Numerical - Mixed Questions13Numerical Reasoning Practice 04

1、Country A has two television channels: BBC1 and BBC4.The following charts specify the rating percentage (out of population) in each of the channels, from 8:00 - 24:00. (Rating percentage is the percent of people of the countrys population watching the channel).（1）答案：BThe charts are in percentage form but since they relate to the same whole (total population), they can be compared.The correct answer is (B).At 17:00, BBC1 has 30% rating and BBC4 has 40% rating. Since there is one single population we can compare the channels and find that BBC4 has 10% more rating (note that we cannot tell how many people 10% are).（2）答案：AThe correct answer is (A).We need to find on what time BBC4 has 25% rating: between 12:00 - 14:00.On those hours BBC1 has 15% rating.（3）答案：CThe correct answer is (C).Well place 100 as the number of population in Limbo so that we can find the number of people watching at a certain time (that number will be equal to the percentage).Answer (A): at 9:00 BBC1 has 15 viewers, and at 11:00 BBC1 has 20 viewers, which are 5 viewers more. Those 5 are a third of the viewers at 9:00 (15 viewers).Answer (B): at 13:00 BBC1 has 15 viewers, and at 15:00 BBC1 has 30 viewers, which are 15 viewers more. Those 15 make a 100% of theviewers at 13:00 (15 viewers).Answer (C): at 17:00 BBC1 has 30 viewers, and at 19:00 BBC1 has 45 viewers, which are 15 viewers more. Those 15 make 50% of the viewers at 17:00 (30 viewers). This is the correct answer.Answer (D): at 19:00 BBC1 has 45 viewers, and at 21:00 BBC1 has 30 viewers which are actually less viewers.（4）答案：BThe correct answer is (B).At 9:00 BBC4 has 10% rating. At 11:00 BBC1 has 20% rating (twice as many). Therefore, If BBC4 has 450 thousand viewers (at 9:00), BBC1 has 900 thousand viewers at 11:00 (twice as many).2、Each one of the 6 economists of The Investor company (marked A-F) has received a budget which he can divide to 5 investment channels:The graph below describes how each of the economists has chosen to divide his budget.Economist As budget is X.The budget of economist C and economist F is 2X each.（1）答案：DEconomist A invested 30% of his budget (X) in bonds: (30/100)*X = 30X/100.Economist C invested 10% of his budget (2X) in bonds: (10/100)*2X= 20X/100.Economist F invested 20% of his budget (2X) in bonds: (20/100)*2X = 40X/100.Altogether they have invested 0.9X in bonds.(30X/100+20X/100+40X/100=0.9X)3、答案：ENumber of robberies in year 1: 0.9 million.Rounded to the nearest million = 1 million = 0.001 billion.4、The following diagram describes the mortgage refunds in D BANK.The mortgage is being refunded in 10 equal annual refunds, and each one of them is made up of interest and fund. The dark part of the diagram describes the interests percentage out of the refund, whereas the white part describes the funds percentage.（1）答案：CThe correct answer is (C).In year seven the white area of the diagram is above 30%, and the dark area of the diagram, stating the interest, is 30%.（2）答案：CThe correct answer is (C).Were looking for a year in which the fund (the white area) intakes 80% thus the interest (the dark area) takes up 20%. That year is year eight.（3）答案：CThe correct answer is (C).The first year that had more fund than interest return is the year where the fund took up more than 50% and the interest less than 50%. In year five the fund and the interest made 50% each and so starting year six there was more fund than interest return.（4）答案：DThe correct answer is (D).Well calculate each year separately:First year: the interest is 90% of the refund (which is 10,000 GBP) (90/100)*10,000=9,000Second year: the interest is 80% of the refund (which is 10,000 GBP) (80/100)*10,000=8,000Third year: the interest is 70% of the refund (which is 10,000 GBP) (70/100)*10,000=7,000The interest David payed thus far is 24,000 GBP (9,000+8,000+7,000)5、*The ratio of men:women in both countries is 48%:52% respectively.（1）答案：CThe answer can be easily discovered without any calculations. Nepal has fewer people than Thailand. If there is a similar percentage, Nepal will naturally have a lower number of people that correspond to that percentage.Since Nepal has less than half the population that Thailand does, and in 1995 had a similar percentage of literate females which was the lowest of any given time frame, Nepal will have the lowest number that year.Note: Always pay attention to the asterisks! In this question, the asterisk provides us with the ratio of men to women. Without this piece of information, the answer would be Cannot say.6、*Percentages reflect the relative number of tables out of all chairs and tables sold that month（1）答案：DThis isa question that can be answered by estimation. Look for low numbers - both in terms of percentage and in in terms of total sales. This would immediately rule out some answer choices.Choosing the long way, the number of tables sold is dependent on the number of all furniture sold, and the percentage of the tables from all furniture. A calculation for each month shows:Month 1: 0.3*250 = 75Month 2: 0.2*200 = 40Month 3: 0.3*200 = 60Month 5: 0.1*250 = 25Month 6: 0.2*225 = 45Therefore, the lowest number of tables was sold in month 5.