APOSTILA I Luciana Chamie * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *D e s e n v o l v i m e n t o e T r e i n a me n t o e mMa t e m t i c a MATEMTICA PARA GMAT NDICE Mdulo A DATA SUFFICIENCY .................................................1 Exerccios...........................................................................................6 Mdulo B PROBLEM SOLVING .................................................9 Exerccios.........................................................................................18 Mdulo 1 RAZO E PROPORO............................................24 Exerccios.........................................................................................36 Mdulo 2 DESLOCAMENTO .....................................................48 Exerccios.........................................................................................54 Mdulo 3 PORCENTAGEM........................................................62 Exerccios.........................................................................................69 Mdulo 4 LGEBRA........... .....................................................80 Exerccios.........................................................................................90 Mdulo 5 WORLD PROBLEM ..................... .............................97 Exerccios.......................................................................................103MDULO A: DATA SUFFICIENCY Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 1 CadaumadasquestesdoDataSufficiencyconsistedeumaperguntaeduasafirmaes, nomeadasde(1)e(2),nasquaisalgumasinformaessodadas.Voctemquedecidirseas informaesdadasnestasafirmaessosuficientespararesponderapergunta.Usandoestas afirmaes mais seus conhecimentos de Matemtica, responda: Ase a informao (1) sozinha suficiente, mas a informao (2) sozinha no suficiente para responder a pergunta B se a informao (2) sozinha suficiente, mas a informao (1) sozinha no suficiente para responder a pergunta Cseambasasinformaes(1)e(2)juntassosuficientespararesponderapergunta,mas nenhuma delas sozinha suficiente D se cada afirmao sozinha suficiente para responder a pergunta E se as informaes (1) e (2) juntas, NO so suficientes para responder a pergunta AS FIGURAS NO FORNECEM INFORMAES SOBRE ASMEDIDASDE NGULOS E LADOS As figuras no Data Sufficiency esto de acordo com as informaes presentes na pergunta, mas no esto necessariamente de acordo com as informaes adicionais constantes nas afirmaes (1) e (2). Vocpodeassumirqueaslinhasdesenhadasretassoretasequetodososngulosso maiores do que zero. Exemplo 1: Is ABCD a square? AB (1) BD is perpendicular to AC (2) BE = ECE DC LEMBRE-SE DAS FRAES, DOS NMEROS NEGATIVOS E DAS RAZES Em todo o GMAT os nmeros so Reais at que o autor diga o contrrio. No Data Sufficiency, em particular, esta informao no deve ser esquecida, ou seja: Exemplo 2::Is x < y ? (1) y = 3x (2) x2 = y MDULO A: DATA SUFFICIENCY Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 2 Responder uma pergunta no Data Sufficiency significa achar uma nica resposta. Exemplo 3: What is the value of x? (1) x2 + 5x + 6 = 0 (2) x2 2x -8 = 0 NO PROCURE PELO SIM, PROCURE PELA CERTEZA Para responder uma pergunta no Data Sufficiency necessrio ter certeza da resposta, seja ela sim ou no. Exemplo 4:Is x > 0? (1) x2 = 9 (2) x < 1 No junte as informaes (1) e (2) antes de analisar cada uma separadamente As informaes (1) e (2) so independentes.Leia a (1). Se ela suficiente sua resposta poder ser A ou D Se ela no suficiente sua resposta poder ser B ou C ou E Em ambas as situaes, esquea-a e v ler a (2) : Leia a (2). Se ela suficiente sua resposta ser D ou B. Se ela no suficiente sua resposta poder ser A ou C ou E.Apenas aps pensar em cada informao separadamente, junte-as se necessrio. Exemplo 5: If R =andyx38y=0 , what is the value of R? (1) x = 32 (2) x = 2y RESOLVER: QUASE NUNCA MONTAR: MUITAS VEZES SIMPLIFICAR: SEMPRE Voc no precisa resolver as questes do Data Sufficiency,voc no precisa achar a resposta para apergunta, muitas vezes voc apenas analisa a pergunta e as informaes e consegue ter certeza de qual a alternativa correta Exemplo 6: What is the area of the triangle above ? (1)a + 9 = 25 xo (2)x = 903 a

5 MDULO A: DATA SUFFICIENCY Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 3 Entretanto, muitas vezes voc precisa montar o exerccio, as equaes, colocar algumas idias nopapel.Istonosignificaquevocestejaperdendotempo,ouquevocestejaresolvendoa questo,massim,quevocestprocurandoamelhorformadeACERTARAQUESTO. Muitas vezes quando voc escreve, a resposta salta aos olhos, voc ganhou tempo e acertou. Ao contrriodaquelequeserecusaapegarnolpis,porquenoprecisaresolveretermina perdendomais tempo e muitas vezes errando a questo. Exemplo 7: A pension fund invested in stock of the ABC Company and bonds of the DEF Corporation . How much money was invested in ABC stock if the pension fund received a total of $162000 in cash from both investments? (1)The pension invested a total of$1 million on both investments. (2)The stocks paid 18% in cash and the bonds paid 15%. Exemplo 8: If x is an integer, is y an integer? (1)The average (arithmetic mean) of x, y, and y-2 is x. (2)The average (arithmetic mean) of x and y is not an integer. Alm de montar, voc deve sempre simplificar tudo que estiver tanto na pergunta quanto nas afirmaes do Data Sufficiency.As aparncias enganam muito no Data Sufficiency. Investigue, aborde de vrias maneiras diferentes, pense fora da caixa. Exemplo 9: Does 2m 3n = 0? (1)m0 = .(2)6m = 9n. Exemplo 10: If a, b, and c are integers, is a b + c greater than a + b c ? (1) b is negative (2) c is positive Exemplo 11: What is the value of x2- y2? (1) x + y = 2x(2) x y = 0 MDULO A: DATA SUFFICIENCY Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 4 Exemplo 12: If xy = -6, what is the value of xy( x+ y ) ? (1) x y = 5 (2) xy2 = 18 ExistemDataSufficiencynosquaisapropostanoverificarconhecimentosdematemtica, mas sim verificar a capacidade de analisar um conjunto de dados e a partir desta anlise tirar concluses.Nestesexercciosnecessrioirnodetalhe,calcularospossveisnmeros, experimentar, sempre com foco na pergunta. Exemplo13:InacertainyeartheUnitedNationstotalexpenditurewere$1.6billion.Ofthis amount,67.8percentwaspaidbythe6highest-contributingcountries,andthe balancewaspaidbytheremaining153countries.WasCountryXamongthe6 highest-contributing countries? (1) 56percentofthetotalexpenditureswaspaidbythe4highest-contributing countries, each of which paid more than Country X. (2) Country X paid 4.8 percent of the total expenditures Exemplo 14: Of the 60 animals on a certain farm, 2/3 are either pigs or cows. How many of the animals are cows? (1) The farm has more than twice as many as cows as it has pigs (2) The farm has more than 12 pigs Exemplo 15: Max has $125 consisting of bills each worth $5 or $20. How many bills worth $5 does Max have? (1)Max has fewer than 5 bills of $5 each (2)Max has more than 5 bills worth $20 each -Voc terminou os exemplos do mdulo A !Faa um RESUMO dos pontos importantes deste mdulo antes de iniciar a lista de exerccios. -Nofinaldestemdulonosite,vocencontraralistadeexerccios resolvida. -Depoisda correo dosexercciosCOMPLETEORESUMOcomoserroscometidos. Lembre-se de estar sempre relendo este resumo MDULO A: DATA SUFFICIENCY Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 5 RESPOSTAS DOS EXEMPLOS DO MDULO A

