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Worked Solutions – Test 7 2021-02-05T14:14:08+00:00

## Worked Solutions – Test 7

#### Question 1 To the nearest whole number, what is the mean percentage decrease of the 3 fish types from 2015 to 2019?

A: 23%

B: 39%

C: 45%

D: 52%

#### Written Solutions

Atlantic salmon have decreased from 25 to 11 tonnes. As a percentage decrease, this can be calculated as follows:

$\dfrac{25-11}{25} \times 100 = 56\%$ decrease

Cod have decreased from 16 to 9 tonnes. As a percentage decrease, this can be calculated as follows:

$\dfrac{16-9}{16} \times 100 = 43.75\%$ decrease

Turbot have decreased from 20 – 13 tonnes. As a percentage decrease, this can be calculated as follows:

$\dfrac{20-13}{20} \times 100 = 35\%$ decrease

Therefore the mean percentage drop of the 3 fish types is:

$\dfrac{56 + 43.75 + 35}{3} = 44.92\%$ or $45\%$ to the nearest whole number

#### Question 2 To the nearest million, what was the value of the average turbot catch per year between 2015 and 2019?

A: £1 million

B: £5 million

C: £6 million

D: £12 million

#### Written Solutions

Over the 5 year period a total of $20 + 12 + 14 + 14 + 13 = 73$ tonnes of turbot were caught.

The average turbot catch was therefore $73 \div 5 = 14.6$ tonnes per year

$14.6 \times 1000 = 14,600 \text{ kilos}$

If turbot sells for £80 per kilo, then the average turbot catch of 14,600 would cost;

$14,600 \times \pounds80 = \pounds1,168,000 \text{ or } 1 \text{ million to the nearest million}$

#### Question 3 For every tonne of fish caught each year, other species are caught accidentally, called bycatch.  The amount of bycatch is typically amounts to 30% of the weight of the salmon, cod and turbot caught.  A fishing company is fined £30,000 for each tonne of bycatch caught.  How much was the fishing company fined in 2017?

A: £285,000

B: £450,000

C: £620,000

D: £525,000

#### Written Solutions

In 2017, the total mass of the fish caught was $24 + 12 + 14 = 50$ tonnes of fish

If 30% of this was bycatch, then the weight of the bycatch can be calculated as follows:

$50 \times 0.3 = 15 \text{ tonnes}$

If the fine is £30,000 per tonne, then the fishing company would be fined:

$15 \times \pounds30,000 = \pounds450,000$

#### Question 4 In 2020, it is predicted that the number of tonnes of cod caught will be 12% greater than the number of tonnes of salmon caught which will itself increase by 20% from the number of tonnes of salmon caught in 2019.  To the nearest £10,000, what will the value of the cod caught in 2020 be if the price of cod falls by 10%?

A: £80,000

B: £129,000

C: £260,000

D: £462,000

#### Written Solutions

In 2019, there were 11 tonnes of salmon caught. If in 2020, this figure increases by 20%, then we can calculate how many tonnes of salmon were caught in 2020 as follows:

$11 \times 1.2 = 13.2 \text{ tonnes}$

We have also been told that the number of tonnes of cod caught is 12% more than the number of tonnes of salmon caught, so the number of tonnes of cod caught in 2020 can be calculated as follows:

$13.2 \times 1.12 = 14.784 \text{ tonnes}$

If the price of cod falls by 10% from the 2019 price, then the price of cod will be:

$£19.50 \times 0.9 = £17.55$

If 14.874 tonnes of cod were caught and sold for £17.55 per kilo, then the value of the cod catch was:

$14.874 \times 1000 \times \pounds17.55 = £259,459.20 \text{ or} £260,000 \text{ to the nearest} £10,000$

#### Question 5 Which country had the biggest percentage increase in income from tourism from 2016 to 2019?

A: Greece

B: Portugal

C: Spain

D: France

#### Written Solutions

In this question, it is probably a lot easier to overlook the fact that the figures present billions since this is a question about proportion and percentages.

