Numerical - Mixed Questions13Numerical Reasoning Practice 02

1、答案：DThe number of Dutch football viewers is 2.865 million (2865 thousand). The population of The Netherlands is 16 million (16000 thousand).The proportion of the Dutch population that watches Dutch football = (2865000 / 16000000) x 100 = 17.9%Another possibility is to ignore the thousand: (2865 / 16,000) * 100 = 17.9%The answer is 17.9%.2、答案：AThe number of UK football viewers is 17,000,000.The number of Australian football viewers is 1,100,000.Theratio of UK to Australian football viewers is 17,000,000 / 1,100,000 = 15.45. The ratio is 15.45 : 1 which is approximately 15.5 : 1. TIP: Just by looking at the figures 17 million and 1.1 million, we already know that the ratio has to be slightly lower than 17: 1. This means that we can eliminate two options from the outset.The answer is 15.5: 1.3、答案： Cannot sayThere is no information about newspaper prices, therefore we cant figure out the answer based on the existing data.The answer is Cannot Say.4、答案：19:1Out of a total of 100% of newspapers that leave the factory, 5% are lost. This means that for every 100 newspapers, 95 papers are delivered and five newspapers are lost.Dividing 95 by 5 = 19. The ratio of successfully delivered newspapers to lost newspapers in London is 19:1.The answer is 19:1.5、答案：D12% of 7,600 adults surf the Internet.10% of 7600 is 760, therefore the number of adults that surf the Internet should be slightly higher (12%) 90016% of 2,400 children surf the Internet.It is easier to calculate it without solving the exact amount by dividing the calculation into two estimations:10% of 2400 is 240, and an additional 5% is 120 = 240 + 120 = 360. The number of children who surf the Internet is slightly higher (16%) 400.900 + 400 = roughly 1300The answer is 1300.6、答案：AOnly 2% of adults play video games compared with 21% of children. The ratio is approx 11:1 (21:2).None of the other categories compare.The answer is video games.7、答案：EWe must add the unemployment figures for each sector in the UK and Australia and the smallest number will indicate the sector with the lowest unemployment. In this particular case we may also look at the actual percentages of the unemployment rate to give us an indication. Healthcare = 122000 + 54000 = 176000 Tourism & Hospitality = 168000 + 65000 = 233000 IT = 82000 + 119000 = 201000 Education = 54000 + 87000 = 141000 Construction = 79000 + 26000 = 105000The answer is Construction.8、答案：CThe quickest way to solve this question is to look at the data before starting any calculations. The question asks about the ratio of Australian to UK unemployed. This means that the higher the Australian number and the smaller the UK number, the greater the ratio.We can immediately eliminate the Healthcare, Tourism & Hospitality and Construction sectors, since the number of unemployed over the UK is greater than that of Australia.Between IT and Education, in which the number of unemployed is greater in Australia, we can perform a direct calculation and find in which sector the requested ratio is higher.The IT sectors ratio is 119000: 82000 = 1.45The Education sectors ratio is 87000:54000 = 1.61.The ratio is higher for the education sector; therefore, this is the correct answer9、Natural Resources Market Annum StatisticsProductNo. of employees(in thousands)Value of Extracted Produce(in millions)Total ValueValue Per CountryAsiaU.S.AOil2,572$7,568$487$1,574Copper1,235$3,587$831$928Coal957$3,456$728$1,375Uranium1,542$6,875$427$3,208Silver1,012$3,500$700$1,789答案：40According to the table ，the USA coal market is worth $1,375 million and the total extracted coal produce is $3,456 million.In order to answer the question, we need to divide the USA coal produce by the total value of extracted coal produce and multiply the result by 100:1,375/3456 x 100 = 0.397 x 100 = 39.7% 40%The answer is 40.10、Natural Resources Market Annum StatisticsProductNo. of employees(in thousands)Value of Extracted Produce(in millions)Total ValueValue Per CountryAsiaU.S.AOil2,572$7,568$487$1,574Copper1,235$3,587$831$928Coal957$3,456$728$1,375Uranium1,542$6,875$427$3,208Silver1,012$3,500$700$1,789答案：DThe ratio can be calculated by roughly dividing the value of extracted produce in the USA by the value in Asia.In oils, it is