1E 2E 3C 4C 5B 6D 7C 8A 9B 10C 11D 12B 13E 14C 15D MDULO A: DATA SUFFICIENCY EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 6 EXERCCIOS 1.If x and y are integers, is x less than y? (1)The cube of x is less than the cube of y. (2) x is less thany + 2 2.When one piece of fruit is taken at random from a fruit bowl, what is the chance that it is an apple? (1)There are half as many apples as oranges in the fruit bowl. (2)A third of the fruit in the fruit bowl are oranges. 3.Each person on a committee with 40 members voted for exactly one of 3 candidates, F, G, or H. Did Candidate F receive the most votes from the 40 votes cast ? (1)Candidate F received 11 of the votes. (2)Candidate H received 14 of the votes. 4.What is the volume of cube X? (1)The diagonal of one of the faces of X is6 . (2)Thediagonalofthecubefromtheupperrearleftcornertothelowerfrontright corner is 3 5.A marathon runner running along a prescribed route passes through neighborhoods J, K, L, and M, not necessarily in that order. How long does it take to run from J to M ? (1)The runner averages 8 miles per hour on the route from J to M.(2)M is 4 miles from K and 12 miles from L, but J is 15 miles from K. 6.Is ABCD a square?BC (1)AB is parallel to CD(2)BCD is an equilateral triangle.AD 7.How heavy is one brick? (Assume that all the bricks are identical) (1)Two bricks weigh as much as three 6-lbs weights. (2)Three bricks weigh as much as one brick plus 18 lbs. 8.In the diagram, find the length of AB.D CAC = 5 (1)ABCD is a rectangle (2)AC AE = AB + BE B A E B 9.What is thevalue of x? (1)x2 + x = 2 (2)x2 + 2x 3 = 0 MDULO A: DATA SUFFICIENCY EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 7 10.John, Peter, and Paul together have ten marbles.If each has at least one marble, how many marbles does each boy have? (1)John has 5 more than Paul. (2)Peter has half as many as John 11.Is x positive? (1)x2 1 = 0 (2)x3 + 1 = 0 12.A rectangle is 40 inches long. What is its area? (1)Its perimeter is 140 inches (2)The length of the diagonal is 50 inches. 13.IftheLincolnLibrarystotalexpenditureforbooks,periodicalsandnewspaperslast year was $35,000, how much of the expenditure was for books? (1)Theexpenditurefornewspaperswas40percentgreaterthantheexpenditurefor periodicals. (2)Thetotaloftheexpenditureforperiodicalsandnewspaperswas25percentlessthan the expenditure for books. 14.A piece of wood 7 feet long is cut into three pieces. What is the length of each of the pieces? (1)The length of the longest piece is equal to the sum of the lengths of the other two pieces. (2)The length of the shortest piece is 6 inches. 15.Is X an integer number? (1)X is the double of an even integer. (2)3X is even 16.How many hours long is time period A? (1)Time period A started at 12 noon Monday and ended at 12 noon Wednesday. (2)Time period A is exactly two days long. 17.What digit does w represent in the decimal 0.w73? (1)w < 5 (2)0.w73 0 (2) r < s MDULO B: PROBLEM SOLVING Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 17 RESPOSTAS DOS EXEMPLOS DO MDULO B 1) C2) A 3) a) D b) D 4.1)a) B b) B 4.2)a) 5060 b) 245 c) 10 2d) 196 4.3) D

5)a) 44 b) D 6.2)E6.3) E 7) a) E b) E c) A d) C -Voc terminou os exemplos do mdulo B !Faa um RESUMO dos pontos importantes deste mdulo antes de iniciar a lista de exerccios. -Quandoterminaralistadeexerccios,vnositeparaaltimapgina deste mdulo onde encontrar alguns exerccios resolvidos(antes do anexo) -Depoisda correo dosexercciosCOMPLETEORESUMOcomoserroscometidos. Lembre-se de estar sempre relendo este resumo -A partir de agora, sempre que voc terminar as listas de exerccios de cada matria, depoisdecorrigir aquelesque errou,crie ohbitodevoltarpara aquelesquevocacertouobservandoseforamresolvidosdamelhor maneira MDULO B: PROBLEM SOLVING EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 18

1) (32+1)( 32-1)(34+1)(38+1)=2) If r = 0.345, s = (0.345)2, and t =345 . 0Whichofthefollowingisthecorrect ordering of, r, s, and t? (A) 316+1 (A) r < s < t (B) 316- 1 (B) r < t < s (C) 38 - 1(C) s < t < r (D) 312+4 (D) s < r < t (E) 312+3(E) t < r < s 3) (16)2 + 2 (9)(16) + 81 = 4) 5102 4902 = (A) 444 (A) 16000 (B) 500 (B) 18917 (C) 625 (C) 19470 (D) 875 (D) 20000 (E) 900(E) 24000 5)= 430024 . 0 548215025 . 06)=+37 . 0103 . 011 (A) 0.1(A) 0.004 (B) 0.2(B) 0.02775 (C) 100 (C) 2.775 (D) 200 (D) 3.6036 (E) 1000(E) 36,036 7) 373 =8)= 289 (A) 50653 (A) 13 (B) 68253 (B) 17 (C) 24653 (C) 23 (D) 50569 (D) 27 (E) 50641 (E) 16 9) 12,345(1) + 12,345(2) + 12,345(3) + 12,345(4) = (A) 66,667 (B) 81,818 (C) 99,999 (D) 123,450 (E) 127,978 MDULO B: PROBLEM SOLVING EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 19 10) Ifr = 1 + 2719131+ +and s = 1 +r31, then s exceeds r by: (A) 1/3 (B) 1/6 (C) 1/9 (D) 1/27 (E) 1/81 11) Which of the following numbers is the largest? (A) 1/.05 (B) 1/(.5)2 (C) 1/.5 (D) 5 (E) 1,000% 12) Which of the following numbers is the closest to zero? (A) (1 - .9)2 (B) 1-(.9)2 (C) 9 . 11 (D) (.09) (E) (.09)2 13) ( 0.50608 . 4 ) 072 . 4 is approximately (A) (B) (C) 1 (D) 2 (E) 4 14) Of the following, which best approximates ?) 1250 . 0 )( 6667 . 0 )( 2222 . 0 () 3333 . 0 )( 8333 . 0 )( 1667 . 0 ( (A) 2 (B) 2.4 (C) 2.43 (D) 2.5 (E) 3.43 MDULO B: PROBLEM SOLVING EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 20 15) Which of the following is the least? (A) 12/118 (B) 1/10 (C) 2/21 (D) 5/49 (E) 8/79 16) Which of the following is the largest? (A) 7/150 (B) 4/83 (C) 5/102 (D) 11/219 (E) 1/20 17) 10. 7 . 21 . 92 = (A) 142884 (B) 119070 (C) 109079 (D) 11907 (E) 142860 18) Ift = 3 95 21is expressed as a terminating decimal, how many zeros will it have between the decimal point and the first nonzero digit to the right of the decimal point? (A) Three (B) Four (C) Five (D) Six (E) Nine 19) Escreva o valor aproximado em porcentagem: a) 1/14 b) 1/15 20) Escreva o valor em decimal: a)66/12 b)123/30 c)27/7 d)90/25 e)1.12/0.8 f)27/25 MDULO B: PROBLEM SOLVINGEXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 21 g)137/5h)11/125 21) Escreva entre quais nmeros decimais as fraes abaixo esto: a)8/370 b) 7/65 c) 16/57 22) Calcule:

a)1.25 x 0.7 x 0.375 =b)625 + 50 x 15 + 152 =c)212 192 =d)0.333 x 0.25 x 0.2 =e)27 x 0.444 =f)2.6/3.35 g)25 x 17 =h)32/2.2856 =23) What is the 25th digit to the right of the decimal point in the decimal form of 6/11? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 MDULO B: PROBLEM SOLVINGEXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 22 24)Ifx,y,andkarepositivenumberssuchthatky xyy xx=||.|

