be true(a) Some of the staff members within that office arejustice party members(b) Some of the staff members within that office aredemocratic partymembers(c) Two of the deputies within the other offices arejustice party members(d) Two of the deputies within the other offices areconservativeparty members(e) Some of the staff members within the other officesare justiceparty members.Ans. (a)2. When the democratic party holds presidency, thestaff of the primeminister's deputies are composedI. Onefourth of democratic party membersII. Onehalf of justice party members and onefourthof conservativeparty membersIII. Onehalf of conservative party members andonefourth of justiceparty members.(a) I only(b) I and II only(c) II or III but not both(d) I and II or I and III(e) None of theseAns. (a)3. Which of the following is allowable under the rulesas stated:(a) More than half of the staff within a given officebelonging to asingle party(b) Half of the staff within a given office belongingto a single party(c) Any person having a member of the same party ashis or herimmediate superior(d) Half the total number of staff members in allthree officesbelonging to a single party(e) Half the staff members in a given office belongingto partiesdifferent from the party of the top office holder inthat office.Ans. (a)4. The office of the Army Chief passes fromConservative to Justiceparty. Which of the following must be fired.(a) The democratic deputy and all staff membersbelonging to Justice party(b) Justice party deputy and all his or hers staffmembers(c) Justice party deputy and half of his Conservativestaff members inthe chief of staff office(d) The Conservative deputy and all of his or herstaff membersbelonging to Conservative party(e) No deputies and all staff members belonging toconservative parties.Ans. (a)40.In recommendations to the board of trustees atuition increase of$500 per year, the president of the university said"There were nostudent demonstrations over the previous increases of$300 last yearand $200 the year before". If the president'sstatement is accuratethen which of the following can be validly inferredfrom theinformation given:I. Most students in previous years felt that theincreases werejustified because of increased operating costs.II. Student apathy was responsible for the failure ofstudents toprotest the previous tuition increases.III. Students are not likely to demonstrate over newtuition increases.(a) I only(b) II only(c) I or II but not both(d) I, II and III(e) NoneAns. (a)41. The office staff of XYZ corporation presentlyconsists of threebookeepersA, B, C and 5 secretaries D, E, F, G, H.The management isplanning to open a new office in another city using 2bookeepers and 3secretaries of the present staff . To do so they planto seperatecertain individuals who don't function well together.The followingguidelines were established to set up the new officeI. Bookeepers A and C are constantly finding faultwith one anotherand should not be sent together to the new office as ateamII. C and E function well alone but not as a team ,they should beseperatedIII. D and G have not been on speaking terms andshouldn't go togetherIV Since D and F have been competing for promotionthey shouldn't be ateam1.If A is to be moved as one of the bookeepers,whichof the followingcannot be a possible working unit.A.ABDEHB.ABDGHC.ABEFHD.ABEGHAns.B2.If C and F are moved to the new office,how manycombinations arepossibleA.1B.2C.3D.4Ans.A3.If C is sent to the new office,which member of thestaff cannot gowith CA.BB.DC.FD.GAns.B4.Under the guidelines developed,which of thefollowing must go to thenew officeA.BB.DC.ED.GAns.A5.If D goes to the new office,which of the followingis/are trueI.C cannot goII.A cannot goIII.H must also goA.I onlyB.II onlyC.I and II onlyD.I and III onlyAns.D42.After months of talent searching for anadministrative assistant tothe president of the college the field of applicantshas been narroweddown to 5A, B, C, D, E .It was announced that thefinalist would bechosen after a series of allday group personalinterviews wereheld.The examining committee agreed upon the followingprocedureI.The interviews will be held once a weekII.3 candidates will appear at any allday interviewsessionIII.Each candidate will appear at least onceIV.If it becomes necessary to call applicants foradditonalinterviews, no more 1 such applicant should be askedto appear thenext weekV.Because of a detail in the written applications,itwas agreed thatwhenever candidate B appears, A should also bepresent.VI.Because of travel difficulties it was agreed that Cwill appear foronly 1 interview.1.At the first interview the following candidatesappear A,B,D.Whichof the follwing combinations can be called for theinterview to beheld next week.A.BCDB.CDEC.ABED.ABCAns.B2.Which of the following is a possible sequence ofcombinations forinterviews in 2 successive weeksA.ABC;BDEB.ABD;ABEC.ADE;ABCD.BDE;ACDAns.C3.If A ,B and D appear for the interview and D iscalled foradditional interview the following week,which 2candidates may beasked to appear with D?I. AII BIII.CIV.EA.I and IIB.I and III onlyC.II and III onlyD.III and IV onlyAns.D4.Which of the following correctly state(s) theprocedure followed bythe search committeeI.After the second interview all applicants haveappeared at least onceII.The committee sees each applicant a second timeIII.If a third session,it is possible for allapplicants to appear atleast twiceA.I onlyB.II onlyC.III onlyD.Both I and IIAns.A43. A certain city is served by subway lines A,B and Cand numbers 1 2and 3When it snows , morning service on B is delayedWhen it rains or snows , service on A, 2 and 3 aredelayed both in themorning and afternoonWhen temp. falls below 30 degrees farenheit afternoonservice iscancelled in either the A line or the 3 line,but not both.When the temperature rises over 90 degrees farenheit,the afternoonservice is cancelled in either the line C or the3 line but not both.When the service on the A line is delayed orcancelled, service on theC line which connects the A line, is delayed.When service on the 3 line is cancelled, service onthe B line whichconnects the 3 line is delayed.Q1. On Jan 10th, with the temperature at 15 degreefarenheit, itsnows all day. On how many lines will service beaffected, including both morning and afternoon.