Numerical - Mixed Questions13Numerical Reasoning Practice 10

1、（1）答案：DIn order to answer this question we first have to calculate the total spent of education for the different respective countries and then work out the ratio. This gives us the following:Amount spent of education in Czech Republic and Spain:7395 + 46030 = 53,425France: 124,751This gives us the ratio of 53,425: 124,751The simplest way of reducing a ratio to its simplest form is to divide the larger number by the smaller. This tells us what is on each side of the ratio equation in the most simple form.124,751 / 53,425 = 2.3This gives us a ratio of 1 : 2.3（2）答案：AIn order to answer this question we have to go through a number of steps. First of all we need to find GDP rate in 2015 and then use the percentage rate from 2012 to calculate the final answer. This gives the following:Total GDP 2011: millions / percentage of GDP represented in a decimal number (1 = 100%, 0.5 = 50% etc.)Total GDP 2011:23,116/0.0626 = 369,265.18369,265.18*1.025 (to calculate the GDP in 2015) = 378,496.81378,496.81*0.0632 = 23,920.9983 rounded up to 2 decimal places is 23,921.0（3）答案：CTo answer this question we first of all need to work out the total GDP. We can do this as we know both % of GDP invested in education and the amount this was. In order to answer the question we use the reverse percentage formula (Relative amount/ Relative size in decimals = Original amount). There are several steps that we need to go through to answer this question. First of all we need to calculate the total GDP of Poland in 2012. Following this, we need to calculate 31.53% of this figure to give us the correct answer.We therefore have the following: 20,814/ 0.0546 = 381,208.79381208.79*0.3153 = 120,195.13Now we need to convert this number into millions which is done by simply moving the decimal place 6 steps to the right or adding zeroes if there is no decimal. Thus the correct answer is 120 195 131 000（4）答案：DIn order to answer this question we simply need to add the two figures together. This gives us the following: 7,395 + 124,751 = 132,1462、（1）答案：CIn order to calculate this question we must first of all calculate the total number of cars from the two years. Then we can compare the two to arrive at the answer.This gives us:2006: 11,667 + 9,380 + 6 = 21,0532011: 10,510 + 11,763 + 4 = 22,277Now we have to find the correct percentage change. We do this by using the following formula:Increase = (new number original number) / original number *10022,277 21,053 = 1,224(1,224 / 21,053) * 100 = 5.81 %（2）答案：DIn order to answer this question we have to calculate the total number of cars in the country in 2011 and work out the ratio from that. This gives us the following:Total cars 2011: 3,285 + 1,206 + 5 = 4,496This gives us the ratio of 16,808 : 4,496In order to reduce this ratio to its simplest form we first divide the large number by the smaller one: 16,808 / 4,496 = 3.74. This means that the ratio is 3.74 : 1.（3）答案：AThere are two different stages that we need to go through to answer this question:1:Number of Petrol cars and 2:Number of diesel cars.Petrol CarsDecrease = Original Number - New NumberNow we divide the decrease by the original number and multiply the answer by 100:% Decrease = Decrease / Original Number 10010,735 9,565 = 1,170(1170 / 9565) * 100 = 12.23Thus there was a 12.23% increase of petrol cars.We now use this figure to calculate the number of petrol cars in 2013:10,735 * 1.1223 = 12,047.89 which we round up to 12,048 like we do in the rest of the table.Diesel CarsNow we work out the 92% increase for diesel cars:4,416 * 1.92 = 8478.72 which we will round up to 8479.Finally we add the two numbers together to give us the correct answer:8479 + 12,048 = 20,527Although the figures here have to be slightly subjective because we do not know the actual compound growth figures since we have to work with the information in the table we have to assume that they are constant.3、（1）答案：EIn this question we need to calculate the percentage increase spent on private expenditure in Frances health industry. This means that we need to calculate the actual amount spent on private health both in 2009 and in 2012 and then calculate the percentage change.In order to do this we will first calculate the actual figure spent on health in 2009, then the percentage of this figure spent on private health. We need to do the same for the year 2012. Finally we compare the two figures and work out the percentage change.This gives us the following:2009:20,114 * 0.1173 (this is the health expenditureas a % of GDP) = 2,359.37 (this is the total health expenditure)2,359.37 * 0.322 = 759.722012:20,114 * 1.02 = 20,516.28 (this is to calculate the 2% percentage increase)20,516.28 * 0.1175(this is the health expenditure as a % of GDP)= 2,410.662,410.66 * 0.321 = 773.82In order to work out the percentage change we use the following formula: (new number old number) / old number *100(773.82 759.72) / 759.72 *100 = 1.86Please note that in this question we are working solely with percentages, the percentage change between 2 numbers. This being the case we dont need to be specific in the figures and calculate the actual GDP, which can be done by using the Health Expenditure column. It is advisable in these situations to simply select the smaller number of the different possibilities and just work with that. If you did do the calculation using the health expenditure column the answer will be the same.（2）答案：AIn order to answer this question, we need to calculate the total GDP of the two countries and then compare them to each other. We do this by using the health expenditure figures in millions and as a percentage of the total GDP. The reason for this is because we know how much the health expenditure was. We also know how much this was as a percentage of the GDP. The actual percentage of the health expenditure was calculated by using the total GDP figures and the amount spent on health expenditure. Since we only have the end solution we can rearrange the formula to give us the correct solution.This gives us the following:Croatia GDP = 4,849 / 0.0779 = 62,246.47Germany GDP = 387,152 / 0.1175 = 3,294,910.64This gives us a ratio of 62,246.47 : 3,294,910.64In order to simplify this ratio we divide the large number by the smaller one as this is essentially what a ratio is. We want to find out how many of “Croatias GDP” fit into “Germanys”.3,294,910.64 / 62,246.47 = 52.93This gives us a ratio of 1 : 52.93 as for each “Croatian GDP” there are 52.93 “German” ones.Please note if you are unsure of the method used please see the percentage and ratios video tutorials found in your pack.