Also, Italy doesn’t feature in the answers, so it would be a waste of time calculating this value.

France went from £184.9 billion to £198.3 billion.

As a percentage increase, this can be calculated as follows:

$\dfrac{\pounds198.3\text{ billion}-\pounds184.9\text{ billion}}{\pounds184.9\text{ billion}} \times 100 = 7.25\%$

Spain went from £142.6 billion to £159 billion.

As a percentage increase, this can be calculated as follows:

$\dfrac{\pounds159\text{ billion}-\pounds142.6\text{ billion}}{\pounds142.6\text{ billion}} \times 100 = 11.5\%$

Portugal went from £28.2 billion to £33.5 billion.

As a percentage increase, this can be calculated as follows:

$\dfrac{\pounds33.5\text{ billion}-\pounds28.2\text{ billion}}{\pounds28.2\text{ billion}} \times 100 = 18.79\%$

Greece went from £11.6 billion to £14.2 billion.

As a percentage increase, this can be calculated as follows:

$\dfrac{\pounds14.2\text{ billion}-\pounds11.6\text{ billion}}{\pounds11.6\text{ billion}} \times 100 = 22.4\%$

Greece had the biggest percentage increase.

#### Question 6 To the nearest euro, how much did the average tourist spend in Spain in 2017?

A: €525

B: €860

C: €930

D: €1050

#### Written Solutions

In 2017, the total spending in Spain was €152.6 billion. 164 million tourists visited Spain. To calculate the average spending we need to simply divide the total spending by the number of tourists, although this may be tricky since the values are written as billions and millions.

$€152.6 \text{ billion} \times 1,000,000,000 = €152,600,000,000$ $164 \text{ million tourists} = 164,000,000 \text{ tourists}$

Rather than typing into our calculators $152,600,000,000 \div 164,000,000$, it is probably better if we simply the question to $152,600 \div 164$ and we will get the answer $€930$ to the nearest euro.

#### Question 7 If 35% of the income from Spanish tourism is generated by tourists going to Barcelona, how much will Barcelona generate in 2020, to the nearest billion euros, if it is predicted that Spain’s total income from tourism will increase by 8% from 2019?

A: €35 billion

B: €46 billion

C: €60 billion

D: €62 billion

#### Written Solutions

If Spain’s 2020 income increases by 8% from 2019, the amount they receive can be calculated as follows:

$€159 \text{ billion} \times 1.08 = €171.72 \text{ billion}$

If 35% of this income comes from tourists in Barcelona, then this is relatively straightforward to calculate:

$€171.72 \times 0.35 = €60.102 \text{ billion or } €60 \text{ billion to the nearest billion}$

#### Question 8 If the number of tourists going to Portugal decreases by 5% in 2020 from the average value, how much would each individual tourist need to spend, to the nearest euro, in order for the 2020 tourism income figures to match the figures for 2019?

A: €678 euros

B: €486 euros

C: €735 euros

D: €795 euros

#### Written Solutions

If the number of tourists going to Portugal decreases by 5% from 2019, then the number of tourists in 2020 can be calculated as follows:

$52 \text{ million} \times 0.95 = 49.4 \text{ million tourists}$

In 2019, Portugal received €33.5 billion. If this figure is to be matched in 2020 with fewer tourists, then each tourist would need to spend:

$€33.5 \text{ billion} \div 49.2 \text{ million}$

Clearly you will have to convert the numbers in full before entering them into your calculator:

$€33.5 \text{ billion} = €33,500,000,000$ $49.2 \text{ million} = 49,200,000$

So the division calculation becomes $€33,500,000,000 \div 49,200,000$ giving us an answer of $€678$

#### Question 9 To the nearest hundred thousand tonnes, what was the difference between the number of tonnes of waste which was collected in England between 2018 and 2019?

