經(jīng)典24題 Test_Answer_Sheet_3

1、NUMERICAL TEST 3Answer B/numericaltestsPlease note the correct answers are shown in bold.Example QuestionsIn 000sCity Trading last 6 months (number of trades made, in 000s)3028252726Phone23202221201915Internet101211101350SeptemberOctoberNovemberDecemberJanuaryFebruaryE

2、x 1 Between which two months was there the greatest change in the number of Internet trades made?SolutionWe calculate the change in the number of Internet trades between months (in 000s):Change=Number trades Month (n) Number trades Month (n 1)BetweenChangeSeptember and October3October and November6N

3、ovember and December1December and January9January and February1From this we can see the greatest change in the number of Internet trades occurred between December and January. As the Question only referred to the change in the number of trades and not whether the change should be positive or negativ

4、e, the change in number between December and January is the correct answer.Tip We should do these calculations mentally without resorting to a calculator. Once we have to resort to a calculator or pen and paper, we start losing time.AnswerABCDESeptemberOctoberNovemberDecemberJanuaryand Octoberand No

5、vemberand Decemberand Januaryand February2 /numericaltestsEx 2 In September, approximately what proportion of the total number oftrades was made up of Internet trades?SolutionWe consider September data.We calculate what proportion of the total number of trades is made up of

6、Internet trades (in 000s): Proportion of trades = Number of Internet Trades Total number of Trades= 10 (10 + 22)= 0.31 or 31%AnswerABCDE25%31%34%37%43%3 /numericaltestsTest QuestionsUS $US Brewers Share Price in US $300280285250231200198Stella175187165153150Henecan1301431251

7、20Arca100989085737565500Year 1Year 2Year 3Year 4Year 5Year 61 For how many years was the price of Arca shares closer to that for Stella than for Henecan?SolutionWe calculate the differences in share prices:YearDifference between Arca shareDifference between Henecan shareprice and Stella share pricep

8、rice and Arca share price1$90 $65 = $25$175 $90= $852$98 $73 = $25$165 $98= $673$125 $85 = $40$231 $125= $1064$130 $75 = $55$187 $130 = $575$153 $120 = $33$280 $153= $1276$198 $143 = $55$285 $198 = $87From these calculations we can see that the difference in share price between Arca and Stella is sm

9、aller than the difference in share price between Henecan and Arca for each of the 6 years. Thus the Arca share price is closer to the Stella share price for all of the 6 years.Tip Visually inspecting the chart provided, we can see that Arca share price is closer to the Stella share price for all 6 y

10、ears except, maybe, Year 4. A quick calculation shows that the Arca share price is closer to the Stella share price even for Year 4.Thus, the Arca share price was closer to the Stella share price for all 6 years.AnswerABCDE234564 /numericaltests2 If the percentage increase i

11、n the Arca share price between Years 5 and 6 is doubled for the period Year 6 to 7, what will the value of the share price be in Year 7?SolutionWe consider the Arca share price.We calculate the percentage increase in share price between Year 5 and Year 6:Percentage increase=(Year 6 share price Year

12、5 share price) 1= ($198/$153) 1= 1.2941 1= 0.2941 or 29.41%The question indicates that the expected increase from Year 6 to Year 7 is double that of the increase from Year 5 toYear 6, an increase of (2 0.2941) = 0.58822.The Year 7 share price is then:Year 7 share price=$198 (1 + 0.58822)=$314.47The

13、closest answer provided is $314.AnswerABCDE$297$314$321$328$3353 Between which two years did the change in Stellas share price most closely match the change in Henecans share price?SolutionWe compare the percentage change in share prices by considering the proportional change in share price between

14、consecutive years per company (this makes the calculations faster without any loss of accuracy):Proportional change=(Share price Year n+1 Share price Year n)YearStella proportional changeHenecan proportional changeYear 1 Year 2$73/$65 = 1.1231$165/$175 = 0.9429Year 2 Year 3$85/$73 = 1.1644$231/$165

