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# Note for MANA 3335 with Professor DeFrank at UH

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This 45 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15

od m s blem 0 Fr W Word Problems Word problems appear ThroughouT The QuanTiTaTive secTion Word problems can be parTicuIarIy Tricky The primary skill used in word roblems isTo Take a Tedious lITTle sTory and concepTualize I maThemaTIcally If you geT a problem ThaT Tells you quotGeor e has Ten dollars less Than Twice as much as Bill I you shoul be Thinking Oh I39ll use G for how much George has and B for how much Bill has Twice as much as Bill means 28 and Ten dollars less means 10 so GZB10quot Once you have masTered This skill you will have masTered The mosT difficulT parT of GMAT word problems Word problems are uTimaTey an exercise in TransIaTion The acTua maTh in GMAT word problems Tends To be fairly eas iT39s The TransIaTion ThaT is The hard parT The word pro lems TransIaTion Table on The nexT page should help THE 3 BASIC PRINCIPLES OF WORD PROBLEMS 1 Read Through The enTire quesTion and The answer choices To gain a general undersTanding of The siTuaTion 2 Keep Track of exachy whaT you39re afTer 3 Learn To recognize The Types of problems ThaT you find easy and Those ThaT ou find difficulT If you Think The quesTion ooks complicaTed or you have less confidence solving This parTicular Type of quesTion and if iT isn39T one of The firsT few quesTions eliminaTe answer choices and guess 45TEP METHOD FOR WORD PROBLEMS IN PROBLEM SOLVING 1 Look for The besT approach To The quesTion and apply iT 2 In mosT cases The besT approach To use in solving word problems is To TransIaTe iT inTo a maThemaTical equaTion If noT use an alTernaTive meThod such as picking numbers and backsolving 3 Reread The quesTion figuring ouT whaT you39re given and whaT you need To know 4 TranslaTe The problem To an equaTion Ifglou39re sTuck TransIaTing or if you JusT don39T un ersTand The problem consider using an alTernaTive meThod Typical Word Problem Jacob is now 12 years younger Than Michael If in 9 years Michael will be Twice as old as Jacob how old will Jacob be in 4 years 3 7 15 21 25 4 Here39s The soluTion Jacob39s age is now Michael39s age buT 12 yrs younger J M 12 We swiTched The order of The senTence as we TranslaTed iT To maTh quot12 years younger Than Michaelquot became quotMichael39s age buT 12 years younger SomeTimes The order of The Terms in English will differ sligthy from The order in maTh If you geT confused pick some sample values If Michael is 15 years old Then Jacob is 12 years younger or 3 Therefore JM12 To continue here s the rest of the solution Michael in 9 years will be twice as old as Jacob M 9 2J 9 50 we know that JN12 and M92J9 The question asks for J4 Solve for J by substituting JN12 J12N M92J9 J1292J18 J212J18 J32J 3J 7J4 Remember that we39re looking for J4 not J so B is correct Combine AnoTher39 way To solve This problem is by combining The equaTions When you have Two equaTions you can add or39 subTr39acT Them from one anoTher39 jusT as Though They were regular numbers You 39usT have To seT iT up r39ighT wiTh like var39iables ir39ecTIy above one anoTher39 M92J 18 M12J 21 J18 3J 7J4 TranslaTion of Word Problem Help If you are having Trouble TranslaTing word problems inTo maTh Two useful sTraTegies are Picking Numbers and Backsolving Picking Numbers There are Two Times To pick numbers FirsT when The problem is made easier by Trying ouT possibiIiTies raTher Than by hassling wiTh The algebra involved Second when you simply don39T undersTand The algebra and cannoT solve The problem WhaT you do in eiTher case is pick few simple numbers keeping Them small if possible so The ariThmeTic will be simple and do To Them whaT has been described in The word problem Picking Numbers Here are a few guidelines for39 when To plug in numbers and whoT numbers you should Tr39y In problems involving per39cenTs a good number39 To sTor39T wiTh is ofTen 100 because iT is so easy To find a per39cenT of 100 In pr39oblems wiTh Two or39 more frocTions Try using The leosT common denominoTor39 of The fr39ocTions involved 4 Picking Numbers Picking numbers is almosT always The fasTesT