\|++||.|

\|+) 20 ( ) 10 ( andifx x (2) They finished their trips at the same time. 10.Train Y leaves New York at 1 a.m. and travels east at an average speed of x mph. If train Z leaves New York at 2 a.m. and travels east, at what average rate of speed will train Z have to travel in order to catch train Y at exactly 5:30 a.m.? (A) 65x (B) 89x (C) 56x (D) 79x (E) 23x 11.Plane P takes off at 2 A.M. and flies at a constant speed of x mph. Plane Q takes off at 3:30A.M.andfliesthesamerouteasPbuttravelsataconstantspeedofymph. Assumingthatyisgreaterthanx,howmanyhoursafter3:30A.M.willplaneQ overtake plane P? (A)hrsx23 (B)hrs23 (C)hrsy 23 (D)hrsx y ) ( 23 (E)hrsx yx) ( 23 MDULO 2 DESLOCAMENTO EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 57 12.A horse can travel at the rate of 5 miles per hour for the first two hours of a trip. After the first two hours the horses speed drops to 3 miles per hour. How many hours will it take the horse to travel 20 miles? (A) 4 (B) 5 (C)315(D)215(E)325 13.Train Y leaves New York at 1 a.m. and travels east at a constant speed of y mph. Train Z leaves New York at 2 a.m. and travels east at a constant speed of z mph. Which train will travel farther by 4 a.m.? (1) y > z (2) y = 1.2 z 14.At 12:00 hour a truck left the city A to the city B, at a constant speed of 45 km/h. One hour later, a car left the city B to the city A, along the same road, at the constant speed of100km/h.IfthedistancebetweenAandBis190km,atwhattimewillthetruck and the car meet each other? (A)12:30 (B)13:00 (C)14:00 (D)14:40 (E)16:00 15.OnehourbeforeJohnstartedwalkingfromPtoQ,adistanceof18miles,Annhad started walking along the same road from Q to P. Ann walked at a constant speed of 3 miles per hour and John at 2 miles per hour. How many miles had Ann walked when they met? (A) 6 miles (B) 8.4 miles (C) 9 miles (D) 9.6 miles (E) 12 miles MDULO 2 DESLOCAMENTO EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 58 16.A bus leaves Burbank at 9:00 a.m., traveling east at 50 miles per hour. At 1:00 p.m. a plane leaves Burbank traveling east at 300 miles per hour. At what time will the plane overtake the bus? (A)12:45 p.m. (B)1:10 p.m. (C)1:40 p.m. (D)1:48 p.m. (E)1:55 p.m. 17.Janlivesxfloorsabovethegroundfloorofahigh-risebuilding.Ittakesher30 seconds per floor to walk down the steps and 2 seconds per floor to ride the elevator. If it takes Jan the same amount of time to walk down the steps to the ground floor as to wait for elevator for 7 minutes and ride down then x equals: (A)4 (B)7 (C)14 (D)15 (E)16 18.A car traveled 75% of the way from town A to town B at an average speed of 50mph. ThecartravelsatanaveragespeedofSmphfortheremainingpartofthetrip.The average speed for the entire trip was 40 mph. Whats S? (A)10 (B)20 (C)25 (D)30 (E)37.5 19.A motorist travels 120 miles to his destination at an average speed of 60 miles per hour and returns to his starting point at an average speed of 40 miles per hour. His average speed for the entire trip is: (A)53 mph (B)50 mph (C)48 mph (D)45 mph (E)52 mph MDULO 2 DESLOCAMENTO EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 59 20.Agirlrodeherbicyclefromhometoschool,adistanceof15miles,atanaverage speed of 15 miles per hour. She returned home from school by walking at an average speedof5milesperhour.Whatwasheraveragespeedfortheroundtripifshetook same route in both directions? (A)7.5 mph (B)10 mph (C)12.5 mph (D)13 mph (E)25 mph 21.CarXandcarYtraveledthesame80-mileroute.IfcarXtook2hoursandcarY traveledatanaveragespeedthatwas50%fasterthanaveragespeedofcarX,how many hours did it take car Y to travel the route? (A)2/3 (B)1 (C)1 1/3 (D)1 3/5 (E)3 22.A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in thesamedirectionalongthesamepathataconstantrateof20milesperhour.The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continues towalkatherconstantrate.Howmanyminutesmustcyclistwaituntilthehiker catches up? (A) 6 2/3 (B)15 (C)20 (D)25 (E) 262/3 23.Did it take Ann more than 2 hours to walk a distance of 10 miles along a certain trail? ( 1 mile = 1.6 kilometers) (1)Ann walked this distance at an average rate of less than 6.4 kilometers per hour. (2)On average, it took Ann more than 9 minutes per kilometer to walk this distance. 24.A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 milespergallonwhendrivenonthehighway.Accordingtotheserates,whichofthe following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway? (A)28 (B)30 (C)33 (D)36 (E)38 MDULO 2 DESLOCAMENTO EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 60 25.Is the number of seconds required to travel d1 feet at r1 feet per second greater than the number of seconds required to travel d2 feet at r2 feet pre second? (1)d1 is 30 greater than d2 (2) r1 is 30 greater than r2 26.Ann traveled x percent of the total distance of her trip at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Anns average speed for the entire trip?

200000 , 12) (115600) (5300) (460) (2180) (++xExDxCxBxA 27.BikeBis10milesaheadbikeA,whichistravelinginthesamedirectionalongthe same route as bike B. Bike A is traveling at a constant speed of 29 miles per hour and bike B is traveling at a constant speed of 25 miles per hour. How many hours will take for bike A to overtake and drive 4 miles ahead of bike B? (A)1.5 (B)2.0 (C)2.5 (D)3.0 (E)3.5 MDULO 2 DESLOCAMENTO EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 61 RESPOSTAS 1. C 2.D 3.C 4.A 5.A 6.A 7.C 8.E 9.B 10.D 11.E 12.C 13.D 14.C 15.E 16.D 17.D 18.C 19.C 20.A 21.C 22.C 23.D 24.D 25.E 26.E 27.E MDULO 3 PORCENTAGEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 62 PREPOSIES a) OF: significa de , o qual em matemtica significa vezes (x) Modelo 1:Find 30% OF240. Modelo 2: What percent OF B is A ? Modelo 3:What percent is A OF B ? Modelo 4:If a is y percent of b,then b is what percent of a? b) TO x BY: aumentou/diminuiu PARA OU aumentou/diminuiu EM Modelo 5: It was $50,00. It increased a) TO $200,00 b) BY $200,00 What was the final price? TIPO 1 : VARIAO PERCENTUAL Determinar qual a taxa de aumento ou desconto aplicada Modelo 1: O preo de um carro aumentou de $25000 para (TO) $29000. Qual foi o aumento percentual do carro? MDULO 3 PORCENTAGEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 63 Modelo 2: 15250alunosterminaramo1ograunasescolasdaredemunicipaldeensinodeSoPauloem 1999.Se em 2000, este nmero diminuiu para (TO ) 13750, qual foi a variao percentual no nmero de alunos que terminou o 1o grau nas escolas da rede municipal de ensino de So Paulo de 1999 para 2000? TIPO 2: PROBLEMAS ENVOLVENDO LUCRO PREO DE VENDA =CUSTO + LUCRO Modelo 1: Um comerciante que pagou $36,00 por uma mercadoria, deseja vend-la com um lucro de 20% sobre o preo decusto. Qual deve ser o preo de venda? Modelo 2:Um comerciante que pagou $36,00 por uma mercadoria, deseja vend-la com um lucro de 20% sobre o preo devenda. Qual deve ser o preo de venda? Modelo 3: Quantos chaveiros devem servendidos por ms, a $5,00 cada, para se conseguir um lucro de $27000,00, se o custo de cada chaveiro $2,00 mais $3000,00 de despesas fixas? MDULO 3 PORCENTAGEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 64 Modelo 4: Quepreodevesercolocadoemumprodutoquecustou$12,60,afimdevend-locomum desconto de 25%sobre o preo de venda e ainda assim ter um lucro de 25% sobre o custo ? ATENO: SE O ENUNCIADO NO ESPECIFICAR, SIGNIFICA QUE O LUCRO SEMPRE PORCENTAGEM DO CUSTO!!!! TIPO 3: AUMENTOS E DESCONTOS SUCESSIVOS ) 1 )....( 1 )( 1 )( 1 (3 2 1 ni i i i Inicial Final = Modelo1:Acharonicoaumentooudescontoequivalenteadoisoumaisaumentose/ou descontos sucessivos. Exemplos:a)Umaumentode25%seguidodeumaumentode30%,equivaleaumnico aumento de quanto? Usando a Frmula Simplificando a Frmula

b) E um aumento de 40% seguido de um de 30%? c)E dois descontos sucessivos de 40% e 25%? d)E umaumento de 50% seguido de um desconto de 30%, equivale aum nico aumento ou desconto de quanto? MDULO 3 PORCENTAGEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 65 e) Aplicao no clculo de multiplicaes em geral. 1.55 x 0.7 = 0.9 x 0.7 x 1.3 = Modelo2:Acharumdosaumentosoudescontosqueaplicadosucessivamentecomoutros,resultou num nico aumento ou desconto dado. Exemplos:a)Umaumentodex%seguidodeumaumentode20%,resultounumnico aumento de 50%. Quanto x? Utilizando a frmula Atribuindo Valores b) Um desconto de x%, seguido de umc) Um desconto de x%, seguido de umaumento aumento de 20%, resultou num descontode 25%resultou num aumento de 20%. Quanto de40%.Ache x. x? MDULO 3 PORCENTAGEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 66 Modelo 3: Depois de aumentos e ou descontos sucessivos, comovoltar ao valor original? Exemplos:a)Apsumaumentode20%,qualdeveserodescontopararetornaraovalor inicial? Usando a frmula Atribuindo valores b) Aps um desconto de 40% , qual deve ser o aumento para voltar ao valor original? Modelo 4:JUROS ANUAIS COMPOSTOS Exemplo : Quanto irrender $1000,00 aplicados a ...... a) Juros anuais de 24% compostos trimestralmente, aps 6 meses? b) Juros anuais de 18% compostos cada 2 meses, aps 4 meses?

