Numerical - Mixed Questions13Numerical Reasoning Practice 13

1、（1）答案：108，000To solve this question we need to calculate the number of Northern Shovelers spotted last season for each park separately. Then we need to add up these numbers to a total sum of Northern Shovelers spotted last season in all parks combined. Finally we need to subtract this sum from the total number of Northern Shovelers spotted this season in all parks combined.*Note that the titles states that the numbers are in thousands. Yet, for the sake of convenience we willignorethe thousands in our calculations and add them accordingly in the end.The rows named last seasons spotting as a percentage of this seasons spotting tell us the percentage of birds spotted last season from the birds spotted this season. For instance, the number of Northern Shovelers spotted this season in Exmond was 645 birds. Last season the number of Northern Shovelers was 120% of the 645 birds spotted this season.*Number of Northern Shovelers spotted last season computed for each park separately:Crangmoor: 435*0.4 = 174Exmond: 645*1.2 = 774Pinebrokeshire: 840*0.95 = 798Ponds District: 520*0.85 = 442Old Forest: 240*1.6 = 384*Total number of Northern Shovelers spotted last season: 174+774+798+442+384 = 2572*Total number of Northern Shovelers spotted this season (from the table): 435+645+840+520+240 = 2680*Difference in number of Northern Shovelers spotted: 2680-2572 = 108*Conclusion: 108,000 more Northern Shovelers were spotted last season compared to this season（2）答案：ATo solve this question we need to divide the number of Tundra Swans in each park by the number of other birds in that park (Northern Shovelers + non-migratory birds). Then we need to compare the results to see which park had the largest proportion of swans to all other birds.*Crangmoor: 950/(435+534) =0.98Exmond: 320/(645+967) = 0.19Pinebrokeshire: 165/(840+534) = 0.12 Ponds District: 435/(520+432) = 0.45Old Forest: 80/(240+323) = 0.14*Conclusion: The greatest result is that of Crangmoor; hence this is the correct answer choice.Take notice:Although the question asks you about the greatest percentage of Tundra Swans from all other birds, this is only meant as a distraction. You do not actually need to convert the resulting proportions into percentages (e.g. 0.45 translates to 45%)（3）答案：CTo solve this question we should examine each answer choice separately.*Answer choice (a) states that there was an increase in the number of Tundra Swans spotted in Crangmoor this season, but in the table we can see that there was actually a decrease in the number of swans (last seasons number was 120% of this seasons number). This helps us eliminate this answer choice.*Answer choice (b), like answer choice (a), indicates a wrong direction of change. It states a decrease in the number of swans in Pinebrokeshire while according to the table, there was an increase from last season (last seasons number was 80% of this seasons number). This helps us eliminate this answer choice.*Answer choice (c) indicates a correct direction and a correct absolute change. Calculating the absolute decrease in number of swans:Last seasons number of swans = 950000*1.20 Last seasons number of swans = 1,140,000Difference: 1,140,000-950,000 = 190,000*Answer choice (d) states a correct direction of change (increase in the number of swans in Pinebrokeshire this season). However, note that the absolute number of increase stated is a fraction (495.23), which doesnt make sense since number of swans spotted must be an integer. This helps us eliminate this answer choice.*Answer choice (e) which states that none of the above is correct cannot be true since we found that answer choice (c) is correct. In conclusion answer choice (c) is the correct one.Solving tip:*Do not make any calculations before you examine whether it is possible to eliminate answer choices based on general trends of change or other irrational statements (e.g. an indication of a fraction where only integers can apply- there are only whole birds, not part birds!)* Remember to take into account the correct units (e.g. thousands in this questions case2、（1）答案：ETo solve this question we should calculate the total earnings according to the information in each answer choice:*Answer choice (a) states that among other rooms, 10 suites were rented out in the Flitz Hotel. This is sufficient for us to eliminate this answer choice: Referring to the table, 10 suites in the Flitz Hotel would generate 10*3470 = 34700 pounds in earnings, already over the 29,180 stated in the question.*Calculate answer choice (b) by referring to The Majestic row in the table: 13*1400+4*900+18*410 = 29,180. This result matches exactly the reported earnings in the question. However, since theres an answer choice stating not possible to tell, we must proceed to test all other answer choices.*Examining answer choice (c) for Ville Dartisto we can see that earnings generated from suites exceed the 29,180 stated in the question: 22 suites * 1820=40,040. Therefore, we can rule out this answer choice. Moreover, note that the number of suites mentioned in this answer exceeds the total number of suites in Ville Dartisto hotel to begin with!*Calculate answer choice (d) by referring to The Plaza Blanca row in the table: 6*1230+26*700+8*450 = 29,180. This result matches the reported total earning indicated in the question as well.