way To problems abouT remainders In algebra in which The problem and iTs answer choices are all expressed in Terms of variables such as x or y you can avoid algebra by simply making up values of x and y When ou plug in numbers or The variables and do The ariT meTic involved you will geT anoTher number as a resuIT Take The numbers you used for x and y and plug Them inTo The variables in The answer chouces assuming only one choice resulTs in The same number as in The problem ThaT choice is The answer Avoid using 0 or 1 because They have special properTies OfTen when you use 1 or 1 more han one answer choice will work and Then you have To Try plug ing in anoTher number To decide beTween T e remaining choices Let39s take a look at Picking numbers in action The value of cer rain an rique car39 increased by 30 per39cen r from 1986 To 1990 and Then decreased by 20 per39cen r from 1990 To 1994 The car39s value in 1994 was wha r percent of HS value in 1986 90 100 104 110 124 Let39s say Le r39s say The car was originally wor rh 100100 in 1986 IT increases by 30 of 100 or 30 which means if was wor rh 130 in 1990 Then if decrease 20 15X130126 So if decreased by 26 Therefore if was wor rh 104 which is 104 of 100 The answer Therefore is C 4 Now work THIS ouT AT an inTernaTionaI dinner 15 of The people aTTending were from SouTh America If The number of NorTh Americans aT The dinner was 23 greaTer Than The number of SouTh Americans whaT fracTion of people aT The dinner were from neiTher SouTh America nor NorTh America 15 25 715 815 23 NOTICE You should no rice immedia rely rha r rhe roblem con rains rwo frac rions 15 and 23 he eas r common denomina ror is 5 so Ie r39s sa rhe ro ral number of eo e a r The dinner was 1 Tha r means we have 3 ou h Americans in The room We also have Nor rh Americans numbering TwoThirds more rhan rha r or 3 233 which Is 5 So There were 8 people from Sou rh America or Nor rh America which means 7 peo e were no r from ei rher place So 715 of The peop e in The room were from nei rher Sou rh America nor Nor rh America The correc r answer Therefore is C Here s anoTher Picking Numbers example If The price of iTem X increased by 20 and Then by a furTher 20 whaT percenT of The original price is The increase in price 24 40 44 6623 140 LeT39s say LeT39s say The price was originally 100 IT increase by 20 of 100 which is 20 so now The price is 120 The price Then increase by 20 of 120 15X12024 which means an increase of 24 So The price is now 144 or 44 more Than iTs original price of 100 The correcT answer Therefore is C 4 Backsolving You will remember ThaT in backsolving you plug in The answer choices and see which one works This approach mighT seem Time consuming buT you already know ThaT you can make iT more efficienT The choices are almosT always in ascending or descending order Assume They39re in ascending increasing order STarT wiTh choice B If ThaT39s Too small Try D If D is Too large we know iT musT be C 4 Try This one An insurance company provides coverage for a cerTain denTal procedure accordin To The following rules The policy pays 80 of The 19lr395 l39 1200 of cosT and 50 of The cosT above 1200 If a paTienT had To pay 490 of The cosT for This procedure himself how much did The procedure cosT 1200 1300 1500 1600 1700 SoluTion Because The policy pays 80 of The firsT 1200 of cosT The paTienT musT pay 20 of 1200 One fif l h of 1200 is 240 LeT39s Try B If The procedure cosT 1300 The paTienT pays 24050 0 of 100 2405o29o which is Too small We need a larger number so Try D If The procedure cosT 1600 Then The paTienT pays 240 plus 50 of 400 which is 240200 ToTaling 440 Too small The answer musT be E Ra l e Problems Some word problems deal wi rh ra res They aren39T really rha r difficul r They Typically spell ou r some kind of ra re early in The problem like The following example If Jose does GMAT word problems aT cons ran r raTe of 2 roblems everky 5 minuTes how many seconds will iT Ta e him To do problems 25N 2N 52N 24N 15ON Two Ways To Do This There are rwo common ways of doing ra re problems algebraically and by plugging in numbers Le r39s rry bo rh for The problem above Algebraic Solution Le r39s call The number of seconds Tha r we39ve been asked To find