A: 480,000 tonnes

B: 480,000,000 tonnes

C: 3,900,000 tonnes

D: 39,000,000 tonnes

#### Written Solutions

In 2018 England collected 53% of 26 million tonnes. The exact tonnage that England collected can be calculated as follows:

$26 \text{ million} \times 0.53 = 13.78 \text{ million tonnes}$

In 2019 England collected 59% of 30 million tonnes. The exact tonnage that England collected can be calculated as follows:

$30 \text{ million} \times 0.59 = 17.7 \text{ million tonnes}$

Therefore the difference is $17.7 \text{ million} – 13.78 \text{ million} = 3.92 \text{ million tonnes}$ $3.92 \text{ million} = 3,920,000$ so this is $3,900,000$ to the nearest hundred thousand tonnes

#### Question 10 How many times more waste was collected in Scotland than in Northern Ireland over both years?

A: 2.17 times as much

B: 3.62 times as much

C: 1.86 times as much

D: 4.95 times as much

#### Written Solutions

In 2018, Scotland collected 15% of 26 million tonnes. The exact amount collected can be calculated as follows:

$26 \text{ million} \times 0.15 = 3.9 \text{ million tonnes}$

In 2019, Scotland collected 21% of 30 million tonnes. The exact amount collected can be calculated as follows:

$30 \text { million} \times 0.21 = 6.3 \text { million tonnes}$

Therefore in 2018 and 2019 combined, Scotland collected $6.3 + 3.9 = 10.2$ million tonnes.

In 2018, Northern Ireland collected 10% of 26 million tonnes. The exact amount collected can be calculated as follows:

$26 \text{ million} \times 0.1 = 2.6 \text{ million tonnes}$

In 2019, Northern Ireland collected 7% of 30 million tonnes. The exact amount collected can be calculated as follows:

$30 \text{ million} \times 0.07 = 2.1 \text{ million tonnes}$

Therefore in 2018 and 2019 combined, Northern Ireland collected $2.1 + 2.6 = 4.7$ million tonnes.

To work out how many times more Scotland collected, we simply need to divide the amount Scotland collected by the amount Northern Ireland collected:

$10.2 \text{ million} \div 4.7 \text{ million} = 2.17$

(Again, you can ignore the fact that these numbers are in millions and simply type $10.2 \div 4.7$ into your calculator.)

#### Question 11 What was the total weight of all waste recycled in England in 2018 and 2019 combined?

A: 13.4378 million tonnes

B: 31.48 million tonnes

C: 2.1682 million tonnes

D: 18.6552 million tonnes

#### Written Solutions

In 2018 England collected 53% of 26 million tonnes. The exact tonnage that England collected can be calculated as follows:

$26 \text{ million} \times 0.53 = 13.78 \text{ million tonnes}$

If England managed to recycle 41% of this, then the amount recycled was:

$13.78 \text{ million} \times 0.41 = 5.6498 \text { million tonnes}$

In 2019 England collected 59% of 30 million tonnes. The exact tonnage that England collected can be calculated as follows:

$30 \text{ million} \times 0.59 = 17.7 \text{ million tonnes}$

If England managed to recycle 44% of this, then the amount recycled was:

$17.7 \text{ million} \times 0.44 = 7.788 \text{ million tonnes}$

Therefore the total amount recycled by England in 2018 and 2019 combined was:

$7.788 + 5.6498 = 13.4378 \text{ million tonnes}$

#### Question 12 To the nearest whole number, what was the percentage decrease in weight of recycled waste from 2018 to 2019 for Wales?