MDULO 3 PORCENTAGEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 67 c) Juros anuais de 6% compostos mensalmente, aps 2 meses? -Vocterminou os exemplos do mdulo3 !Faa um RESUMO dos pontos importantes deste mdulo antes de iniciar a lista de exerccios. -Quandoterminaralistadeexerccios,corrijaevolteparaaquelesque voc errou. Tente entender POR QUE voc errou . Em seguida, volte para aqueles que voc acertou e veja se foram resolvidos da MELHOR maneira. -Naltimapginadomdulonositevocencontraralgunsexercciosda lista resolvidos -Depoisda correo dosexercciosCOMPLETEORESUMOcomoserroscometidos. Lembre-se de estar sempre relendo este resumo RESPOSTAS DO MDULO 3 PREPOSIES :Modelo 1: 72 Modelo 2:100BA Modelo 3:100BA Modelo 4: y000 , 10 Modelo 5: a)$200.00 b)$250.00 MDULO 3 PORCENTAGEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 68 TIPO 1: Modelo 1: 16% Modelo 2:aproximadamente 10% TIPO 2: Modelo 1: $43.20 Modelo 2: $45.00 Modelo 3: 10,000 chaveiros Modelo 4: $21.00 TIPO 3: Modelo 1: a) 62.5% b) 82% c) desconto de 55% d) aumento de 5% e) 1.085 e 0.819 Modelo 2: a) 25% b)50% c) 4% Modelo 3: a) 16.6% b)66.6%

Modelo 4: a) $123.6 b) $60.9 MDULO 3 PORCENTAGEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 69 1.AndreywentshoppingwithDdollars.Shespent20%ofhermoneyonablouseand 25%ofwhatwasleftonapairofshoes.WhatpercenttheoriginalDdollarsdidshe spend? (A) 25% (B) 40% (C) 45% (D) 47% (E) 50% 2.In order to give to his customers a 25% discount on the price and still net a 25% profit onthecostofanitem,atwhatpriceshouldamerchantmarkanitemifitcosthim $16.80? (A) $21.00 (B) $21.90 (C) $25.20 (D) $26.25 (E)$28.00 3.What percent of the total number of points scored in a basketball game was scored by Alan? (1)Ben scored one-sixth of the total number of points scored in the game, and David scored one-third of the total number of points scored in the game. (2)Only Alan and two other people scored points in the game. 4.Ajoggerdesirestorunacertainlesstimethansheusuallytakes,bywhatpercent must she increase her average running speed to accomplish this goal? (A)20% (B)25% (C) 3133 % (D)50% (E)75%

5.Rich sold skis for $160.00 and his ski boots for $96.00. He made a profit of20% on his boots and took a 10% loss on his skis. He ended up with a? (A)loss of $1.78 (B)loss of $1.50 (C)gain of $3.20 (D)gain of $7.53 (E)gain of $17.06 MDULO 3 PORCENTAGEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 70 6.Apensionfundhastotalof$1millioninvestedinstockoftheABCCompanyand bonds of the DEF Corporation. The ABC stocks yields 12% in cash each year, and the DEF bonds pay 10% in cash each year. The pension fund received a total of $115,000 in cash from ABC stock and DEF bonds last year. How much money was invested in ABC stock? (A)$750,000.00 (B)$600,000.00 (C)$500,000.00 (D)$333,333.33 (E)$250,000.00 7.The expenses of the ABC corporation are each billed to one and only one of its three divisions: division A, division B, and division C. What percentage of the expenses of the ABC corporation were billed to division A? (1)The expenses of division A are twice as much as the expenses of division B. (2)The expenses of division B are the same as the expenses of division C. 8.Afterpayinga10%taxonallincomeover$3,000,apersonhadanetincomeof $12,000. What was the income before taxes? (A)$13,300 (B)$13,000 (C)$12,900 (D)$10,000 (E)$9,000 9.Astorebuyspapertowelsfor$9.00acarton,eachcartoncontaining20rolls.The storesellsarollofpapertowelsfor50cents.Aboutwhatpercentofthecostisthe selling price of a roll of a paper towels? (A)11 (B)89 (C)100 (D)111 (E)119 10.What percentage is Ys salary of Xs salary? (1) Xs salary is 80% of Zs salary. (2) Ys salary is 120% of Zs salary. MDULO 3 PORCENTAGEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 71 11.At a special rate, 5 tickets can be purchased for the price of 3 tickets. If 5 tickets are purchased at this sale, the amount saved will be what percent of the original price of the 5 tickets? (A)20% (B)33 1/3% (C)40% (D)60% (E)66 2/3% 12.Mary is paid $600 a month on her job. During July in addition to her regular job, she makes$400fromasecondjob.Approximatelywhatpercentageofherannual incomedoesMarymakeinJuly?AssumeMaryhasnootherincomeexceptthe income mentioned above. (A)8 (B)8 1/3 (C)12 1/2 (D)13 (E)14 13.Jimsweightis140%ofMarciasweight.Bobsweightis90%ofLeesweight. Lees weight is twice as much as Marcia. What percentage of Jims weight is Bobs weight? (A)64 2/7 (B)77 7/9 (C)90 (D)128 4/7 (E)155 5/9 14.Onapurchaseof$120,astoreofferedapaymentplanconsistingofa$20down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan? (A)16.7% (B)30% (C)75.8% (D)106.7% (E)107.5% MDULO 3 PORCENTAGEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 72 15.ThepriceofamodelMacamerais$209andthepriceofaspeciallensis$69. Whenthecameraandlensarepurchasedtogether,thepriceis$239.Theamount savedbypurchasingthecameraandlenstogetherisapproximatelywhatpercentof the total price of the camera and lens when purchased separately? (A)14% (B)16% (C)29% (D)33% (E)86% 16.Ifacompanymakesaprofitof$250onsalesof$1,900,theprofitwas approximately what percentage of sales? (A)10% (B)12% (C)13% (D)15% (E)17% 17.Apersonboughtatickettoaballgamefor$15andlatersoldtheticketfor$60. What was the percent increase in the price of the ticket? (A)25% (B)33 1/3% (C)75% (D)300% (E)400% 18.Achairoriginallycost$50.00.Thechairwasofferedforsaleat108%ofitscost. Afteraweekthepricewasdiscounted10%andthechairwassold.Thechairwas sold for: (A) $45.00 (B) $48.60 (C) $49.00 (D) $49.50 (E) $54.00 19.Toms salary is currently $35,000. When Tom was hired 5 years ago, his salary was $10,000. By what percentage has Toms salary increased since he was hired? (A) 28 4/7% (B) 40% (C) 50% (D)250%(E)350% MDULO 3 PORCENTAGEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 73 20.If in 1967, 1968, and 1969 a worker received 10% more in salary eachyear than he did the previous year, how much more did he receive in 1969 than in 1967? (A)10% (B)12% (C)19% (D)20% (E)21% 21.A merchant increased the original price ifan item by 10 percent.If she then reduce the new price by 10 percent, the final result in terms of the original price is: (A) a decrease of 11 percent (B) a decrease of 1 percent (C) no net change (D) an increase of 1 percent (E) an increase of 11 percent 22.The price of a dress was first discounted by a certain percent and later by 25 percent of the discounted price.If these two discounts are equivalent to a singlediscount of 40 percent of the original price, what was the first discount? (A)10% (B) 15% (C) 20% (D) 30% (E) 65% 23.Successive discounts of 20% and 15% are equal to a single discount of: (A)30% (B)32% (C)34% (D)35% (E)36% 24.How much interest will $2,000 earn at an annual rate of 8% in one year if the interest is compounded every 6 months? (A)$160.00 (B)$163.20 (C)$249.73 (D)$332.80 (E)$2,163.20 MDULO 3 PORCENTAGEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 74 25.A pair of skis originally cost $160. After a discount of x%, the skis were discounted Y%. Do the skis cost less than $130 after the discounts? (1) x = 20 (2) y = 15 26.Amanufacturerofboxeswantstomakeaprofitofxdollars.Whenhesells5,000 boxes it costs 5 cents a box to make the first 1,000 boxes and then it costs y cents a boxtomaketheremaining4,000boxes.Whatpriceindollarsshouldhechargefor the 5,000 boxes? (A)5,000 + 1,000y (B) 5,000 + 1,000y + 100x (C) 50 + 10y + x (D) 5,000 + 4,000y + x (E) 50 + 40y + x 27.Acompanymakesaprofitof7%sellinggoodswhichcost$2,000;italsomakesa profit of 6% selling a machine that cost the company $5,000. How much total profit did the company make on both transactions? (A) $300 (B) $400 (C) $420 (D) $440 (E) $490 28.How much was the original cost of a car which sold for $2,300? (1)The car was sold for a discount of 10% from its original cost. (2)The sales tax was $150. 29.In a certain community, property is assessed at 60% of its appraised value and taxed at the rate of $4.00 per $100 of assessed value. If a taxpayer pays $960 in property taxes, what is the appraised value of the property? (A)$6,000 (B)$22,500 (C)$24,000 (D)$40,000 (E)$60,000 30.By what percent did the amount of imported car sold annually in the USA increase , from 1995 to 1998? (1)In 1995, 18.8% of the total cars sold in the USA were imported. (2)In 1998, 30.8% of the total cars sold in the USA were imported. MDULO 3 PORCENTAGEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 75 31.Acertainmanufacturerproducesitemsforwhichtheproductioncostsconsistof annual fixed costs totaling $130,000 and variable costs averaging $8 per item. If the manufacturers selling price per item is $15, how many items must the manufacturer produce and sell to earn an annual profit of $150,000? (A)2,858 (B)18,667 (C)21,429 (D)35,000 (E)40,000 32.If$400isdepositedinasavingsaccountat4%annualinterest,compounded quarterly, how much interest will it earn in one year? (A)$16.64 (B)$16.24 (C)$16.08 (D)$16.04 (E)$16.00 33.What is the total amount of interest earned in 3months on $10,000 at rate of 218 % simple annual interest? (A) $21.25 (B) $85.00 (C) $212.50 (D) $283.33 (E) $850.00 34.Theassessedvalueofhouseis$72,000.Theassessedvalueis60%ofthemarket value of-the house. If taxes are $3 for every $1,000 of the market value of the house, how much are the taxes on the house? (A) $216 (B) $360 (C)$1,386 (D)$2,160 (E)$3,600 MDULO 3 PORCENTAGEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 76 35.A business firm reduces the number of hours its employees work from 40 hours per weekto36hoursperweekwhilecontinuingtopaythesameamountmoney.Ifan employee earned x dollars per hour before the reduction in hours, how much does he earn per hour under the new system? (A)101 (B)9x (C) 109x (D)910x (E) 9x 36.Asaleiteminagrocerystorewasmarkeddownto5/6ofitsoriginalprice.Joe bought the item with a coupon that provided for a further 20% discount off the new price.By what percentwould the amount paidby Joe have to be increased to equal the original price? (A)25% (B) 3133 % (C)50% (D)3267 % (E)75% 37.Thepriceofaleft-handedwidgetincreased20%in1981and10%in1982.By approximately what percent would the price at the end of 1982 have to be decreased to restore the price of the widget to its pre-1981 price? (A) 40% (B) 35% (C) 30% (D) 26% (E) 24% 38.Agrocerpurchased1,000Kgofproduceat$1,20perkilogram.If20%ofthe produce is lost through handling, what should the selling price per kilogram be order for the gross profit to be 10% of the purchase price? (A) $1.32 (B) $1.38 (C) $1.44 (D) $1.56 (E) $1.65 MDULO 3 PORCENTAGEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 77 39.If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar? (A)45 (B)67 (C)75 (D)83 (E)150 40.Bobboughtsharesofstock,whichhesoldfor$96each.Ifhehadaprofitof20 percentonthesaleofoneofthesharesbutalossof20percentonthesaleofthe other share, then on the sale of both shares combined Bobby had (A)a profit of $10 (B)a profit of $8 (C)a loss of $8 (D)a loss of $10 (E)neither a profit nor a loss 41.A store purchased 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price. What was the stores gross profit on the 20 coats? (1) Ifthesellingpricepercoathadbeentwiceasmuch,thestoresgrossprofiton the 20 coats would have been $2,400 (2) If the selling price per coat had been $2 more, thestores gross profit on the 20 coats would have been $440 42.Marthaboughtanarmchairandacoffeetableatanauctionandsoldbothitemsat herstore.Hergrossprofitfromthepurchaseandsaleofthearmchairwaswhat percent greater than her gross profit from the purchase and sale of the coffee table? (1) Martha paid 10 percent more for the armchair than for the coffee table. (2)Martha sold the armchair for 20 percent more than she sold the coffee table. 43.If m > 0 and x is m percent of y, then, in terms of m, y is what percent of x? (A)100m (B) m 1001 (C) m1 (D) m100 (E) m10000 MDULO 3 PORCENTAGEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 78 44.Theannualrentcollectedbyacorporationfromacertainbuildingwasxpercent more in 1998 than in 1997 andy percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997? (1) x > y (2) y xxy 0 as duas razes so nmeros reais distintos A = 0 as duas razes so nmeros reais iguais A < 0 no existem razes reais Exemplos: a ) 2x2+ 3x + 1 = 0A = 9 4.2.1= 9 8 = 1x = 41 3 x = -1 ou x = 21 b) 9x2 + 12x + 4 = 0 A = 144 4.9.4 = 144 144 =0 x = 180 12 x = 32

