Numerical - Mixed Questions13Numerical Reasoning Practice 12

1、（1）答案：BTo solve this question we need to calculate the sales income for each theme park separately and then compare the results. To do this we should refer to the two bottom rows of the chart. Since the last row indicates total balance (which is equal to sales-costs) and the row above it shows total costs, we can use the data in these rows to extract the sales income for each park.*For instance, calculating for the Andromeda Park: -24 (total quarter balance) = sales-2,446(total costs);sales = -24+2,446 = 2,422 (thousand pounds). Continuing with the other parks, following the same process:*7 flags: 14,844 = sales-10,587;sales = 14,844+10,587 = 25,431*Dilniland: -234 = sales-1,233;sales = -234+1,233 = 999*ZumbaWorld: 12,343 = sales-1,111;sales = 12,343+1,111 = 13,454*RollerCoaster Fiend: -2 = sales-10,998;sales = -2+10,998 = 10,986*Finally comparing the results we see that 7 flags park had the largest sales income, which means that answer choice (b) is the correct one.（2）答案：DTo solve this question, we need to calculate the earnings made by the theme park in question.*To do this, we should simply multiply the two figures stated, namely 31*434,000 = 13,454,000. (You can calculate 31*434 and add three zeros to the end to make this easier.)*Secondly, we need to compare this number to the earnings made by each park to find a match. As we have already calculated all incomes for the previous question, we can see that the number calculated using the data from this question matches the earnings made by ZumbaWorld. Therefore, answer choice (d) is the correct answer.（3）答案：BAlternatively, you could solve this question using the concept of balance.Total quarter balance = sales-costsThe reduction in the insurance costs results in a reduction in total costs. The sales stay constant, consistent with this change. If total costs are lower, the balance would therefore be higher. For example: if one decides to spend less money on outings this month and his/her income and other expenditures stay the same, it will lead to having a more positive balance in ones account. We know that the insurance is reduced by 60%, which is a 0.6*1455=873 thousand pound reduction. Andromeda Park will have an extra 873 thousand pounds of income. The original balance was -24 thousand pounds. Therefore, the current balance is -24+873=849 thousand pounds = 849,000.2、（1）答案：1985To find out when all countries had the smallest range of emissions we should look in the graph for a point where the points representing the countries emissions were nearest to each other (vertically). There is in fact no need to take into account any numbers or to make any calculations. This point in time was 1985 and therefore the correct answer choice is (c).（2）答案：CTo solve this question we should refer to the graph and check the difference in emissions between the two years mentioned in each answer choice separately. Then we should compare our results and choose the one representing the smallest change.*For answer choice (a)- Bardonia: In 2000 the graph reads 2 and in 1985 it reads 6. The change was therefore 2-6= -4. However note that the question asks about absolute (!) change, so for this question that would be 4. Following the same logic for the next answer choices:*Answer choice (b)- The Near West: 16-7 = 9*Answer choice (c) Featherlands: 4-4 = 0*Answer choice (d)- United Republics: 8-2 = 6*Comparing the results we see that answer choice (c) relates to the smallest change in emissions and is the correct answer. Note that the full calculations were made here for explanatory purposes. It is advised to solve this kind of question merely by observing the lines in the graph (noting that the Fetherlands line in the indicated time period increases and then decreases back to the same height and therefore represents no change in emissions).（3）答案：27To solve this question we should first mentally extend the lines to 2020 as instructed; maintaining absolute changes in opposite directions.*These would be the different line positions in 2020: Bardonia = 4, Featherlands = 4; United Republics = 6 and The Near West = 13. As we can see all lines return to their 2010 positions (understanding this one can simply make the calculation based on the 2010 positions).*Summing up the numbers we get:4+4+6+13 = 27 which is the final answer4、（1）答案：EIn theory, to calculate the proportion of the working force to the overall population in each country we would need to divide the number representing the workforce in the country by the number representing the overall population in the same country. The question tries to trick you into referring to the graph and pick the county with the highest line as the correct answer. This is wrong as it is not equivalent to the proportions that the question asks about. Since we dont know what the overall populations in each county are, we cannot infer the discussed proportions. The correct answer choice is therefore (e).（2）答案：0To solve this question, we need to mentally extend the Canadria line and the Zingdonia line into 2040 following the same linear trends seen from 2000 to 2020.*The Canadria line ascended by one unit between 2000 and 2020. By 2040, it should therefore ascend by another single unit, from 3 to 4.*The Zingdonia line descended by one unit between 2000 and 2020. By 2040, it should therefore descend by another single unit, from 5 to 4.*The two lines will thus meet at 4, and so the difference between them will be 0, which is the final answer（4）答案：ETo solve this question we should first calculate the proportion of the working force to the overall population in 1960 in Glendon Islands. Then we need to use this proportion to calculate the size of the overall population in 1980.*Calculating the proportion of the working force to the overall population: It is given that the Glendon Islands population in 1960 was 1.5 million. Referring to the graph we see that in that year the size of the working force there was 1 million, so the proportion was: 1/1.5 = 2/3.*Next, calculating the size of the overall population in 2000 knowing that the proportion of 2/3 remained the same: 2/3 = 2/overall population; overall population = 2*3/2 = 3 million. This means that the correct answer choice is (e).4、（1）答案：DTo solve this question we need to refer to the ABC Bros. row in the table and note that ABC Bros. stock was bought for 483 pounds. Then using the conversion rate stated below the chart we should convert the 483 pounds to USD and multiply by 100 to find the sum in cents: 483*1.59207*100 = 76,896.98 USD cents. Therefore answer choice (d) is the correct one.