15、= 1.4Year 3 Year 4$75/$85 = 0.8824$187/$231 = 0.7229Year 4 Year 5$120/$75 = 1.6$280/$187 = 1.4973Year 5 Year 6$143/$120 = 1.1917$285/$280 = 1.0179Comparing these values we see that the difference in proportional change in share price between Year 4 and Year 5 is the smallest and, thus, they are the

16、closest match.Tip A visual scan of the chart provided shows that the likely years would be, Year 4 to Year 5 or Year 5 to Year 6. We calculate the proportionate changes for these 2 time periods only, reducing the number of calculations necessary.AnswerABCDEYear 1 toYear 2 toYear 3 toYear 4 toYear 5

17、toYear 2Year 3Year 4Year 5Year 65 /numericaltests4 If in the year prior to Year 1 the share prices of Henecan and Stella were both 10% higher, what was the actual difference in these share prices in that year?SolutionWe calculate the share price for each company for the year

18、 prior to Year 1. Taking each company in turn, we calculate the 10% increase in share price as follows:Prior share price=1.1Company Year 1 share priceSo,Henecan:Prior share price=1.1$175= $192.5Stella:Prior share price= 1.1$65= $71.5Now we calculate the difference in share price:Difference in share

19、price=$192.5 $71.5= $121Tip A faster way of calculating this value is to consider the increase in difference in share price. We can do this as both share prices increase by the same amount, 10%.Difference in share price=($175 $65) 1.1= $121AnswerABCDE$121$125$131$137$1426 /n

20、umericaltestsValue of Corporate Bonds Traded Last Year in Euros (millions)Euros (millions)180160140120100806040200LondonFrankfurtZurichParisMilanLong termMedium termShort term5 What was the difference in the value of Medium Term Bonds trades in Frankfurt compared to Paris?SolutionWe calculate the di

21、fference in value of Medium Term Bonds trades (in Euro millions):Difference=Value of trades in Frankfurt Value of trades in Paris= 50 20= 30AnswerABCDE30 million euros40 million euros50 million euros60 million euros70 million euros6 By how much did the total value of all Short Term Bonds traded exce

22、ed that of all Long Term Bonds traded?SolutionWe calculate the difference in value of all Short Term Bonds traded and all Long Term Bonds traded (in Euro millions):Difference=total value Short Term Bonds total value Long Term Bonds= (90 + 50 + 40 + 60 + 20) (20 + 30 + 30 + 20 + 10)= 150AnswerABCDE12

23、0 million euros130 million euros140 million euros150 million euros160 million euros7 /numericaltests7 As a proportion, which location traded the fewest Medium Term Bonds?SolutionWe calculate the value Medium Term Bonds traded as a proportion of the total Bonds Traded per Loc

24、ation. The Location with the smallest proportion is what we are looking for:Proportion=Medium Terms Bonds traded Total Bonds tradedLocationProportionLondon0.267Frankfurt0.385Zurich0.300Paris0.200Milan0.250From this we can see that Paris, as a proportion, traded the fewest Medium Term Bonds.Tip To fi

25、nd the correct answer we have to look for a location where a small amount of Medium Bonds are traded and a large overall amount of Bonds. This will provide a small proportion which is what we are looking for. Looking at the chart provided, there are two likely locations: London and Paris. Looking at

26、 the Paris trades and comparing to Paris we can see London should have at least a total value of trade over 200 million Euros to have a smaller proportion than Paris. This makes Paris the answer.AnswerABCDELondonFrankfurtZurichParisMilan8 Across these 5 locations, by what proportion would the volume

27、 of trading in Long Term Bonds have to increase in order to match the current volume of trading in Medium Term Bonds?SolutionWe calculate the total volume of trading in both Long Term and Medium Term Bonds. We then calculate the percentage increase in trading of Long Term Bonds in order to match the

28、 current volume of trading in Medium Term Bonds.Total Volume traded (working in millions of Euros):Long Term=110Medium Term=150Percentage difference=(150/110)100%=36.4%AnswerABCDE31.6%33.5%36.4%38.1%39.4%8 /numericaltestsDirect Wine Company: Annual Sales and Profit figures (