c) 2x2 + 5x + 9 = 0 A = 25 4.2.9 = 25 -72 = -47 x = 447 5 A equao no possui razes reais d)Determine os possveis valores de k para que a equao 2x2 + kx + 8 = 0 tenha duas razes iguais. R: k = 8 ou k = -8 MDULO 4 LGEBRA Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 84 III) Aplicao da Fatorao na Resoluo de Equaes do 2o grau Exemplos :a) x2 + 8x = 0b)0 ) )( ( = + + | o x xc) x2 + 6x + 8 = 0

S = {0,-8}S= {- | o , }S= {-2,-4} d) x2 + 7x + 12 = 0 e) x2 8x + 15 = 0f) x2 + 2x 8 =0 S= {-3,-4}S= {3,5} S= {+2,-4} g) Sabendo-se que ( x 4 ) um fator de x2 + bx + 24 , determine o valor de b.R: b = -10 h) Sabendo-se que 5 uma raiz de x2 + 12x + c, determine a outra raiz R:-17 MDULO 4 LGEBRA Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 85 IV) Casos particulares nos quais no necessrio fatorar: a) x2 = 16b) ( x 4 )2 = 36c) ( 20 - x)2 =1 S= {-4,4}S= {10,-2} S= {19,21} d)x2 = (y + 2 )2e)x( 5 4x) = 7xf) x2 = xy S={y+2,-(y+2)}S= {0,-1/2}S= {0,y} V) Equaes redutveis equao do 2o grau Exemplos:a) x4 10x2 + 9 =0b) x6 9x3 + 8 = 0

S= {1,-1,3,-3 }S= {2,1} MDULO 4 LGEBRA Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 86 VI)Equaes Irracionais Exemplos: a) x +x= 6 S= {4}

b) y =20 4 + y- 2 S= { 4}

c) If a = 225 10 b ab , the value of a, in terms of b, is:S ={5b} MDULO 4 LGEBRA Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 87 SISTEMA DE EQUAES DO 1O GRAU Umsistemadeequaesumconjuntodeduasoumaisequaesconsideradas simultaneamente(ligadaspeloconectivoe).Oconjuntosoluodeumsistemacomposto pelos valores das incgnitas que satisfazem todas as equaes do sistema simultaneamente, ao mesmo tempo. Sistemas de 2 equaes do 1o grau com 2 incgnitas Modelo :ax + by = ca1x + b1y = c1 Discusso do sistema: Graficamente as equaes do 1o grau representam retas. Encontrar as solues de um sistema de equaesdo1ograuencontrarospontosquepertencemsduasretas,aomesmotempo. Existem trs posies possveis relativas a duas retas. CONCORRENTES PARALELAS PARALELAS DISTINTAS COINCIDENTES r P s rr s s 1 nica soluonenhuma soluoinfinitas solues Possvel DeterminadoImpossvel Possvel Indeterminado x + y = 2 x + y = 2x + y = 2 Ex.: 6x 5y = 23Ex.:3x + 3y = 9 Ex.: 3x + 3y = 6 Exemplos: 1) What is the value of x + 2y ?(B) (1) 3x + 5y = 11 (2) 2x + 4y = 3 MDULO 4 LGEBRA Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 88 2) What is the value of x + 2y ? (E) (1) 3x 5y = 2 (2) 12x 20y = 8 3)What is the value of x + 2y ?(C) (1) 18x + 47y = 165 (2)29x 39y = 478 4) What is the value of x?(D) (1) 21 + x= 3 (2)5 . 222 3+ + =+y xy x Resoluo do sistema: Mtodo da Adio: x + y = 2S = {(3,-1)} 6x 5y = 23