(A) 2(B) 3(C) 4(D) 5Ans. DQ2. On Aug 15th with the temperature at 97 degreesfarenheit it beginsto rain at 1 PM. What is the minimum numberof lines on which service will be affected?(A) 2(B) 3(C) 4(D) 5Ans. CQ3. On which of the following occasions would servicebe on thegreatest number of lines disrupted.(A) A snowy afternoon with the temperature at 45degree farenheit(B) A snowy morning with the temperature at 45 degreefarenheit(C) A rainy afternoon with the temperature at 45degree farenheit(D) A rainy afternoon with the temperature at 95degree farenheitAns. B44. In a certain society, there are two marriagegroups, red andbrown. No marriage is permitted within a group. Onmarriage, malesbecome part of their wives groups; women remain intheir own group.Children belong to the same group as their parents.Widowers anddivorced males revert to the group of their birth.Marriage to morethan one person at the same time and marriage to adirect descendantare forbiddenQ1. A brown female could have hadI. A grandfather born RedII. A grandmother born RedIII Two grandfathers born Brown(A) I only(B) III only(C) I, II and III(D) I and II onlyAns. DQ2. A male born into the brown group may have(A) An uncle in either group(B) A brown daughter(C) A brown son(D) A soninlaw born into red groupAns. AQ3. Which of the following is not permitted under therules as stated.(A) A brown male marrying his father's sister(B) A red female marrying her mother's brother(C) A widower marrying his wife's sister(D) A widow marrying her divorced daughter'sexhusbandAns. BQ4. If widowers and divorced males retained theirgroup they had uponmarrying which of the following would be permissible (Assume that noprevious marriage occurred)(A) A woman marrying her dead sister's husband(B) A woman marrying her divorced daughter'sexhusband(C) A widower marrying his brother's daughter(D) A woman marrying her mother's brother who is awidower.Ans. DQ5. I. All G's are H'sII. All G's are J's or K'sIII All J's and K's are G'sIV All L's are K'sV All N's are M'sVI No M's are G's45. There are six steps that lead from the first tothe second floor.No two people can be on the same stepMr. A is two steps below Mr. CMr. B is a step next to Mr. DOnly one step is vacant ( No one standing on that step)Denote the first step by step 1 and second step bystep 2 etc.1. If Mr. A is on the first step, Which of thefollowing is true?(a) Mr. B is on the second step(b) Mr. C is on the fourth step.(c) A person Mr. E, could be on the third step(d) Mr. D is on higher step than Mr. C.Ans: (d)2. If Mr. E was on the third step & Mr. B was on ahigher step thanMr. E which step must be vacant(a) step 1(b) step 2(c) step 4(d) step 5(e) step 6Ans: (a)3. If Mr. B was on step 1, which step could A be on?(a) 2&e only(b) 3&5 only(c) 3&4 only(d) 4&5 only(e) 2&4 onlyAns: (c)4. If there were two steps between the step that A wasstanding andthe step that B was standing on, and A was on a higherstep than D , Amust be on step(a) 2(b) 3(c) 4(d) 5(e) 6Ans: (c)5. Which of the following is falsei. B&D can be both on oddnumbered steps in oneconfigurationii. In a particular configuration A and C must eitherboth an oddnumbered steps or both an evennumbered stepsiii. A person E can be on a step next to the vacantstep.(a) i only(b) ii only(c) iii only(d) both i and iiiAns: (c)46. Six swimmers A, B, C, D, E, F compete in a race.The outcome is asfollows.i. B does not win.ii. Only two swimmers separate E & Diii. A is behind D & Eiv. B is ahead of E , with one swimmer interveningv. F is a head of D1. Who stood fifth in the race ?(a) A(b) B(c) C(d) D(e) EAns: (e)2. How many swimmers seperate A and F ?(a) 1(b) 2(c) 3(d) 4(e) cannot be determinedAns: (d)3. The swimmer between C & E is(a) none(b) F(c) D(d) B(e) AAns: (a)4. If the end of the race, swimmer D is disqualifiedby the Judgesthen swimmer B finishes in which place(a) 1(b) 2(c) 3(d) 4(e) 5Ans: (b)47. Five houses lettered A,B,C,D, & E are built in arow next to eachother. The houses are lined up in the order A,B,C,D, &E. Each of thefive houses has a colored chimney. The roof andchimney of eachhousemust be painted as follows.i. The roof must be painted either green,red ,oryellow.ii. The chimney must be painted either white, black,or red.iii. No house may have the same color chimney as thecolor of roof.iv. No house may use any of the same colors that theevery next houseuses.v. House E has a green roof.vi. House B has a red roof and a black chimney1. Which of the following is true ?(a) At least two houses have black chimney.(b) At least two houses have red roofs.(c) At least two houses have white chimneys(d) At least two houses have green roofs(e) At least two houses have yellow roofsAns: (c)2. Which must be false ?(a) House A has a yellow roof(b) House A & C have different color chimney(c) House D has a black chimney(d) House E has a white chimney(e) House B&D have the same color roof.Ans: (b)3. If house C has a yellow roof. Which must be true.(a) House E has a white chimney(b) House E has a black chimney(c) House E has a red chimney(d) House D has a red chimney(e) House C has a black chimneyAns: (a)4. Which possible combinations of roof & chimney canhouseI. A red roof 7 a black chimneyII. A yellow roof & a red chimneyIII. A yellow roof & a black chimney(a) I only(b) II only(c) III only(d) I & II only(e) I&II&IIIAns: (e)48. Find x+2y(i). x+y=10(ii). 2x+4y=20Ans: (b)49. Is angle BAC is a right angle(i) AB=2BC(2) BC=1.5ACAns: (e)50. Is x greater than y(i) x=2k(ii) k=2yAns: (e)
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