T 2 560 NT Now we cross mulTiply and solve for T 2T300N T15ON The answer is E Picking Numbers Solution Le r39s say Tha r N2 Tha r means Jose does exac rly 2 problems every 5 minu res or 300 seconds 5X605econds300 seconds Now look for The answer choices Tha r yield 300 when N2 The only one Tha r does is E so Tha r mus r be The answer 4 Picking Numbers SOIU39HOI39I conT By The wa IT39ll help if you know The DisTance illor39mula DRXT as iT usually shows u once or39 Twice on The TesT IT jusT means T aT The disTance you Tr39aveled equals The r39aTe you were going aT mulTiplied by The Time iT Took you To geT There For39 insTance if you Travel for39 Two hours aT 30 miles per hour39 Then you Tr39avel 2X30 or39 60 miles 4 Word Problems Word problems involving work occasionally show up on The GMAT They will be easy if you use This formula The reciprocal of The Time iT Takes everyone working TogeTher The sum of The reciprocals of The Times iT would Take each working individually The reciprocal of A is lA 4 Word Problem Example Working Toge rher John David and Roger require 214 hours To comple re a cer rain rask if each of Them works at his respec rive cons ran r ra re If John alone can comple re The Task in 45 hours and David alone can comple re The Task in 9 hours how many hours would if rake Roger ro comple re The Task working alone 213 412 634 9 12 Work Equation 0139 Work Here39s The solu rion employing The work equa rion 1T 1J1D1R 122514519lR 4929191R 191R R9 4 Break i39l39 Down An alTernaTive ap roach To This kind of problem ThaT some find in uiTive and quick is To break down The work on an hourbyhour basis Take David firsT Ev himself he could do The enTire Task in 9 ours Therefore during every single hour ThaT The guys work To eTher David will be doing 19 of he Task 1 9 is jusT The reciprocal of 9 In The second our he39ll do anoTher 19 And in ThaT exTra 14 hour he39ll do 14X19 or 136 of The Task Add Them up David will be doing 191913614 of The enTire Task during The period in The quesTion WhaT39s Their share How abouT John He39s much fasTer39 Than David Working alone he could do The enTir39e Task in 45 or39 95 hours So during each hour39 he works he39ll do The reciprocal of 92 or39 29 of The Task MulTiply ThaT 29 of a Task per39 hour39 by The 225 hours The guys work and you see ThaT John himself will accounT for39 29 X 94 or39 12 of The Task 4 WhoT39s Their share WiTh David and John occounTing for39 14 and 12 of The Task r39especTively ThoT leaves exocTIy 14 of The Task To be performed by Roger39 You can eiTher39 see ThoT This means ThoT Ro er39 and David wor39k IT The some r39oTe so iT Toke Roger39 9 hours Too or39 jusT divide 225 hours by 25 Task To geT 9 hours per39 Task choice D 4 Does Backsolving Help No re Tha r even where backsolving helps if does no r absolve you of Thoroughly under39s randing The ques rion You mus r under39s rand wha r39s being asked before you can apply backsolving 4 Da39l39a Sufficiency Da ra sufficiency word problems are a li r rle differen r from o rher r pes of word problems Thy offen require very li r rle ca cula rion and if you affack fhem wi rhou r Thinking firs r you will nearly always was re Time and end up crunching numbers If a dafa sufficiency word problem is based on some kind of formula such as The disfance formula dr r or The area of a circle ask yourself wha r kind of informafion would give you The area of a circle Then if sfa remenf 1 Tells you The circle39s circumference don39f calcula re If is sufficien r To know rha r you could have calcula red Your mo 0 shoua be quotThink don 397 crunch 3 STEP METHOD FOR WORD PROBLEMS IN DATA SUFFICIENCY MeThods for approaching These problems 1 Quickly skim The quesTion sTem 2 If sTuck Try TranslaTing The quesTion sTem and The sTaTemenTs inTo maTh 3 IF and when each sTaTemenT is insufficienT by iTself and you need To consider The sTaTemenTs TogeTher Think of The problem as one long word problem and TranslaTe iT as one uniT WhaT39s Needed You should keep in mind whaT kind of infor39maTion is needed To answer39 The quesTion Do only as much work as you need in order To deTer39mine sufficiency and remember To ignor39e The oTher39 sTaTemenT Try To concepTualize whaT you need wiThouT acTually