（2）答案：CThe total number of tables sold in month 2 is: 0.2*200 = 40.The price of one table was $180 in month 2, and $140 in month 5. Since the same amount is bought and sold at each transaction, we can just find the differences between the prices and multiply it by the number of tables.(180-140)*40 = $1,600.7、Mental Performance Differences Between Age Groups (n= # of people surveyed, M=mean, SD=standard deviation)*Success rate = (average score/maximal score)（1）答案：CSuccess rate = (average score/maximal score).The table specifies the maximal score for the vocabulary test: 33The success rate of young people: 15.7/33 = 0.4757 - 47.57%The success rate of older people: 23.2/33 = 0.7030 - 70.3%The absolute difference between the two age groups: 70.3% - 47.57% = 22.73%Note: as the question requires calculating the absolute difference between two rates, it may also be regarded as a percentage points question.The term percentage points refers to the absolute difference between two percentage values.（2）答案：AThe weighted average success rate can be found by giving each experiment group a new average score which is proportional to the size of the two groups combined.Number of young people in experiments 1 and 2 combined: 20+15=35.Success rate = average score/maximal test scoreGroup 1:Proportinal size: 20/35.Average success rate: 99.5/130=0.765=76.5%Group 2:Proportional size: 15/35Average success rate: 94.2/130=0.725=72.5%Weighting:(15/35)*72.5 + (20/35)*76.5 758、*gha= global hectare.（1）答案：BWe need to calculate how many global hectares are occupied by USA and Japan, and then compare between them on a percentage change basis.USA: (300 mil) x (8 gha/person)=2,400 global hectaresJapan: (125 mil)x(5 gha/person)=625global hectares% change = (Difference/Original)x100% = (2400 - 625)/625x100% = (2400/625)-(625/625)x100% =(2,400/625)-1x100% = 284%（2）答案：BThis question is not just about adding up all the ecological footprint values and then dividing that of Japan by the calculated sum. We must bring into consideration the population of each country:Gha = Ecological Footprint x PopulationSouth Africa: 50x2.5 = 125France: 60x5 = 300Romania: 25x2.5 = 62.5Germany: 75x3 = 225Japan: 125x5 = 625USA: 300x8 = 2400Total gha: 125+300+62.5+225+625+2400 = 3737.5.Japan: 625Japans ratio: 625/3737.5 = 0.167The correct answer is approximately 17%.（3）答案：AFirst we need to calculate the total gha output for each country.South Africa: 50 * 2.5 = 125France: 60 * 5 = 300Romania: 25 * 2.5 = 62.5Germany: 75 * 3 = 225Japan: 125 * 5 = 625USA: 300 * 8 = 2400(Note that since all population numbers are in millions, the millions can be cancelled out to simplify the calculations.)In order to calculate the weighted average, we must find the total population so that we can find the percentage of the total population represented by each country. The total population (in millions) is: 50 + 60 + 25 + 75 + 125 + 300 = 635. Therefore, the fraction of the total population represented by each country is as follows.South Africa: 50 / 635 = 10/127France: 60 / 635 = 12/127Romania: 25 / 635 = 5/127Germany: 75 / 635 = 15/127Japan: 125 / 635 = 25/127USA: 300 / 635 = 60/127The weighted global average equals the sum of each countrys total gha output multiplied by the countrys fraction of the total population. Therefore, the weighted global average equals: (125 * 10/127) + (300 * 12/127) + (62.5 * 5/127) + (225 * 15/127) + (625 * 25/127) + (2400 * 60/127) = 168162.5/127 = 1324.114.Since Romanias total gha output is only 62.5, which is less than the weighted global average, Romania will not pay any fine.A faster method:While we can calculate the weighted average of all countries, its better to examine the data first. A fine will be incurred if the value for a country is above the weighted average. Romania has the lowest value, alongside South Africa, and therefore at the lowest risk for a fine. Given the fact that there is more than two different values in a calculation of an average, the lowest value will always be below average.Secondly, the USA has roughly twice the total population of the other countries combined, while also having the highest gha value. This will affect the weighted average and increase it even higher, as the USAs relative weight to other countries is substantial.An educated guess would be that Romania would incur no fine.9、Prices for specific advertising products (in GBP)1. BrandMad offers 10% discount on any purchase above 1000.2. HIP offers 20 free match boxes for each 1000 lighters.3. Big-time offers 15% discounts on annual contracts.（1）答案：BSince we are dealing with equal time periods, there is no need to take into calculation the number of months! Simply look for the price difference and the fact that Big-time offers 15% percent off for annual campaigns (1920*0.85)-1310/1310 =0.2458 = 24.58%.A quicker way to calculate percentages is:(1920*0.85/1310)-1 = 0.2458=24.58