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Graphs 469Problem Set U: Solutions begin on page 611.Questions 1-5 refer to the following graphs.Profit And Revenue Distribution For Zippy Printing, 1990-1993, Copying And Printing.Total Profit Total Revenue(in thousands of dollars) (in millions of dollars)01002003004005006007009 0 9 1 92 9 3CopyingPrinting012345679 0 9 1 92 9 3Distribution of Profit from Copying, 1992(in thousands of dollars)Corporate35%Individual45%Government20%1. In 1993, the total profit was approximately how much greater than the total profit in 1990?(A) 50 thousand (B) 75 thousand (C) 120 thousand (D) 200 thousand (E) 350 thousand2. In 1990, the profit from copying was approximately what percent of the revenue from copying?(A) 2% (B) 10% (C) 20% (D) 35% (E) 50%3. In 1992, the profit from copying for corporate customers was approximately how much greater thanthe profit from copying for government customers?(A) 50 thousand (B) 80 thousand (C) 105 thousand (D) 190 thousand (E) 260 thousand4. During the two years in which total profit was most nearly equal, the combined revenue from printingwas closest to(A) 1 million (B) 2 million (C) 4.5 million (D) 6 million (E) 6.5 million5. The amount of profit made from government copy sales in 1992 was(A) 70 thousand (B) 100 thousand (C) 150 thousand (D) 200 thousand (E) 350 thousand258PercentsProblems involving percent are common on the test. The wordpercent means divided by one hundred.When you see the word percent, or the symbol %, remember it means 1100.For example,25 percent 25 1100 =14To convert a decimal into a percent, move the decimal point two places to the right.For example,0.25 = 25%0.023 = 2.3%1.3 = 130%Conversely,toconvertapercentintoadecimal,movethedecimalpointtwoplacestotheleft. Forexample,47% = .473.4% = .034175% = 1.75To convert a fraction into a percent, first change it into a decimal (by dividing the denominator [bottom]into the numerator [top]) and then move the decimal point two places to the right.For example,78= 0.875 =87. 5%Conversely, to convert a percent into a fraction, first change it into a decimal and then change the decimalinto a fraction.For example,80% =. 80 =80100 =45Following are the most common fractional equivalents of percents:3313%=136613% =2325% =1450% =1220% =1540% =2560% =3580% =45Percents 259Note!Percent problems often require you to translate a sentence into a mathematical equation.Example 1: What percent of 25 is 5?(A)10% (B)20% (C)30% (D)35% (E)40%Translate the sentence into a mathematical equation as follows:What percent of 25 is 5 x1100.25 = 525100x = 514x = 5x = 20The answer is (B).Example 2: 2 is 10% of what number(A)10 (B)12 (C)20 (D)24 (E)32Translate the sentence into a mathematical equation as follows:2 is 10 % of what number 2 = 101100. x2 =10100x2 =110x20 = xThe answer is (C).Example 3: What percent of a is 3a ?(A)100% (B)150% (C)200% (D)300% (E)350%Translate the sentence into a mathematical equation as follows:What percent of a is 3a x1100.a = 3ax100 a = 3ax100= 3 (by canceling the as)x = 300The answer is (D).260 GMAT Math BibleExample 4: If there are 15 boys and 25 girls in a class, what percent of the class is boys?(A) 10%(B) 15%(C) 18%(D) 25%(E) 37.5%The total number of students in the class is 15 + 25 = 40.Now, translate the main part of the sentence intoa mathematical equation:what percent of the class is boys x1100.40 = 1540100x = 1525x = 152x = 75x = 37.5The answer is (E).Note!Often you will need to find the percent of increase (or decrease). To find it, calculate theincrease (or decrease) and divide it by the original amount:Percent of change: Amount of changeOriginal amount100%Example 5: The population of a town was 12,000 in 1980 and 16,000 in 1990. What was the percentincrease in the population of the town during this period?(A) 3313%(B) 50%(C) 75%(D) 80%(E) 120%The population increased from 12,000 to 16,000.Hence, the change in population was 4,000.Now, trans-late the main part of the sentence into a mathematical equation:Percent of change:Amount of changeOriginal amount100% =400012000 100% =13 100% =(by canceling 4000)3313%The answer is (A).Percents 261Problem Set Q:Medium1. Which one of the following must p q equal if 60% of m equals p and 3/5 of m equals q ?(A) 0(B) m/11(C) 2m/11(D) 3m/55(E) 6m/552. In January, the value of a stock increased by 25%; and in February, it decreased by 20%. In March, itincreased by 50%; and in April, it decreased by 40%. If Jack invested $80 in the stock on January 1and sold it at the end of April, what was the percentage change in the price of the stock?(A) 0%(B) 5%(C) 10%(D) 40%(E) 50%3. If b equals 10% of a and c equals 20% of b, then which one of the following equals 30% of c ?(A) 0.0006% of a(B) 0.006% of a(C) 0.06% of a(D) 0.6% of a(E) 6% of a4. If 500% of a equals 500b, then a =(A) b/100(B) b/10(C) b(D) 10b(E) 100b5. If a/2 is 25% of 30 and a is c% of 50, then which one of the following is the value of c ?(A) 5(B) 10(C) 15(D) 20(E) 306. 8 is 4% of a, and 4 is 8% of b. c equals b/a. What is the value of c ?