（2）答案：1039.5To solve this question we need to realize that if a single units price is expected to decrease by 10% (as indicated in the fourth column), then the overall last months cost should decrease by 10%. Therefore, we should take the overall last month cost and multiply it by 0.9 (90% - a 10% reduction):1155*0.9 = 1039.5 pounds, which is the final answer.（3）答案：ATo solve this question we should follow these steps:*First we need to calculate the price per Global Exchange stock unit. Referring to the table we should divide the relevant last month cost by the number of units purchased. Note that a single units price should be calculated per the original amount of stocks bought!This would yield: 4289.76/1324 = 3.24 pounds. *Now we should calculate the next months price per unit applying the relevant expected change from the table: 3.24*1.25(a 25% increase) = 4.05 pounds.*If 50% more Global Exchange units were bought last month, there would be 1324*1.5 = 1,986 units.*The next month expected value would therefore be: 1,986*4.05 = 8,043.3 pounds, our final answer5、答案：840We should calculate the monthly caloric exertion for each sport activity separately and then subtract one result from the other in order to get the difference. The main idea in this question is to extract the data correctly when referring to the table and to multiply correctly in order to reach to monthly terms.*The monthly exertion resulting from high intensity swimming would be: 704(high intensity caloric exertion per hour)*3(the recommended three hours of workout per week)*4(four weeks a month) = 8,448 calories a month.*Applying the same logic for the low intensity running: 774*3*4 = 9,288 calories a month.*The difference between the two would therefore be: 9,288-8,448 = 840 calories which is the final answer（2）答案：BWe should follow the next steps to solve the question:*We would first need to calculate the caloric exertion per hour for an individual weighing 72 Kg. To do so we should add 10% for the increase from 70 Kg to 71 kg and then again for the increase from 71 Kg to 72 Kg. Calculating for the first increase: 422*1.1 = 464.2. Then for the second increase: 464.2*1.1 = 510.62 calories per hour.*Now we should use the result to calculate for a weekly caloric exertion: 510.62*1.5(a hour and a half weekly exercise time) = 765.93 calories a week; the final answer.（3）答案：BTo solve this question we need to calculate the caloric exertion for each of the four activities stated in the answer choices, assuming workout at high intensity and half the recommended weekly workout time. Then well need to pick the lowest number:*Cycling: 712(caloric exertion in high intensity per hour)*2(recommended workout time for this activity)*0.5(half the time) = 712 calories a week*Running: 1056*1*0.5 = 528 calories a week*Walking: 443*3*0.5 = 664.5 calories a week*Swimming: 704*3*0.5 = 1,056 calories a week*As we can see running in high intensity for half the recommended weekly time will engender the least caloric exertion. Thus, the correct answer choice is (b)6、（1）答案：CTo calculate the average we should first calculate recruiting expenses for each year separately. Then we would need to add up the expenses across the three years and divide the result by the number of years in that time period (3).*Calculating the recruiting expenses for 2012: 423(as indicated in the line graph for this year)*0.06(6% is the relative share of expenses invested in recruitment according to the pie chart) = $25.38 million*Calculating the same way for 2013: 512*0.06 = $30.72 million*and for 2014: 605*0.06 = $36.3 million*Calculating the average expense on recruitment per year between 2012-2014: (25.38+30.72+36.3)/3 = $30.8 million; answer choice (c) is therefore the correct answer（2）答案：BTo solve this question we should first calculate the expense on production for each year. Then we would need to subtract one result from the other to get the difference.*The expense on production in 2011: 123(as indicated for this year in the left graph)*0.3 (30% is the productions share in expenses according to the pie chart) = $36.9 million *Calculating the same way for 2010: 356*0.3 = $106.8 million*Finally, calculating the difference: $69.9 million, which means that answer choice (b) is the correct answer choice（3）答案：196To solve this question we need to follow the next steps:*First we would need to determine what the absolute increase from 2011 to 2012 was. Referring to the line graph we can see it would be 423-123 = $300 million.*It is stated that the increase from 2014 to 2015 would be 25% more than that seen between 2011 and 2012. Therefore, the 2015 total expense would be: 605(the 2014 expense)+300 (the prospective increase as we calculated)*1.25(a 25% increase) = 980$ million.*Since the question asks specifically about the expense on research in 2015 so we should calculate this referring to the relevant share of research indicated in the pie chart:980*0.2 (20%) = 196 million USD which is the final answer7、（1）答案：CTo determine which toy will run out of stock by the end of November we need to subtract the predicted demand from the current stock for each month from August through November, for each toy separately. The relevant data is found in both charts.*Calculating for the Teddy Bear Xtreme: 3,200(current level of stock)-400-500-600-1,000(predicted demand for August through November) = 700. The fact that the result is positive means that this toy will not run out of stock by the end of November.*Following the same process for the rest of the toys:* The Horbit Doll: 5,220-750-800-1,000-1,800 = 870 (will not run out of stock)*Dino: 350-100-200-400-900 = -1,250. The Dino toy will run out of stock well before the end of November. There is no need to proceed checking for the other toys as answer choice (c) is the correct one.*If you have time you can continue the calculations for the rest of the toys in order to verify your choice. Calculating for My First Science Kit: 1,200-20-100-300-700 = 80 (will not run out of stock).*Tycoon Board Game: 1,600-250-300-400-450 = 200 (will not run out of stock).*Solving tip: Since the Dino has the lowest initial stock level it is reasonable to guess that it will run out of stock the quickest. It is therefore worthwhile to begin your inspection with this toy. One can quite quickly make the calculations starting off with an initial low number such as 350（2）答案：90Stopping for a minute to think about this question will help you realize that no calculations are in fact necessary. If total sales fell short 10% below the total predicted demand, then the percentage of actual sales out of the predicted demand would simply be 90% (10% short).*This question tries to trick you into making elaborate calc