solving for39 iT Keep The r39elevanT formulas in mind and ask yourself quotwhaT do I needquot and quotWhaT kind of sTaTemenT would give iT To mequot Sufficiency If There are 32 guesTs aT a par39Ts whaT is The average ar39iThmeTic mean age of The guesTs 1 The sum of The ages of The guesTs is 1536 2 The youngesT guesT Tracy is 24 years old and The oldesT guesT PaT is 68 years old 4 Average Formula Remember The average formula Average sum of Terms number of Terms sum32 50 we jusT need The sum To calcuIaTe The average Does eiTher of The sTaTemenTs give us The sum Yes sTaTemenT 1 does STaTemenT 2 does noT give us The sum There39s no way To figure iT ouT from 2 because The guesTs in beTween can be of all sorTs of ages 50 The answer is A Here39s a second example A rec rangle has leng rh y fee r and wid rh z fee r Wha r is i rs area in square fee r 1 z is The reciprocal of y 2 The fence around The perime rer of The rec rangle is 720 fee r AREA FirsT recall The formula for The area of a recTangle Area lengTh X widTh Here you mighT wanT To draw a picTure of a recTangle wiTh The lengTh and widTh labeled y and z respecTively This would be a hard problem buT if you focus on whaT you need To know you39re less likely To be fooled We need The area of This recTan le which is leEgTh x widTh or in This case y x z e need a num er Looking The STaTemenTs Would sTaTemenT 1 give us a number39 IT39s noT clear39 on a fir39sT glance so leT39s TesT iT z 1y so sz y X1y1 The area musT be 1 and sTaTemenT 1 is sufficienT How abouT sTaTemenT2 IT gives us The per39imeTer39 BuT This doesn39T give us sz iT Tells us ThaT 2yz720 or39 yz360 BuT This doesn39T Tell us The individual values of y and z or39 The pr39oducT of y and 2 so This sTaTemenT is insufficienT A is cor39r39ecT Ma l hema39l39ical Principle Remember This ma rhema rical principle Wha rever number of differen r variables you need To solve for you will need rha r same number of differen r equa rions rela ring a r leas r one of Those variables There are usually a few Tough Da ra Sufficiency problems rha r can be made easy by ap lying rhis Winciple and The Me rhod for Da ra Sufficiency ord Problems IF you ge r such a robem ask yourself quotHow many variables do need To solve for How many equa rions do I havequot Simul39l39aneous Questions The following is a Typical ques rion involving simul raneous ques rions Jessica has imi red inves rmen r por rfolio of s rocks and bonds If she sells half her39 s rocks how many s rocks and bonds will she be lef r wi rh 1 If she were To buy 6 more s rocks she would have Twice as many s rocks as bonds 2 If she were ro rr39iple The number39 of her39 bonds she would have rhr39ee less rhan rwice The number39 of her39 s rocks Solve in Seconds We geT one equoTion in SToTemenT 1 and onoTher39 equoTion in SToTemenT 2 You need boTh equoTions To answer The quesTion so you need boTh sToTemenTs The answer is C Thus you solve a difficulT problem in 10 seconds and The Time you save can help you geT onoTher39 quesTion r39ighT 4 THE 3 BASIC PRINCIPLES OF WORD PROBLEMS 1 Read Through The enTire quesTion and The answer choices To gain a general undersTonding of The siTuoTion 2 Keep Track of exocTIy whoT you39re ofTer 3 Learn To recognize The Types of problems ThoT you find easy and Those ThoT you find difficulT 4 4STEP METHOD FOR WORD PROBLEMS IN PROBLEM SOLVIN 1 Look for The besT approach To The quesTion and apply iT 2 In mosT cases The besT approach To use in solving word problems is To TranslaTe iT i nTo a maThemaTica equaTion If noT use an aTernaTive meThod such as picking numbers and backsolving 3 Reread The quesTion figuring ouT whaT you39re given and whaT you need To know 4 TranslaTe The problem To an equaTion If you39re sTuck TranslaTing or if you jusT don39T undersTand The problem consider using an aTernaTive meThod 3 Tep MeThod for Word Problems in DaTa Sufficiency 1 Quickly skim The quesTion sTem 2 If sTuck Tr39y Tr39anslaTing The quesTion sTem and The sTaTemenTs i nTo maTh 3 If and when each sTaTemenT is insufficienT by iTself and you need To consider The sTaTemenTs TogeTher39 Think of The problem as one long word problem and Tr39anslaTe iT as one uniT 4

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