MDULO 4 LGEBRA Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 89 APLICAO DO PRODUTO NOTVEL EM SISTEMAS DE EQUAES DO 2O GRAU Exemplos: a) Se x2 + y2 = 20 e xy = 40, calcule o valor de x + y.R:10 ou -10 b) Se x2 + y2 = 200 e x + y = 40, calcule o valor de xy.R: 700 -Vocterminou os exemplos do mdulo4 !Faa um RESUMO dos pontos importantes deste mdulo antes de iniciar a lista de exerccios. -Quandoterminaralistadeexerccios,corrijaevolteparaaquelesque voc errou. Tente entender POR QUE voc errou . Em seguida, volte para aqueles que voc acertou e veja se foram resolvidos da MELHOR maneira. -Naltimapginadomdulonositevocencontraralgunsexercciosda lista resolvidos -Depoisda correo dosexercciosCOMPLETEORESUMOcomoserroscometidos. Lembre-se de estar sempre relendo este resumo MDULO 4 LGEBRA EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 90 1.Which of the following is equal to 3x3 + 3x2 + 3x ? (A) 9x6 (B) 3x6 (C) 3x(x3 + x2 + x) (D) 3x(3x2 + 3x + 3) (E) 3x( x2 + x + 1) 2.If ( x + y ) 2 ( x y )2 = 20, then xy = (A) 0 (B) 1 (C) 2 (D) 5 (E) cannot be determined from the information given 3.=++ +11 22xx x (A) x (B) x +1 (C) x 1 (D) x2 (E) x3 4.If x = 29 6 y xy , the value of x, in terms of y, is: (A) 3y + 6 (B) 3y(C) 3y (D) 3y + 6 (E) 6y 5.Whatis the value of pq? (1) ( p q )2 ( p + q )2 = 1 (2) p + q = 2 6.What is the value of x y ? (1) x2 y2 = 10 (2) x + y = 2 MDULO 4 LGEBRA EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 91 7.If x=3 and 43292= xyx, then, in terms of y, x = (A) 26 y (B) 23 y (C)y 3 (D)y 6 (E) 26 + y 8.If x2 y2 = 15 and x + y = 3,then x y is (A) 3 (B) 0 (C) 3 (D) 5 (E) cannot be determined 9.If x y = 3, then=+y xy x2 2 (A) 0 (B) 1 (C) 3 (D) 9 (E) cannot be determined from the information given 10.If x2 + 6x + c = ( x + a ) ( x + b ), what is the value of c ? (1) a = 1 (2) b = 5 11. In the equation x2 + b x + 12 = 0, x is a variableand b is a constant. What is the value of b? (1) x 3 is a factor of x2 + b x + 12 (2) 4 is a root of the equation x2 + b x + 12=0 12. For every value of x, there is the equation as follows: x2 + bx + c = (x + d) 2. What is the value of c ? (1) d = 3 (2) b = 6 MDULO 4 LGEBRA EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 92 13. What is the value of b + c ? (1) ab + cd + ac + bd = 6 (2) a + d = 4 14. If v and w are different integers , does v = 0 ? (1) vw = v2 (2) w = 2 15. What is the value of x y ? (1) x = 5 (2) x + 2y = 2x + y 16. Ifa, b, and c are constants, a > b > c, and x3 x = ( x a ) ( x b)( x c )for all numbers x, what is the value of b?

(A) -3 (B) -1 (C) 0 (D) 1 (E) 3 17. Is x positive? (1) x2 + 3x 4 = 0 (2) x > -2 18. If x is a number such that x2 3x + 2 = 0 and x2 x 2 = 0, what is the value of x ? (A) 2 (B) 1 (C) 0 (D) 1 (E) 2 19. If x + y = 5 and 2x + y = 12, then 3x + y is (A) 11 (B) 13 (C) 17 (D) 19 (E) 39 MDULO 4 LGEBRA EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 93 20. If the product of two numbers is 10 and the sum of the two numbers is 7, then the larger of the two numbers is (A) 2 (B) 2 (C) 3 (D) 4 (E) 5 21. What is the value of a4 b4 ? (1)a2- b2=16 (2)a + b = 8 22. What is the value ofx + y ? (1) 12x 3y = 15 (2) y = 4x - 5 23. What is the value of x + y ? (1) 2x + y = 4 (2) x + 2y = 5 24. What is the value of p q? (1) p + r = 12 (2) r + q = 4 25. If x = 4y, then 12y 3x = (A) 0 (B) 1 (C) 7 (D) 15 (E) cannot be determined from the information given 26. How many of the numbers x, y, and z are positive? X, y, and z are all less than 30. (1)x + y + z = 61 (2)x + y = 35 27. How many solutions does the equation x ( x + 3 ) = 5xhave? (A) 0 (B) 1 (C) 2 (D) 3 (E) Infinite MDULO 4 LGEBRA EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 94 28. The equation 35335 =y yy has (A) an infinite number of roots, all of them real (B) exactly two roots, both no integral (C) exactly two roots, both integral (D) exactly one root, which is integral (E) no roots 29. If ( t- 8 ) is a factor of t2 kt 48, then k = (A) 6 (B) 2 (C) 2 (D) 6 (E) 14 30. If x =x yx 2 , the value of x, in terms of y, is: (A) y (B) y + 2 (C) 2 - y (D) y - 2 (E) 2y 31. What is the best value of99,9992 12 ? (A)99,9982 (B)99,998 . 104 (C)99,998 . 105 (D)109 (E)1010 32. What is the best value of(1.00001)(0.99999) (1.00002)(0.99998) ? (A)0 (B)-10-10 (C) 10-10 (D)2.10-10 (E) 3.10-10 33. If w + x < 0, is w y > 0? (1) x + y < 0 (2) y < x < w MDULO 4 LGEBRA EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 95 34. If k= 0, 1, or 1, is 1/k > 0?

(1)011> k

(2) 011>+ k 35. If 0 < x < y, what is the value of 22) () (y xy x+? (1)x2 + y2 = 3xy (2)xy = 3 36. If 4111 1+=+x x x. Then x could be (A) 0 (B) -1 (C) -2 (D) -3 (E) -4 37. If x x2211 = + , then x = (A) -1 (B) 1/3 (C) 2/3 (D) 2 (E) 3 38. What is the value of x in the equation 69684x x x += ? (A) -2 (B) -1 (C) 0 (D) 1 (E) 2 39.If x and y are different integers and x2 = xy, which of the following must be true? I.x = 0 II. y = 0III. x = -y (A)I only (B)II only (C)III only (D)I and III only (E)I, II, and III MDULO 4 LGEBRA EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 96 40. If x2 + y2 = 29, what is the value of ( x y )2 ? (1)xy = 10 (2)

x = 5 41. For which of the following values of x isx 2 1 NOTdefined as a real number? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 RESPOSTAS 1. E 2.D 3.B 4.C 5.A 6.C 7.A 8.D 9.C 10.D 11.D 12.D 13.C 14.A 15.B 16.C 17.C 18.E 19.D 20.E 21.C 22.E 23.C 24.C 25.A 26.A 27.C 28.E 29.C 30.D 31.C 32.E 33.B 34.A 35.A 36.C 37.E 38.A 39.A 40.A 41.E

MDULO 5 WORD PROBLEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 97 TIPO 1:Sistema de Equaes do 1o grau. Mtodo de resoluo:ADIO Assuntos: a) Aplicao financeira. Eu tinha $4000.00. Apliquei uma parte a 5% ao ano eoutra parte a 8% ano. Se no final de um ano eu recebi $230.00 de juros, quantos reaiseu apliquei a 8%? b) Resultado de prova. Um teste tem 22 questes. Joo respondeu todas e fez 36 pontos. Quantas questes ele errou, se o nmero de pontos composto somando-se 3 pontos para cada resposta correta e subtraindo-se2 pontos para cada incorreta? c) Idades. Hoje, Paulo 10 anos mais velho do que Ana. H8 anos atrs, a idade do Paulo era o dobro da idade da Ana. Qual a idade da Ana hoje? MDULO 5 WORD PROBLEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 98 TIPO 2: Sistema de Equaes com Multiplicao das Variveis Mtodo de resoluo: BACK SOLVING Assuntos: a) Rateio. Umcertonmerodepessoas(x)sereuniuparacomprarumpresentecujopreo $240.00.Naltimahora2pessoasdesistiram,eaquelasquepermaneceramtiveramque contribuir com $20.00 a mais cada uma. Quantas eram as pessoas inicialmente? b) Deslocamento.Ontem eu percorri 240 milhas. Se eu tivesse ido 20 milhas por hora mais rpido, eu teria levado 2 horas a menos. Quanto tempo eu levei para percorrer as 240 milhas ontem? c) Receita Se o preo dos cadernos amanh abaixar $2.00cada um, eu conseguirei comprar 20 cadernosamaiscom$240.00doqueeuconsigocomprarhoje.Quantoopreodecada caderno? d) rea geometria Areadeumretngulo240cm2.Quaissosuasdimenses,sabendo-sequese diminuirmos sua largura em 2cm eaumentarmos seu comprimento em 20 cm, sua rea no se alterar ? Sistema: x.y = 240 ( x - 2) ( y + 20) = 240

Alternativas: (A) 3 (B) 4 (C) 5 (D)6 (E) 8 MDULO 5 WORD PROBLEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 99 TIPO3: Os primeiros.........custam .........Os demais custam............ Quanto custar .....? ( Preo em Partes ) Exemplos: a)Osprimeiros10diasdeumaexcursocustam$50.00pordia.Osdemais,apartirdo11o, custam $ 40.00 por dia. Quanto custar uma excurso de 15 dias? b)Umtaxicobra$0.25peloprimeiroumquartodemilhae$0.10pelosdemaisquartosde milha. Quanto custar uma corrida de 3 milhas? c)Umtaxicobra$xcentavospeloprimeiroquartodemilhaex/5pelosdemaisquartosde milha. Quanto custar uma viagem de y milhas?