(A) 1/32(B) 1/4(C) 1(D) 4(E) 32262 GMAT Math Bible7. TheannualexportsofthecompanyNeuStarincreasedby25%lastyear.Thisyear,itincreasedby20%. If the increase in the exports was 1 million dollars last year, then what is the increase (in milliondollars) this year?(A) 0.75(B) 0.8(C) 1(D) 1.2(E) 1.258. Carlos & Co. generated revenue of $1,250 in 2006. This was 12.5% of its gross revenue. In 2007, thegross revenue grew by $2,500. What is the percentage increase in the revenue in 2007?(A) 12.5%(B) 20%(C) 25%(D) 50%(E) 66.3%9. In an acoustics class, 120 students are male and 100 students are female. 25% of the male studentsand 20% of the female students are engineering students. 20% of the male engineering students and25%ofthefemaleengineeringstudentspassedthefinalexam.Whatpercentageofengineeringstudents passed the exam?(A) 5%(B) 10%(C) 16%(D) 22%(E) 25%10. If x + yxy =43 and x0, then what percentage (to the nearest integer) of x + 3y is x 3y ?(A) 20%(B) 25%(C) 30%(D) 35%(E) 40%Hard11. Evans sold apples at 125% of what it cost him. What is the percentage of profit made by selling 100apples?(A) 0%(B) 20%(C) 25%(D) 33.3%(E) 50%12. Williams has x eggs. He sells 12 of them at a profit of 10 percent and the rest of the eggs at a loss of10 percent. He made neither a profit nor a loss overall. Which one of the following equals x?(A) 10(B) 12(C) 13(D) 14(E) 24Percents 26313. The value of a share of stock was $30 on Sunday. The profile of the value in the following week wasasfollows:Thevalueappreciatedby$1.2onMonday.Itappreciatedby$3.1onTuesday.Itdepreciatedby$4onWednesday.Itappreciatedby$2onThursdayanditdepreciatedby$0.2onFriday. On Friday, the stock market closed for the weekend. By what percentage did the value of theshare increase in the five days?(A) 3.2%(B) 4%(C) 5.6%(D) 7%(E) 10%14. Thepercentageofintegersfrom1 through100whosesquaresendwiththedigit1isx%,andthepercentage of integers from 1 through 200 whose squares end with the digit 1 is y%. Which one of thefollowing is true?(A) x = y(B) x = 2y(C) x = 4y(D) y = 2x(E) y = 4x15. The cost of painting a wall increases by a fixed percentage each year. In 1970, the cost was $2,000;and in 1979, it was $3,600. What was the cost of painting in 1988?(A) $1,111(B) $2,111(C) $3,600(D) $6240(E) $648016. Thelistpriceofacommodityisthepriceaftera20%discountontheretailprice.The festivaldiscountpriceonthecommodityisthepriceaftera30%discountonthelistprice.Customerspurchase commodities from stores at a festival discount price. What is the effective discount offeredby the stores on the commodity on its retail price?(A) 20%(B) 30%(C) 44%(D) 50%(E) 56%Very Hard17. Eachyear,fundsAandBgrowbyaparticularpercentagebasedonthefollowingpolicyoftheinvestment company:1) The allowed percentages of growths on the two funds are 20% and 30%.2) The growth percentages of the two funds are not the same in any year.3) No fund will have the same percentage growth in any two consecutive years.Bob invested equal amounts into funds A and B. In the first year, fund B grew by 30%. After 3 years,how many times greater is the value of fund B than the value of the fund A?(A) 12/13(B) 1(C) 13/12(D) 1.2(E) 1.3264 GMAT Math Bible18. Selling 12 candies at a price of $10 yields a loss of a%. Selling 12 candies at a price of $12 yields aprofit of a%. What is the value of a?(A) 11/1100(B) 11/100(C) 100/11(D) 10(E) 11270GraphsQuestionsinvolvinggraphsarecommononthetest. Rarelydothesequestionsinvolveanysignificantcalculating.Usually, the solution is merely a matter of interpreting the graph.Questions 1-4 refer to the following graphs.SALES AND EARNINGS OF CONSOLIDATED CONGLOMERATESales Earnings(in millions of dollars) (in millions of dollars)010203040506070809010085 86 87 88 89 9002468101285 86 87 88 89 90Note:Figure drawn to scale.1. During which year was the companys earnings 10 percent of its sales?(A)85 (B)86 (C)87 (D)88 (E)90Reading from the graph, we see that in 1985 the companys earnings were $8 million and its sales were $80million.This gives810 =110 =10100 =10%The answer is (A).2. During the years 1986 through 1988, what were the average earnings per year?(A)6 million (B)7.5 million (C)9 million (D)10 million (E)27 millionThe graph yields the following information:Year Earnings1986 $5 million1987 $10 million1988 $12 millionGraphs 271Forming the average yields 5+10+123=273= 9.The answer is (C).3. In which year did sales increase by the greatest percentage over the previous year?(A)86 (B)87 (C)88 (D)89 (E)90To find the percentage increase (or decrease), divide the numerical change by the original amount. ThisyieldsYear Percentage increase8670 8080=1080=18= 12.5%8750 7070=2070=27 2%8880 5050= 3050 = 35= 60%890 8080= 1080= 18=12.5%9010000= 100= 1 11%The largest number in the right-hand column, 60%, corresponds to the year 1988.The answer is (C).4. If Consolidated Conglomerates earnings are less than or equal to 10 percent of sales during a year,thenthestockholdersmusttakeadividendcutattheendoftheyear


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