Numerical - Mixed Questions13Numerical Reasoning Practice 05

1、The following diagram describes the percentage of applicants accepted to University for the years 2000-2007:（1）Which of the following statements is always correct?AThe number of accepted applicants in 2003 and 2006 was equal.BThe number of accepted applicants in 2007 was the lowest between the years 2000-2007.CIn 2004 more students were accepted to the school than in 2003.DIn 2002 the number of students accepted was 3 times bigger than those who were not accepted.ENone of the above答案：DThe diagram discusses only percentages and not absolute numbers, meaning answers A-C are eliminated, since they compare between quantities of students in different years. For example- statement A is incorrect since while 2003 and 2006 are equal in the percentage of acceptance, they may differ in the actual number of applicants. If the total is different, equal percentages represent different actual numbers.In 2002 75% were accepted, meaning 25% were not accepted. 75% is 3 times bigger than 25%.（2）答案：BAccording to the diagram, in 2005 60% of all the applicants were accepted. According to the question, 1/3 of them (60/3 = 20%) had outstanding test results, meaning that 40% did not have outstanding test results, but were still accepted.40% are 2/5 of the entire applicants.（3）答案：AIn this question you can relate to the number of people accepted since a ratio is given regarding the number of people accepted in different years. Well place numbers: The number of people accepted in 2006 = 1. The number of people accepted in 2007 = 5.In 2006, 50% of the candidates were accepted, well look for the whole:50% - 1 candidate100% - 2 candidatesIn 2007, 20% of the candidates were accepted, well look for the whole:20% - 5 candidates100% - 25 candidatesThe number of applicants in 2007 is 12.5 times bigger (25/2=12.5).(4)答案：BThe diagram presents complementary data to the requested data - the percentage of students who were accepted to university.The lowest percentage of people who were NOT accepted is the same as the year that had the highest percentage of people who were accepted, which according to the chart is 2004.（5）答案：DThe correct answer is (D).The gragh shows the percent of those who passed the exam but we can not tell the number of students that took it in the first place (there may be a different number of students who took the exam each year).Since we dont know the actual number of students who took the exam, we cant refer to the number of students that passed or failed with one exception: In 1995 no student passed the exam (0% passed), and so it is not possible that in 1993 there was a smaller number of students (smaller than 0) that passed the exam. As statement (D) cannot be true, it is the correct answer.（5）答案： AThe correct answer is (A).In this question you can either relate to the students who passed or the students who failed the exam since we have a ratio of students taking the exam each year. Lets place numbers:Answer (A): in 1990, 100 students took the exam, 60% passed, meaning 40% failed which make 40 students.In 1991, 200 students (twice as many) took the exam, 80% passed, meaning 20% failed which make 40 students.The number of students failing in 90 and 91 remains the same.This is the correct answer.Answer (B): in 1992, 100 students took the exam, 40% passed meaning 40 students.In 1993, 200 students took the exam, 20% passed meaning 40 students.The number of students that failed in 92 and 93 remained the same and did not grow.Answer (C): in 1993, 100 students took the exam, 20% passed meaning 20 students.In 1994, 200 students took the exam, 50% passed meaning 100 students.The number of students failing grew between 93 and 94.Answer (D): in 1995, 100 students took the exam, 0% passed meaning all 100 students failed.In 1996, 200 students took the exam, 60% passed, meaning 40% failed which make 80 students.The number of students failing lessened between 95 and 96.2、The following chart describes price ranges of different types of cars, as published in a price list dated January 2009.（1）答案： CAnswer (A): Not correct since you can buy both kinds for 130 thousand GBP.Answer (B): Not correct since you can buy both kinds for 70 thousand GBP.Answer (C): The most expensive compact Japanese car costs 70 thousand GBP and the least expensive American car costs 90 thousand GBP, so there can be no overlap.Answer (D): Not correct since you can buy both kinds for any number between 140 - 170 thousand GBP.