d) A parking lot charges $2.00 a hour for the first 3 hours and $1.4 for each houror fraction of hour over 3 hours. How much will it charge to park 6.5 hours? MDULO 5 WORD PROBLEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 100 TIPO 4: Problemas Literais Exemplos: a) A factory normally produces x units per working day. In a month with 22 working days, no unitsareproducedinthefirstyworkingdaysbecauseofastrike.Howmanyunitsmustbe producedperdayoneachoftherestoftheworkingdaysofthemonthinordertohaveanaverage of xunits per working day for the entire month ? (A)11x (B)22x (C) 22xy

(D) 2222xy (E) 2222xxy y b)Whenticketsalesbegan,Patwasthenthcustomerinlineforaticket,andcustomers purchasedtheirticketsattherateofxcustomersperminute.Ofthefollowing,whichbest approximatesthetime,inminutes,thatPathadtowaitinlinefromthemomentticketsales began ? (A)(n - 1)x (B)n + x - 1 (C) nx 1 (D) xn 1 (E) nx 1 c)Asmallfirmspentoftheannualbudgetduringthefirst2monthsofitsfiscalyearand spent of its remaining budget during the next 5 months. What fraction of the annual budget remained unspent at the end of the first 7 months? (A) 3/16 (B) (C) 5/16 (D) 3/8 (E) 5/12 MDULO 5 WORD PROBLEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 101 d)A total of n trucksand carsare parked in a lot.If the number ofcars is of the number of trucks,and2/3ofthetrucksarepickups,howmanypickups,intermsofn,areparkedinthe lot? (A)n61 (B)n125 (C)n21 (D)n158 (E)n1211 TIPO 5: Problemas com dgitos

Exemplos: a)Ifatwo-digitpositiveintegerhsitsdigitsreversed,theresultingintegerdiffersfromthe original by 27. By how much do the digits differ? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 b) What is the ten digit of the integer n? (1)The hundred digit of 10n is 4 (2) The unit digit of n/10 is 4

MDULO 5 WORD PROBLEM Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 102 -Vocterminou os exemplos do mdulo5 !Faa um RESUMO dos pontos importantes deste mdulo antes de iniciar a lista de exerccios. -Quandoterminaralistadeexerccios,corrijaevolteparaaquelesque voc errou. Tente entender POR QUE voc errou . Em seguida, volte para aqueles que voc acertou e veja se foram resolvidos da MELHOR maneira. -Naltimapginadomdulonositevocencontraralgunsexercciosda lista resolvidos -Depoisda correo dosexercciosCOMPLETEORESUMOcomoserroscometidos. Lembre-se de estar sempre relendo este resumo RESPOSTAS DO MDULO 5 Tipo 1: a) $1,000 c)6 questes c) 18 anos Tipo 2: a) 6 pessoas b) 6 horas d)$6.00 d) 6 cm e 40 cm Tipo 3: a) $700.00 b)$1.35 c)54 4 xy x + d) $11.60

Tipo 4: a) D b) C c) D d) D Tipo 5: a) A b) D MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 103 1)If a taxi driver charges x cents for the first quarter-mile of a trip and x/5 cents for each additional quarter-mile, what is the charger, in cents, for a trip whose distance in miles is the whole number y? 25) (54) (5004) (54 4) (125) (xyExy xDxy xCxy xBxy xA++++ 2)Eggs cost 50 cents a dozen for the first 100 dozen a store buys from a wholesaler and 47centsadozenforalldozenboughtinadditiontothefirst100dozen.Howmuch does it cost to buy 150 dozen eggs from the wholesaler? (A) $70.50 (B) $72.00 (C) $73.50 (D) $123.50 (E) $150.00 3)If it cost x cents to produce a single sheet of paper for the first 800 sheets and if every subsequentsheetcostsx/15cents,howmuchwillitcosttoproduce5,000sheetsof paper? (A)800x cents (B)1,080x cents (C)1,400x cents (D)2,430x cents (E)3,500x cents 4)Ifelectricitycostxcentsperkilowatthourforthefirst30kilowatthoursandycents per kilowatt hour for each additional kilowatt hour, what is the cost of z kilowatt hours (z > 30)? (A)30(x y) + yz (B)30y 30x + yz (C)30(x y + z) (D)(z 30)x + 30y (E)30x + (y 30)z MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 104 5)A shipping firm charges 2 cents a pound for the first 20 pounds of package weight and 1.5centsforeachpoundorfractionofapoundover20poundsofpackageweight. How much will it charge to ship a package which weighs 23 pounds? (A)6 cents (B)8 cents (C)45 cents (D)46 cents (E)47 cents 6)Feathers cost $500 a ton for the first 12 tons and $(500-x) a ton for any tons over 12. What is x, if it costs $10,000 for 30 tons of feathers? (A)270.00 (B)277.00 (C)277.70 (D)277.78 (E)280.00 7)Ataxicabcharges$1.00forthefirstone-fifthmileofatripand20centsforeach followingone-fifthmileorpartthereof.Ifatripis 212 mileslong,whatwillbethe fare? (A)$2.60 (B)$3.10 (C)$3.20 (D)$3.40 (E)$3.60 8)A man invested $1,000, part at 5% and rest at 6%. His total investment with interest at the end of the year was $1,053. How much did he invest at 5%? (A)$500 (B)$600 (C)$700 (D)$900 (E)$950 9)Macey is three times as old as Mike. In 8 years, she will be twice as old as Mike. How old was Macey 3 years ago? (A)5 (B)8 (C)21 (D)24 (E)30 MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 105 10)Multiply by 3 my age 3 years from now and subtract from this number 3 times my age 3 years ago. The result is my age now. How old am I? (A)Zero (B)3 (C)6 (D)9 (E)18 11)What is the capacity of the tank P? (1) When tank P was full to 1/16 of its capacity, it took 24 liters of gasoline to fill it to capacity. (2) It costs $22.50 to fill tank P to capacity. 12)How many raffle tickets were sold if ticket sales brought in receipts of $10,000? (1)Each ticket was sold for 25 cents. (2)4000 books of tickets were sold. 13)A gift worth x dollars is being bought by n students. If 6 of the purchasers drop out and someremain,howmanymoredollarswilleachoftheremainingcontributorshaveto pay? (A) 6x (B) 6 nx (C) nx 6 + (D) |.|