A: 9%

B: 12%

C: 16%

D: 24%

#### Written Solutions

In 2018, Wales collected 22% of 26 million tonnes of waste and recycled 44% of this. Therefore, the amount that Wales recycled was:

$26 \text{ million} \times 0.22 \times 0.44 = 2.5168 \text{ million tonnes}$

In 2019, Wales recycled 13% of 30 million tonnes and recycled 57% of this. Therefore, the amount that Wales recycled was:

$30 \text{ million} \times 0.13 \times 0.57 = 2.223 \text{ million tonnes}$

The percentage decrease from 2018 to 2019 can be calculated as follows:

$\dfrac{2.5168 \text{ million tonnes}-2.223 \text{ million tonnes}}{2.5168 \text{ million tonnes}} \times 100 = 11.67\%$ or $12\%$ to the nearest whole number.

#### Question 13  What was the approximate profit made by the Newcastle office as a percentage of total revenue?

A: 65.5%

B: 32.6%

C: 49.7%

D: 56.3%

#### Written Solutions

The total revenue of the Newcastle office was $£4.26 \text{ million} + £5.16 \text{ million} = £9.42 \text{ million}$

The total expenses of the Newcastle office was $£0.85 \text{ million} + £0.9 \text{ million} + £1.5 \text{ million} = £3.25 \text{ million}$

Therefore the total profit for the Newcastle office was $£9.42 \text{ million} - £3.25 \text{ million} = £6.17 \text{ million}$

The question is asking us to calculate the profit as a percentage of the total revenue, which can be calculated as follows:

$£6.17 \text{ million (total profit)} \div £9.42 \text{ million (total revenue)} \times 100 = 65.5\%$ to the nearest given approximation.

Again, in this question, the fact all the figures are in millions is not important since this is a question about proportionality. Forget that the numbers are in millions and the questions is far less complicated.

#### Question 14  What was the approximate ratio of total lettings to sales revenue?

A: 1 : 1.09

B: 1 : 1.12

C: 1 : 1.18

D: 1 : 1.16

#### Written Solutions

The total sales revenue was $£8.25 + £4.26 + £3.79 + £3.25 + £5.45 = £24.95 \text{ million}$

The total lettings revenue was $£7.88 + £5.16 + £4.52 + £3.82 + £6.62 = £28 \text{ million}$

We have a ratio of £24.95 million : £28 million. This can easily be simplified to a ratio of $24.95 : 28$

In order to work out a ratio so that the first part is 1, we need to divide both numbers by 24.95. Clearly when we divide 24.95 by 24.95, we will have 1 for the first part of the ratio share, so all we have to do is divide 28 by 24.95 to work out the second ratio share: $28 \div 24.95 = 1.12$ to the nearest given approximation, so the ratio is $1 : 1.12$

#### Question 15  If the Newcastle office increases its revenue by 12% next year, by what percentage does the Bristol office need to increase its revenue to match the same revenue as the Newcastle office?  Give your answer to the nearest whole number.

A: 27%

B: 32%

C: 16%

D: 24%

#### Written Solutions

The total revenue of the Newcastle office was $£4.26 \text{ million} + £5.16 \text{ million} = £9.42 \text{ million}$

If this is increased by 12%, then the following year, the revenue of the Newcastle office will be:

$£9.42 \text{ million} \times 1.12 = £10.5504 \text{ million}$

The total revenue of the Bristol office is $£3.79 \text{ million} + £4.52 \text{ million} = £8.31 \text{ million}$

Therefore we need to work out the percentage increase for an increase in revenue from £8.31 million to £10.5504 which can be calculated as follows:

$\dfrac{£10.5504-£8.31}{£8.31} \times 100 = 27\%$ to the nearest whole number

#### Question 16  The Plymouth office’s revenue in 2019 was up by 21% from the previous year although expenses were up by 30%.  What was the profit made in 2019?