（3）答案：CIn this question we need to calculate the percentage increase of private expenditure. In other words, we need to first of all calculate the total GDP, then, using this figure we can calculate the amount spent on health as a percentage of the GDP. Finally we use this new figure to calculate the percentage spent on private expenditure. This gives us the following:GDP 2009: 141,777 / 0.0962 = 1,473,773.39GDP 2012: 1,473,773.39 * 1.035 = 1,525,355.46Health expenditure 2012: 1,525,355.46 * 0.0962 = 146,739.20Private expenditure 2012: 146,739.20 * 0.766 = 112,402.22Private health expenditure 2009 = (Health expenditure) 141,777 * 0.748 = 106,049.20Now we know the two figures that we need we can calculate the percentage change. In order to work out the percentage change we use the following formula: (new number old number) / old number *100(112,402.22 - 106,049.20) / 106,049.20 *100 = 5.99（4）答案：CTo answer this question we simply need to calculate the labour force of the countries and minus them from each other:EU-28 total labour force: 18838 + 5589 = 24427Labour force for Latvia and France: 73 + 29 + 5207 + 1686 = 699524427 6929 = 17,432（5）答案：CIn order to answer this question we first of all need to calculate the labour force total. Following this we must work out the 3% increase and then calculate the unemployment rate. This gives us the following:Labour force: 3629 + 963 = 45924592 * 1.03 = 4729.764729.76 * (21% 5.5%) = 4729.76 * 0.1554729.76 * 0.155 = 733.11（6）答案：EIn order to answer this question we need to work out the respective ratios and see which of them is the lowest. This gives us:Germany 8.1 : 4.1Croatia 43.0 : 12.7Latvia 28.4 : 11.4Netherlands 9.5 : 6.6France 24.4 : 21.4Using these figures the quickest way to work out the ratio is to divide the larger number by the smallest one. The one with the lowest number will be the country with the lowest unemployment rate to ratio.Germany: 1.98Croatia: 3.39Latvia: 2.50Netherlands: 1.44France: 1.14Thus we can say that the correct answer is France.There is in fact a much quicker way to answer this question and that is by using estimation. By looking at the figures we can see that Croatia and Latvia have large discrepancies between the 2 numbers. This tells us that the ratio will be high. However, this isnt true regarding Germany ,Netherlands and France. Hence we only need to calculate the ratios for these three countries to give us the correct answer. Using estimation is an easy way to save you valuable time when answering these questions.4、（1）答案：DIn order to answer this question we need to calculate the GDP in the two countries. We do this by using the total exports of goods and services column. We know that the number in the exports of goods and services column is a percentage of the total. The percentage of the total is related in the first column. This gives us the following:Total GDP * percentage = Total exports for goods and services.We can convert this equation to the following: Total exports for goods and services / percentage:Italy: 485878 / 0.24 = 2,024,491.6Belgium: 334,405 / 0.74 = 451,898.64Hence we have a ratio of 2,024,491.6 : 451,898.64We can simplify this ratio by dividing the 2 sides of the ratio. i.e. 2,024,491.6 / 451,898.64 = 4.48 This means that there is approximately 4.5 times more in Italy than in Belgium. : 4.5 : 1（2）答案：C Please note that since we are dealing with percentages from beginning to end, it isnt imperative that we know the actual GDP figure. For this reason we can use the GDP per head figure and will get the same answer. The more common form of answering these style of questions is found in other questions in this and other EPSO preparation tests.ExplanationTo answer this question we need to calculate the GDP of 2012 which is 2.5% more than in 2009.GDP: 2009 = 41,130GDP: 2012 = 41,130 * 1.025 = 42,158.25Now we can calculate the amount of exports of services in the two years:2009: 41,130 * 0.28 = 11,516.42012: 42,158.25 * 0.32 = 13,490.64Now we need to calculate the percentage of that that went on ICT service which we do by using the numbers that we have just calculated:2009: 11,516.4 * 0.378 = 4,353.202012 13,490.64 * 0.39 = 5,261.35In order to work out the percentage change we use the following formula:(new number old number) / old number *100(5,261.35 - 4,353.20) / 4,353.20 * 100 = 20.86(3)答案：E In this question, we do not know the GDP levels in 2012 as we have no way of finding this out as we only have the rates in 2009 and not in 2012.5、（1）答案：ETo answer this question we first need to calculate the GDP increase, then work out this amount as a percentage of the world GDP. In truth though, since the GDP level remains constant all we are asked for is to calculate the percentage increase. This gives us:8.3% * 1.04 = 8.63%The full explanation is given below:5,950,936 * 1.04 = 6,188,973.44Now we need to calculate the GDP of the world. There are a few different options available to calculate this but we will choose the EU-28 as our base figures. Since we know that 23.2% of the total GDP is 16,633,942 we simply rearrange the formula in order to arrive at the total world GDP. This gives us:16,633,942 / 0.232 = 71,698,025.86Now we divide the two numbers by each other and multiply by 100 to give us the percentage change.(6,188,973.44 / 71,698,025.86) * 100 = 8.63（2）答案：AIn order to answer the question we first of all need to calculate the population density of the countries, then calculate the GDP and finally work out the ratio. This gives us the following:Land area of Japan, Russia and