roughly 3:1 (1574/487), in Copper 1:1, in Coal: 2:1 (1375/728), in Uranium 8:1 (3208/427), and in Silver 2.5:1 (1789/700).Thus, Uranium shows the highest ratio of the value in the USA to the value in Asia.The answer is Uranium.Tip: In this case, we could have saved a considerable amount of time and avoided unnecessary calculations if we had just looked at the table.The question asks about the ratio of USAs value of extracted produce to that of Asia. This means that the higher the value in the USA and the lower the value in Asia, the greater the ratio.We can easily see that Uranium is both responsible for the highest value in the USA and the lowest value in Asia, thus it is the product with the highest ratio of USAs value of extracted produce to that of Asia11、答案：C55% of the 1995 sample suffered from depression.The sample consists of 2500 participants 0.55 = 1,375 patients suffered from depression in 1995.The answer is 1375 patients.12、答案：DIn 2000, 15% of the sample (2500) suffered from Bipolar disorder= 2500 x 0.15 = 375 patients.In 2005, 5% of the sample (2500) suffered from Bipolar disorder = 2500 x 0.05 = 125 patients. 375-125=250 less patients suffered from Bipolar disorder in 2005 than in 2000.An additional way to do the math is simply look at the graph and note the difference in percentages between 2005 and 2000 which is 10% (15-5). 10% of the entire sample (2500) is 250 and we can calculate this without making use of a calculator.The answer is 250 patients13、答案：AThe original sample includes 2,500 patients. The medication reduces mental illness by 20% in each treatment. The medication is first introducedin 2005: 0.2 x 2500 = 500 cured patients, and a total of 2000 (2500-500) patients remain ill.In 2010another 20% will be cured from the remaining group of 2000 patients: 0.2 x 2000 = 400 additional patients are cured, and a total of 1600 (2000-400) remain ill.In 2015another 20% will be cured from the remaining group of 1600 patients: 0.2 x 1600 = 320 additional patients are cured, and a total of 1280 (1600-320) remain ill.In 2020another 20% will be cured from the remaining group of 1280 patients: 0.2 x 1280 = 256 additional patients are cured, and a total of 1024 (1280-256) remain ill.The answer is1,024Patients.Tip:Another way to solve this question is to immediately calculate the percentage of patients who remain ill in each treatment: if 20% are cured, it means that 80% remain ill each time. Thus, in 2005: (2,500 x 0.8) remain ill. We will have to multiply by 0.8 again for 2010, 2015 and 2020. Eventually, we will have: (2,500 x 0.8 x 0.8 x 0.8 x 0.8), or 2,500 x (0.8)4, which is a much shorter calculation.14、答案：EBetween 2000 to 2005 there was a reduction of 5% from 30% to 25% of patients suffering from Anxiety. In the same time frame the prevalence of OCD remained 10%. Assuming this trend continues - OCD will remain constant at 10% while Anxiety is expected to loose 5% every 5 years. i.e., drop from 25% in 2005, to 20% in 2010, to 15% in 2015, and finally to 10% in 2020. The ratio of Anxiety to OCD in 2020 assuming the present trend continues will be 1:1 (10%:10%).The answer is 1:115、Rate the ratio of Depression to OCD patients in the sample from largest to smallest by years.1985, 1990, 1995, 2000, 20051990, 1985, 1995, 2005, 20002000, 2005, 1995, 1985, 19901990, 2000,1995, 1985,20052000, 2005, 1985, 1990, 1995Cannot Say答案：B The Depression to OCD ratio in 1985 = 60% : 5% = 12 :1 The Depression to OCD ratio in 1990 = 65% : 5% = 13:1 The Depression to OCD ratio in 1995 = 55% : 5% = 11:1 The Depression to OCD ratio in 2000 = 45% : 10% = 4.5:1 = 9:2 The Depression to OCD ratio in 2005 = 60% : 10% = 6:1Therefore, putting the ratio in order from largest to smallest by years =1990, 1985, 1995, 2005, 2000.The answer is 1990, 1985, 1995, 2005, 2000A faster way than finding the ratios for each year would be to note that in 1990, Depression is at its maximum value while OCD is at its minimum value. Therefore, 1990 must be the first year in the list which eliminates three of the five answer choices. Also note that in 2000, Depression is at its minimum value while OCD is at its maximum value. Therefore, 2000 must be the last year in the list which leaves us with only one answer choice.16、答案：CWe first have to determine how many thousands of litres of beer and water were produced. We know the amount of beer produced (8000 litres), which represents 60% of the total output.