*Since both answer choices (b) and (d) present possible room combinations that match the exact total earning, we cannot tell which of them was responsible for the earnings. Hence, answer choice (e) is the correct one（2）答案：888To solve this question, we first need to calculate the total price the 10 friends would need to pay for the described combination of rooms and nights. Then we should divide the resulting number by the number of people, i.e. by 10:Calculating the total price for all friends and the described combination: 5 double rooms * 3 nights of normal price * 480 (one double room price at Ville Dartisto) + 5 double rooms* 1 last night* (1-0.3)*480 (price per room accounting for the 30% discount) = 8880* Now, remember to divide this number by the number of friends (10 friends): 8880/10 = 888Note: Alternatively, we could solve this question by making the calculations for one person from the beginning. If a group of 10 friends are renting 5 double rooms, we know there are two people in a room (this could be extracted from the word double). The price for a room per night in Ville Dartisto is 480. For one person, it would be half the price: 480/2 = 240. We know there is a 30% discount for the last night, meaning that one will only pay 70% of the rate. 70% of 240 is 7/10*240 = 168. Total: (240*3)+168 = 720+168=888（3）答案：C To solve this question we should follow two steps. First, we need to calculate the average maintenance cost for one night in a single room in each of the hotels mentioned. We should do this for each hotel separately by calculating 10 percent of the total monthly operation expenses (single rooms maintenance expense) and then dividing the resulting figure by the number of rooms. In the second step we need to calculate the difference between the two maintenance costs (of a single room in each hotel):*For The Majestic hotel- one single room maintenance cost = 0.1 (10 percent)* 390,680 (total monthly operation expenses)/220 (number of single rooms in the Majestic) = 177.58 (average maintenance cost for one single room)*Following the same procedure, this time for The Flitz: 0.1*620,000/420 = 147.61*The difference between the two figures = 177.58-147.61 = 29.973、答案：BExposure and media coverage of tax evasion practices is most likely to affect the discussed companys reputation and therefore cause a substantial withdrawal of contracts by customers. We should therefore look at the graph for a dramatic decrease in number of customers. The decline marked for Telefonicon during 2010-2011 is the most dramatic one and thus this is most probably the company discussed in the question（2）答案：EThis question tries to trick us into relating to the number of customers (indicated in the graph) as equivalent to earnings. However, we cannot do so since other factors may come into play. For example, it is possible that the company that has the most customers (AC&T) is in great debt or that it charges the lowest prices and as a result earns the least. We can therefore deduce that it is not possible to tell which company earned the most at any given time; hence answer choice (e) is the correct answer（3）答案：66.6To solve this question we first need to find out the total increase in number of Telefonicon customers between 2011 and 2014. Then, to calculate the average yearly increase we would need to divide the resulting number by the number of years in that period (3 years):*Referring to the graph we can see that Telefoincon had 300,000 customers in 2011 and 500,000 customers in 2014. I.e. there was an increase of 200,000 customers.*Calculating average yearly increase: 200,000/3 = 66,666.66. Now note that the answer format states thousands after the blank space, so we should only type in66.63、（1）答案：DThe question implies that we should relate to the percentage distribution in determining our answer. Doing so for each secondary school:*Answer choice (a)-Bancroshire: 740*0.5(percent of boys) = 375; 740*0.5(percent of girls) = 375. This is a viable distribution.*Answer choice (b)-Haberdashers Heights: 260*0.4(percent of boys) = 104; 260*0.6(percent of girls) = 156. This is another viable distribution.*Answer choice (c)-Rushden: 800*0.75(percent of boys) = 600; 800*0.25(percent of girls) = 200. Yet another possible distribution.*Answer choice (d)- Tastingham: 621*0.3(percent of boys) = 186.3; We can stop here and conclude that this percentage distribution is the wrong one. A number of people cannot be a fraction- there cant be 0.3 of a boy. Therefore answer choice (d) is the correct one.Solving tip:Before blindly beginning to calculate for each secondary school, it is worthwhile having a quick look through the numbers in the Number of students column searching for something that could raise our suspicion towards one particular school. In doing so we can see that only Tastingham has an odd number of students (621) that should be multiplied by an even percentage number (30 percent). An odd number multiplied by an even fraction (0.30) always yields a fraction- try it out yourself! Even if you didnt realise this, then the mere uniqueness of this number of students (621 being the only odd number) should draw you to start your calculation with this school（2）答案：CExplanation: To solve this question we should first calculate the percentage of failed students for each school separately and then compare the numbers to find the lowest percentage. To do so we need to refer to the first table and sum up, for each school, the total number of failed students across all subjects. Then we need to divide that number by the total number of students as indicated in the lower table.