29、in $000s)Year 1Year 2Year 3Year 4Year 5Year 6Total Sales5,0204,4004,8505,1505,2205,820Total Profits600270-230-380310580= (Total Sales - Total Costs)9 In which year did Total Costs equal approximately 90% of Total Sales?SolutionWe calculate the Total Costs and then the percentage this value is for ea

30、ch of the years (in $ 000s):Total Costs=Total Sales Total ProfitsYearTotal CostsAs Percentage of Total SalesYear 1442088.0%Year 2413093.9%Year 35080104.7%Year 45530107.4%Year 5491094.1%Year 6524090.0%From this we can see Year 6 is the correct answer.Tip Considering the table of data provided, we loo

31、k for the year for which the Total Profits is 10% of the Total Sales. We can ignore Year 3 and Year 4 as these do not have any profits and thus will have greater Costs than Sales.We can see that Year 6 has a Total Profits that is 10% of Total Sales, which is what we are looking for.AnswerABCDEYear 2

32、Year 3Year 4Year 5Year 610 In which one of the following years were Total Costs the highest?SolutionWe calculate the Total Costs for each of the years and from this establish the year with the highest Total Costs (in $ 000s):YearTotal CostsYear 14,420Year 24,130Year 35,080Year 45,530Year 54,910Year

33、65,240From this we can see Year 4 is the year with the highest Total Costs.9 /numericaltestsTip Looking at the data provided, we can see that Year 4 or Year 6 would have the highest Total Costs as these years have the highest Total Sales values. For Year 4 we add $380,000 to

34、 the Total Sales to establish Total Costs. Comparing this value of Total Costs to Year 6 Total Costs (Total Sales minus Total Profits) we see Year 4 is the correct answer.AnswerABCDEYear 2Year 3Year 4Year 5Year 611 What was the average annual profit over the 6-year period?SolutionWe calculate the av

35、erage profit over the 6-year period (in $ 000s):Average Profit=Total Profits 6= (600 + 270 + (-230) + (-380) + 310 + 580) 6= 191.666AnswerABCDE$187,666$191,666$212,333$223,133$266,63312 In Year 1, compared with the previous year, both Total Sales and Total Profits rose by 10% each. What approximatel

36、y were the Total Costs in the year prior to Year 1?SolutionAs we are asked for an approximate value for Total Costs, we can calculate the value using mental arithmetic. Working in $ 000s:Both Total Sales and Total Profits are 10% less in the year prior to Year 1. From this we know that the Total Cos

37、ts will also be 10% less than the Total Costs in Year 1. Total Costs in Year 1 is a bit less than 4,500. 10% of this value is a bit less than 4,050.The answer is thus 4,018 or A.AnswerABCDE$4,018,182$4,096,000$4,128,573$4,282,000$4,376,92510 /numericaltestsValue of financial

38、 products sold in $000sValue in $000s15000140001300012000110001000090008000700060005000Year 1Year 2Year 3Year 4Year 5Year 6BondsonlyAllproducts(Bondsandequities)13 What was the average value of Bonds sold per annum over the 6-year period?SolutionWe calculate the average value of the Bonds Sold per a

39、nnum over the 6-year period. (Considering the chart we have to remember that the “Value in $000s” does not start at 0 but 5000.) Working in $ 000s:Average Value=(6000 + 8000 + 7000 + 9000 + 9000 + 10000) 6= 8166The answer closest to this value is C: $8.17 million.AnswerABCDE$7.33 million$7.83 millio

40、n$8.17 million$8.53 million$8.83 million11 /numericaltests14 The biggest proportional increase in the sales of Equity products took place between which two years?SolutionWe calculate the proportional change in the sales of Equities (in $ 000s):Value of Equities sold= All Pro

41、ducts Bonds onlyProportional Change= (Value Year n Value Year n1) Value Year n1YearProportional changeYear 1 Year 2-0.25Year 2 Year 30.67Year 3 Year 4-0.20Year 4 Year 5-0.50Year 5 Year 61.00From this we can see the biggest proportional increase in the sales of Equity products is Year 5 Year 6.Tip Visually inspecting the chart, we can see the only increases in the sales of Equity products were for Year 2 to Year 3 and