(Monthly output Torino beer x 100) / 60 = monthly output of beer and water = (8000 x 100) / 60 = 13333 litresSubtract the amount of beer produced from the total amount of water and beer produced to determine the amount of water produced.Monthly output of water and beer monthly output of beer = monthly output of water = 13333 8000 = 5333 litres of waterThe answer is 5333.Another way to tackle this question is by using the triangle trick; step 1- arrange the information in two columns so the real real values are adjacent to their corresponding % (? represent the amount of water):8000 60% ? 40%Step 2- multiply the numbers along the diagonal and then divide by the remaining number:? = (8000/60)*40= The amount of water = 5333 litres.17、答案：CCalculate the 25% increase in marketing and development costs: marketing and development costs x 1.25 = 7 x 1.25 = 8.75Calculate the 35% increase in revenues: revenues x 1.35 = 8 x 1.35 = 10.8Calculate the new ratio for marketing and development costs to revenues = 8.75 / 10.8 = 0.81The answer is 0.81:1.18、答案：DFlightsfrom Sydney arrive to Heathrow at 04:45, 09:15, 13:45 and every4.5 hours until 22:45. Therefore, there is an additional flight at 18:15, and overall there are five daily flights.Flightsfrom SydneyarrivetoGatwick at 04:00, 09:30, 15:00 and 20:30(every 5.5 hours and there is no additional flight). Therefore there are four daily flights.The total number of flights from Sydney to London is 9.The answer is 9.19、答案：AFlights to Sydney leave from Heathrow at 06:00, 12:00,18:00and 24:00. Therefore, the earliest time after 5pm (17:00) from Heathrow is 18:00.Flights to Sydney from Gatwick leave at 10:00, 12:30 and at intervals of 2.30 hours until 22:30. Therefore, the additional flights are at 15:00,17:30and 20:00, so the first flight after 17:00 from Gatwick is at 17:30.The first available flight after 17:00 from London is the 17:30 (5:30 pm) flight from Gatwick.The answer is 17:30.20、答案：DThe first flight to leave London in the morning is the 6:00am from Heathrow. The flight duration is 26 hours, which means the flight arrives at 8:00am GMT the following day. Since Sydney time is GMT + 10, local time will be 18:00 of the next day.The answer is 6 pm + 1 day.21、答案：BFlight duration is 26 hours and the schedule shown is in GMT.We need to look for flights that depart from Sydney and land at Heathrow and Gatwick between 15:00 and 17:30.That is, we can subtract 26 hours from the range of hours mentioned above and get 13:00-15:30. Now we need to look for flights that correspond to this hour range in the To Heathrow and To Gatwick columns. We find the 13:45 to Heathrow(4:30 hrs after 9:15)is due to arrive at 15:45 the following day and the 15:00 to Gatwick(5:30 hrs after 9:30)is due to arrive at 17:00 the following day.Therefore, there are 2 flights22、答案： ESince the flight duration is more than 24 hours, there is no possibility of reaching Australia the same day.The answer is No Flight.23、答案：BIn 2000, Royal Airlines sold 2,005,000 tickets.The number of tickets each airline is expected to sell in 2006 is 10% greater than this number: 2,005,000 x 1.1 = 2,205,500.The combined revenues in 2006 from ticket sales is = (2,205,500 x 75) + (2,205,500 x 232) = 677,088,500 677 millionThe answer is 677 million24、Royal Air Services Passengers(in thousands)答案：BYou can answer this question by looking at the graph, rather than adding up the number of passengers travelling each year. The graph shows us that thered line is highest in 1999-2000. Therefore, Royal Airlines had the greatest number of passengers during this two-year period.The answer is 1999-2000.25、答案：AThe red block represents SUV sales. In the 2002 column, the SUV section spans from 20 to 35.Therefore, 35 - 20 = 15 hundred vessels of SUVs were sold.The answer is 1526、答案：DTo make the calculation easier, well initially use the numbers in the graph without adding the hundreds.The total number of minivan vessels sold between 2000-2004 = 50 + 30 + 20 + 15 + 20 = 135 minivan vessels. The total number of SUV vessels sold between 2000-2004 = (60-50) + (45-30) + (35-20) + (35-15) + (40-20) = 80.The difference bet