（2）答案：CThe data in the graph state the possible price range for each type of car, yet we cannot tell how many cars are there within the range. Therefore, we cannot know the exact average of each type, only that it is somewhere within the range (except the top or bottom end).The correct answer is (C).Answer (A): The average can be anywhere in the range, including 90,000.Answer (B): It is possible that most Japanese cars are relatively expensive and most American cars are relatively not expensive and so the average price of Japanese cars is higher than the average price of American cars.Answer (C): There is no overlap between the two types of cars. Even if the average price of a Japanese car is as high as possible (a bit less than 130,000) and the average price of a European car is as low as possible (a bit higher than 140,000), this statement is still incorrect.Answer (D): This statement is always correct. Since all compact Japanese cars are less expensive than all executive American cars the average price of the Japanese car is necessarily lower than the average price of the executive American car.（3）答案：D Well examine the two extreme cases:If both cars were the least expensive, the couple would pay 130 thousand GBP for the executive American car and 50 thousand GBP for the compact Japanese car, all together 180 thousand GBP.If the cars were the most expensive, the couple would pay 160 thousand GBP for the executive American car and 70 thousand GBP for the compact Japanese car, all together 230 thousand GBP.Any number between those amounts is possible. The only amount not within the range of 180,000 and 230,000 is 240,000.(4)答案：DThe greatest loss will occur if Dylan bought the most expensive car within the given range (200 thousand GBP) and sold it for the cheapest price (120 thousand GBP). In this case the loss is 80 thousand GBP (200-120).The minimal loss will occur if Dylan bought the least expensive car within the range (140 thousand GBP) and sold it for the highest price possible (130 thousand GBP). In this case the loss is 10 thousand GBP.Please note that once reaching the maximal loss of 80 thousand GBP we got our answer since only one of the answers has that number.3、（1）This year petroleum usage cost the country 65.3 million, and the government plans to increase its petroleum spending by 12 percentage points next year. How much money will be spent on petroleum, assuming the total expenditure on all fuel sources remains the same?答案：DNotice:Percentage Points is a confusing term. It is an absolute increase in the percentage number, not a relative increase!Find the total expenditure on all fuel sources in the present year.Let X represent the total expenditure on all fuel sources. Since Petroleum cost 65.3 million and comprises 37% of total fuel expenditure we can calculate:0.37 * X = 65.3 million - X = 176.49 million.We were told that next year the consumption of petroleum would increase by 12 percentage points: 37%+12%=49%. (0.37+0.12) = 0.49.Next we multiply the updated percentage by the total expenditure that remained constant, in order to find its cost.0.49*176.49 = 86.48 million.4、Country YImport/Export Year on Year Changes Since 2004 (millions of $)*In 2004, import was $350 million and export was $450 million.（1）If the difference between country Ys imports and exports is 250 mil in2011, what is the relative increase in the difference between country Ys imports and exports from 2005 to 2011?答案：EWhen calculating import and export values in 2005, we need to remember to take those of 2004 into account as well:Import:In 2004: $350mIn 2005: $350m + $100m = $450mExport:In 2004: $450mIn 2005: $450m + $0 = $450mTherefore, the import/export difference in 2005 is:Import - Export = $450m - $450m = $0In order to find the relative profit, we need to divide the difference in 2011 by the difference in 2005:$250m / $0Since division by zero is undefined, none of the above figures is correct.（2）The conversion rate from Euro to Egyptian Pound is 8.3442. How many Egyptian poundsdid country Ymakefrom export in 2009?*Unless mentioned otherwise, dollars ($) are USD. 