* Answer choice (a)- Bancroshire: (22+53+42+14+12)/740 = 0.19 (19%)* Answer choice (b)-Haberdashers Heights: (42+11+9+22+8)/260 = 0.35 (35%)* Answer choice (c)-Rushden: (2+0+5+12+7)/800 = 0.03 (3%)* Answer choice (d)- Tastingham: (69+123+43+101+22)/621 = 0.57 (57%)*By comparing the results we see that Rushden school had the lowest percentage of students who failed, hence answer choice (c) is the correct one（3）答案：6To figure out the number of girls who failed their history exam at Rushden we first need to find out how many boys failed and then subtract that number from the total number of students who failed (in History). We should follow the next steps:*Referring to the bottom table we will figure out the number of boys who failed in history (at Rushden): 0.75 (75% of students are boys)*800 (number of students)= 600 (number of boys who study at Rushden)*0.01(the given percent of boys who failed in history)*600 (the number of boys as we found out) = 6 (six boys failed in history)*Referring to the upper table: 12 (total number of students who failed their history exam at Rushden) 6 (number of boys who failed) =6 (number of girls who failed their history exam at Rushden- our final answer)4、（1）答案：6258.6To solve this question we need to calculate the CO2emissions for one litre for each car separately and then calculate the difference. We should follow these steps:* For the Bellini S40: The column chart indicates that this car travels 20.2 kilometres on one litre of fuel. Therefore, referring to the table we see that in city driving the Bellini S40 emits 633 grams of CO2per one kilometre. Hence, multiplying these two numbers should give us the total amount of CO2emissions in grams per litre:20.2 (kilometres per one litre) * 633 (grams of CO2per kilometre) = 12,786.6 grams (total amount of Bellini S40 CO2emissions in grams per one litre of fuel in city driving).*Following the same logic for the Namborlini: 12*544 = 6,528 grams* Calculating the differences in emissions: 12,786.6 6,528 =6258.6 is our final answer（2）答案：CTo solve this question we need to calculate as follows:1.5*42(Neo GTI fuel tank capacity)*27(number of kilometres per litre according to the column chart)*378(Neo GTI CO2 emissions in grams for highway driving- according to the table) = 642,978 grams.*Now, noting that the answer choices are stated in kilograms, we should mentally convert our result to 642,978/1,000 = 642.9 kg which corresponds to answer choice (c)（3）答案：CTo solve this question we should follow these steps:*Referring to the table: Half of a Volskart ZOE fuel tank capacity is: 30/2 = 15 litres*Referring to the column chart to determine the amount of kilometres Volskart ZOE drives on 1 litre: 17.2 km*Referring back to the table to find out this cars CO2 emissions for one kilometre in city driving and in highway driving: 120 and 145 grams/km respectively*Formulating our calculation: 15 (half a fuel tank)*17.2 (kilometres per 1 litre)*120 (city drive emission)+ 15 (the other half of the fuel tank)*17.2*145(highway driving emission) = 68,370 grams.*In order to find the average CO2 emissions per litre we now need to divide the number we got by the number of litres in a full fuel tank: 68,370/30 = 2,279 (grams per litre)5、（1）答案：ETo solve this question we need to calculate how many tickets were sold for all MegaPlex theatres combined and then divide the result by the number of theatres in MegaPlex:* It is indicated below the right pie chart that a single ticket in all cinemas was sold for 10. According to this pie chart we also know that MegaPlex earned a total of 3500 thousand pounds from ticket sales. Therefore, we can deduce that the number of tickets sold by MegaPlex was: 3,500,000/10 = 350,000 tickets.*Dividing this number by the number of theatres (as indicated in the left pie chart) we get the average of: 350,000/25 = 14,000. Therefore, we should select answer choice (e)（2）答案：B To solve this question we first need to calculate the average ticket sales for a single theatre in each cinema and then subtract one result from the other to find the difference.*For The Projector cinema: 658,000 (revenues as indicated in the right pie chart)/ 8(number of theatres as indicated in the left pie chart) = 82,250 (average revenue per theatre of The Projector).*Following the same process, this time for the Fellini Cinema: 493,000/6 = 82,166.66*Subtracting one average from the other to find the difference: 82,250-82,166.66 = 83.34 (our final answer)(3)答案：3180000In order to solve this question we simply need to multiply The Park Theatre revenues as presented in the right pie chart by 1.2 (a 20% increase):*2,650,000*1.2 =3180000 pounds; this is our final answer.7、（1）答案：55To solve this question we need to refer to both diagrams. For each branch we should extract the number of complaints filed this year from the left bar chart. Then by referring to the right bar chart we can infer last years number of complaints (using the information regarding the relative change). Finally we will be able to calculate the difference between the numbers of complaints by subtracting one from the other.*For the Peccadillo Street branch: 14 complaints were filed this year (according to the relevant bar in the left diagram). According to the right diagram this number (14) represents an increase of 4 complaints from last year. Therefore, the number of complaints filed last year for this branch was: 14-4 = 10.*Following the same logic for the Darling Cross branch: 98-33 = 65 complaints were filed last year.*Calculating the difference by subtracting one result from the other:65-10 = 55 (the final answer)（2）答案：EIn figuring out relative improvement we should only take into account relative changes from last year and not the absolute number of complaints. We should therefore focus solely on the right diagram. Note that improvement will in fact be denoted by a negative number in the right diagram (indicating that this years number of complaints was less than that of last year). Keeping that in mind we can straight away rule out all the branches showing positive numbers. We remain with the Glass Palace Road branch and the Gater Street branch to choose from.The Gater Street branch column shows a reduction of -42 complaints from last year. This means that the number of complaints last year was 103+42 = 145 and that the relative improv