\||.|

\| nxnx6 (E) |.|

\||.|

\|6 nxnx 14)Aworkerispaid$20foreachdayheworks,andheispaidproportionatelyforany fraction of a day he works. If during one week he works 1/8,2/3,3/4,1/3 and 1 full day. What are his total earnings for the week? (A)$40.75 (B)$52.50 (C)$54 (D)$57.50 (E)$58.25 MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 106 15)At a certain bowling alley, it costs $0.50 to rent bowling shoes for the day and $1.25 to bowl 1 game. If a person has $12.80 and must rent shoes, what is the greatest number of complete games that person can bowl in one day? (A)7 (B)8 (C)9 (D)10 (E)11 16)Attendancefor a three-game seriesat a baseballpark averaged 25,000 persons for the three games. If the second and third games drew crowds of 1 and 2 times as large as the first game, respectively, what the attendance for the second game? (A)15,000 (B)18,000 (C)22,500 (D)25,000 (E)37,500 17)The sum of the digits of a three-digit number is 16. If the tens digit of the number is 3 timestheunitsdigit,andtheunitsdigitisofthehundredsdigit,thenwhatisthe number? (A)446 (B)561 (C)682 (D)862 (E)914 18)Adealerownsagroupofstationwagonsandmotorcycles.Ifthenumberoftires (excludingsparetires)onthevehiclesis30morethantwicethenumberofvehicles, then the number of station wagons the dealer owns is (A)10 (B)15 (C)20 (D)30 (E)45 19)An instructor scored a students test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answer. if the student answered all of the questions and received a score of 38, how many questions did that student answer correctly ? (A)19 (B)38 (C)41 (D)44 (E)46 MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 107 20)How much money did the Suppertime Theatre make from ticket sales? The theatre sells two kinds of tickets: reserved seat and general admission. (1) The theatre made $2,000 from sales of reserved seats. (2) The theatre sold 400 general tickets. 21)The amount of fat in an ounce of food A plus the amount of protein in an ounce of food A is 100 grams. The amount of protein in an ounce of food A minus twice the amount of fat in an ounce of food A is 10grams.Howmanygrams of protein are there in an ounce of food A? (A)30 (B)45 (C)50 (D)55 (E)70 22)In a garage there are 23 vehicles between motorcycles and cars. If each car can take 5 peopleeach,andeachmotorcyclecantake2peopleeach,howmanypeoplecanall these vehicles take? (1)There are a total of 74 wheels in this garage (excluding spare tires). (2)There are 5 more cars than motorcycles in this garage. 23)Bob drove 150 milesyesterday at aconstant rate.If he had increased thespeed by 25 milesperhour,hewouldhavetakenhalfhourlesstodrive150miles. Atwhatspeed did Bob drive yesterday? (A)25 (B)50 (C)75 (D)100 (E)125 24)AgroupofstudentsdecidedtobuyacomputerthatcostsU$2,100.00.Because3of themgaveup,eachoftheremainingstudentshadtopayU$90.00more.Whatisthe totalamountindollarsthateachstudentwouldhavepaidtobuythecomputer,if nobody had given up? (A)30 (B)70 (C)210 (D)300 (E)420 MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 108 25)Sally has an amount of money equal to the amount Charles has plus $6. If the amount Charleshasisequalto0.6theamountthatSallyhas,thenhowmuchmoneydoes Charles have? (A)$9 (B)$12 (C)$36 (D)$100 (E)$120 26)For a certain concert, 570 tickets were sold for a total of $975. If childrens tickets sold forhalftheregularpriceof$2.50,howmanyoftheticketssoldwerechildrens tickets? (A)210 (B)235 (C)260 (D)325 (E)360 27)18 years ago Paul was 3 times as old as his son. Today Paul is twice as old as his son. How old is Pauls son? (A)18 (B)19 (C)36 (D)54 (E)72 28)Astorehasaparkinglotwhichcontains70parkingspaces.Eachrowintheparking contains the same number of parking spaces. The store has bought additional property in order to build an addition to the store. When the addition is built, 2 parking spaces will be lost from each row; however 4 more rows will be added to the parking lot. After the addition is built, the parking lot will still have 70 parking spaces, and each row will contain the same number of parking spaces as every other row. How many rows were in the parking lot before the addition was built? (A)5 (B)6 (C)7 (D)10 (E)14 MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 109 29)Originally, agroup of 11 students were supposed to share equally acash prize.If one morestudentisaddedtothegroupandthe12studentssharetheprizeequally,then each new share is worth what fraction of the each original share? (A)1/12 (B)1/11 (C)1/10 (D)10/11 (E)11/12 30)For a certain performance, a theater charged $4 for each student ticket sold and $5 for eachnonstudentticketsold.Ifreceiptsforstudentticketstotaled$600andfornon student totaled $1,250, then the number of non student tickets sold was what fraction of total number of ticket sold? (A)3/8 (B)4/9 (C)5/9 (D)5/8 (E)4/5 31)The bookstore at Union College buys used text-books from students and offers them for resale at a price that is a fixed percent of the original price of the book when it was new, regardlessofthetitleofthebookoritscondition.Ifanewfreshmanchemistrybook sells for $40, at what price should it be offered for resale? (1) A student saves $7.50 by buying a used rather than a new freshman biology book.(2) A biology book that cost $30 when new is offered for resale at $22.50. 32. How much time did it take a certain car to travel 440 km? (1) The car traveled the first 200 km in 2.5 hours (2) Ifthecarsaveragespeedhadbeen20kmperhourgreaterthanitwas,itwould have traveled the 440 km in 1 hour less than it did. 33. In a certain year the United Nations total expenditure were $1.6 billion. Of this amount, 67.8 percent was paid by the 6 highest-contributing countries, and the balance was paid bytheremaining153countries.WasCountryXamongthe6highest-contributing countries? (1) 56percentofthetotalexpenditureswaspaidbythe4highest-contributing countries, each of which paid more than Country X. (2) Country X paid 4.8 percent of the total expenditures MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 110 34.Ratesforhavingamanuscripttypedatacertaintypingserviceare$5perpageforthe firsttimeapageistypedand$3perpageeachtimeapageisrevised.Ifacertain manuscript has 100 pages, of which 40 were revised only once, 10 wererevised twice, andtherestrequirednorevisions,whatwasthetotalcosttohavingthemanuscript typed? (A) $430 (B) $620 (C) $650 (D) $680 (E) $770 35.Ofthe60animalsonacertainfarm,2/3areeitherpigsorcows.Howmanyofthe animals are cows? (1)The farm has more than twice as many as cows as it has pigs (2) The farm has more than 12 pigs 36. A certain business produced x rakes each month from November throughFebruaryand shippedx/2rakesatthebeginningofeachmonthfromMarchtoOctober.Thebusiness paidnostoragecostsfortherakesfromNovemberthroughFebruarybutitpaidstorage costs of $0.10 per rake each month from March to October for the rakes that had not been shipped.Intermsofx,whatwasthetotalstoragecost,indollars,thatthebusinesspaid for the rakes for the 12 months from November through October? (A) $0.40x (B) $1.20x (C) $1.40x (D) $1.60x (E) $3.20x 37.Juanboughtsomepaperbackbooksthatcost$8eachandsomehardcoverbooksthat cost$25each.IfJuanboughtmorethan10paperbackbooks,howmanyhardcover books did he buy? (1) The total cost of the hardcover books that Juan bought was at least $150 (2) The total cost of all the books that Juan bought was less than $260 38.Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2barseach.Hehandedout2/3ofthechocolatebarsand3/5ofthetoffeebars.How many packages of chocolate bars did Rasheed buy? (1) Rasheed bought 1 fewer package of chocolate bars than toffee bars. (2) Rasheed handed out the same number of each kind of candy bar MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 111 39.Alicestake-homepaylastyearwasthesameeachmonth,andshesavedthesame fraction of her take-home pay each month. The amount that she saved at the end of the year was 3 times the amount of that portion of her monthly take-home pay that she did not save. If all the money came from her take-home pay, what fraction of her take-home pay did she save each month? (A) 1/2 (B) 1/3 (C) 1/4 (D) 1/5 (E) 1/6 40.How many minutes doesit take John to typey words if he types at the rate ofx words per second? (A) yx (B) xy (C) xy (D) yx 60 (E) xy60 41.When ticket sales began, Pat was then the customer in line for a ticket, and customers purchasedtheirticketsattherateofxcustomersperminute.Ofthefollowing,which bestapproximatesthetime,inminutes,thatPathadtowaitinlinefromthemoment ticket sales began ? (A)(n - 1)x (B)n + x 1 (C) nx 1 (D) xn 1 (E) nx 1 MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 112 42.Working alone, Sumio can mow a certain field in x hours. Yoko can mow 50% more field in the same time. When the two work together, they are paid m dollars each one. IfSumiodecidestopayYokondollarssotheywouldhavereceivedthesame compensation per field mowed, what is n in terms of m? (A)m21 (B)m31 (C)m41 (D)m51 (E)m61 43.If the tens digit x and the units y of a positive integer n are reversed the resulting integer is 9 more than n. What is y in terms of x? (A) 10 x (B) 9 x (C) x + 9 (D) x 1 (E) x + 1 44.Is the hundredths digit of the decimal d greater than 5? (1)The tenths digit of 10d is 7. (2)The thousandths digit of d/10 is 7. 45.Atabakery,alldonutsarepricedequallyandallbagelsarepricedequally.Whatisthe total price of 5 donuts and 3 bagels at the bakery? (1)At the bakery , the total price of 10 donuts and 6 bagels is $12.90 (2)At the bakery, the price of a donut is $0.15 less than the price of a bagel. 46.Of the goose eggs laid at a certain pond, 2/3 hatched, and of the gees that hatched from those eggs survived the first month. Of the geese that survived the first month , 3/5 did not survivethefirstyear.If120geesesurvivedthefirstyearandifnomorethanonegoose hatched from each egg, how many goose eggs were laid at the pond? (A)280 (B)400 (C)540 (D)600 (E)840 MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 113 47.Atthebakery,Lewspentatotalof$6,00peronekindofcupcakeandonekindof doughnut. How many doughnuts did he buy? (1)The price of 2 doughnuts was $0,10 less than the price of 3 cupcakes (2)The average ( arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35. 48.Atacertainbakery,eachrollcostsrcentsandeachdoughnutcostsdcebts.IfAlfredo bought rolls and doughnuts at the bakery, how may cents did he pay for each roll? (1)Alfredo paid $5,00 for 8 rolls and 6 doughnuts. (2)Alfredo would have paid $10,00 if he had bought 16 rolls and 12 doughnuts. 49.If k is a positive integer and the tens digit of k + 5 is 4, what is the tens digit of k? (1)K > 35 (2)The units digit of k is greater than 5. MDULO 5 WORD PROBLEM EXERCCIOS Luciana Chamie Desenvolvimento e Treinamento em Matemtica Tel.:3845-0226 114 RESPOSTAS 1. B 2.C 3.B 4.A 5.D 6.D 7.D 8.C 9.C 10.E 11.A 12.A 13.D 14.D 15.C 16.C 17.D 18.B 19.E 20.E 21.E 22.D 23.C 24.C 25.A 26.E 27.C 28.D 29.E 30.D 31.B 32.B 33.E 34.D 35.C 36.C 37.C 38.C 39.D 40.E 41.C 42.D 43.E 44.D 45.A 46.D 47.E 48.E 49.B