答案：CThe figures in the chart represent thechangesin export, not the actual export values each year. To find theactualexport value in 2009, we have to start with the given export for 2004 and then add-up the changes in each year until 2009. Thus:Export incomes in 2009 are 450+0+100+50-100-120 = $380milCalculating the currency differences between US Dollars and Euros:380*0.7155 = 271.89And nowto Egyptian Pounds:271.89*8.3442 =2268.7Please note: The direction of the conversion can be easily determined by the leftmost column. The 1 in front of each currency indicates that each row contains the conversion rates from the left currency to the others. For example, the first row indicates the conversion rates from USD to other currencies. Thus, 1 USD equals 0.7155 EUR.4、（1）Which of the four cities had the biggest average cost per person last year?答案：CGiven the percent changes from last year, calculate the average expenditures.Northern Coresis highest: 55/1.06=51.88（2）An expected rise of 3.5% in CPI next year will reduceGeremaia and Klara Citysaverage monthly costs per personby 7.5% and 3.5% respectively. What would be the percentage difference between Klara Citys new average monthly costs and Geremaias new average monthly costs？答案：E Although CPI is mentioned in this question, it can be neglected, as itwould equally affect both cities.We need to find the new average monthly cost per person in Geremaia and Klara City, and then calculate the percentage change. Lets start with Geremaia. The average cost should be reduced by 7.5%. This means that the new value is 92.5% of the old value (100%-7.5% = 92.5%). Therefore, Geremaias new average monthly cost per person is 35*0.925.Similarly, Klara Citys new average cost per person is 45*0.965.In order to find the percentage change, we divide Klara Citys new value by Geremaias new value, and subtract 1. This leaves us with:(45*0.965) / (35*0.925)-1=0.3413= 34.13%5、Prices of HD Televisions（1）答案：D$245 (HD television price in year 1)*1.025 (inflation rate between year 1 and year 2) = $251.125.That is a price, affected only by inflation- not by any other increase. Having takeninflation into account, we can now calculate theeffectiveincrease in HD televisions price, without the increase caused by inflation.$253 (HD television price in year 2) - $251.125= $1.875（2）答案：DIn order to calculate the rise in inflation from the beginning of year 1 to year 6, we need to find the product of the rise in inflation each year. 1.025*1.023*1.017*1.015*1.016*1.02=1.1217, which is rounded to a12.2% increase. The reason we multiply the inflation of each year (and do not add them) is because the inflation is given as the % it rose each year.If for example the price level at the beginning of year 1 is 100 and over the course of the year it goes up by 2.5%, then by the end of year 1 (and at the beginning of year 2) the price level will be 100*1.025=102.5.As such, at the beginning of year 2 the price level will be 102.5 and after a 2.3% increase, the price level at the end of the year 2 (and beginning of year 3) will be 102.5*1.023=104.86.This will continue every year: Price level at the beginning of year 3: 104.86. Price level at end of year 3 after 1.7% increase: 104.86*1.017=106.64.Price level at beginning of year 4: 106.64. Price level at end of year 4 after 1.5% increase: 106.64*1.015=108.24.Price level at beginning of year 5: 108.24. Price level at end of year 5 after 1.6% increase: 108.24*1.016=109.97.Price level at beginning of year 6: 109.97. Price level at end of year 6 after 2% increase: 109.97*1.02=112.169.We can see that from the beginning of year 1 to the end of year 6 the price level rose from 100 to 112.16 which (rounded to the nearest tenth) is a 12.2% increase.5、（1）Mr.Xs Shoe FactoriesFactory AFactory BFactory CFactory DFactory ETotal Weekly Rent Expenses$6000$3500$5500$5000$4300Production per hour350710390470580Hours per week7550658045% of Production Faulty5%12%8%14%4%The table shows details of Mr. Xs five shoe factories. Mr. X has decided that he can no longer support five factories and that he will close down the least cost efficient one.Assuming that factors other than those which appear in the table are negligible, which one should he close?答案：AThis question is fairly straight forward, as long as we know the correct operations to perform. In order to compare levels of cost efficiency we must calculate total production, taking only the percent of production that isnt faulty into account. We must then compare this output with the cost, in this case factory rent.Production at A= 350 x 75 x 0.95 = 24,937.50Divided by rent = 24,937.50 / 6000 = 4.16Production at B = 710 x 50 x 0.88 = 31,240Divided