A: £4,479,200

B: £3,364,750

C: £4,137,895

D: £5,161,700

#### Written Solutions

The Plymouth office’s revenue was $£3.25 \text{ million} + £3.82 \text{ million} = £7.07 \text{ million}$

If the Plymouth office’s revenue was up by 21% the following year, then the revenue for 2019 would be:

$£7.07 \text{ million} \times 1.21 = £8.5547 \text{ million}$

The Plymouth office’s expenses were $£0.64 \text{ million} + £0.72 \text{ million} + £1.25 \text{ million} = £2.61 \text{ million}$

If this figure was 30% greater the following year, then expenses in 2019 would be:

$£2.61 \times 1.3 = £3.393 \text{ million}$

The overall profit is the total revenue minus the total expenses:

$£8.5547 \text{ million} - £3.393 \text{ million} = £5.1617 \text{ million} = £5,161,700$

#### Question 17 Express the combined GDP percentage of Los Angeles and New York in 2016 as a ratio compared to 2019.

A: 1 : 1.102

B: 1 : 1.083

C: 1 : 1.623

D: 1 : 1.78

#### Written Solutions

The combined GDP of Los Angeles and New York for 2016 was $40 + 32 = 72$

The combined GDP of Los Angeles and New York for 2019 was $50 + 28 = 78$

Therefore this can be written as a ratio of $72 : 78$

To make the first share, the 2016 share, 1, we are dividing 72 by 72. Therefore to get the equivalent share for the second share, the 2017 share, we need to perform the same operation (dividing by 72) to the 2017 figure as well.

$78 \div 72 = 1.083$

Therefore, the ratio is $1 : 1.083$

#### Question 18 In 2017, 16% of Los Angeles’ GDP was from car production and had a value of $337.92bn. What was the value of the GDP of the three cities in 2017? A:$4,800bn

B: $560bn C:$3,825bn

D: $978bn #### Written Solutions If 16% of Los Angeles’ car production had a value of$337.92 billion, we need to work out what the value of their total car production (100%) is.

$\text{ If} \337.92 = 16\%$

then $1\% = \337.92 \div 16$

so 100% is:

$\337.92 \div 16 \times 100 = \2112\text{ billion}$

In 2017, Los Angeles was worth 44% of the overall GDP, so 44% of the total GDP of the three cities is $2112 billion. We now need to work out the value of the three cities combined. $\text{ If} \2112 = 44\%$ then $1\% = \2112 \div 44$ so 100% is $\2112 \div 44 \times 100 = \4800 \text{ billion}$ #### Video Solutions #### Question 19 If the total GBP for 2018 was$5215bn and for 2019 $5430bn, what was the percentage increase in the value of Los Angeles’ GDP from 2018 to 2019 to one decimal place? A: 13.2% B: 3.9% C: 12.8% D: 19.6% #### Written Solutions If the total GDP in 2018 was$5215 billion and Los Angeles was 46% of this, then Los Angeles’ value was:

$\5215 \times 0.46 = \2398.9 \text{ billion}$

If the total GDP in 2019 was $5430 billion and Los Angeles was 50% of this, then Los Angeles’ value was: $\5430 \times 0.5 \text{ (or} \5430 \div 2) = \2715 \text{ billion}$ The GDP of Los Angeles increased from$2398.9 to $2715. As a percentage increase, this can be calculated as follows: $\dfrac{\2715-\2398.8}{\2398.8} \times 100 = 13.17\%$ or $13.2\%$ to one decimal place #### Video Solutions #### Question 20 The GDP of the next wealthiest city in 2016, Seoul, was$780bn. This then increased by 5% year-on-year. If added to the data in 2020, what would the GDP of the 4 cities combined be to the nearest billion if Seoul represented 18% of the combined GDP of the four cities?

A: $2688 billion B:$3268 billion

C: $4812 billion D:$5267 billion

#### Written Solutions

If Seoul’s GDP in 2016 was \$780 billion which increased by 5% per year, then 4 years later, the GDP would be:

$\780 \text{ billion} \times 1.05 \times 1.05 \times 1.05 \times 1.05 = \948.094875 \text{ billion}$

If this figure represents 18% of the overall GDP of the four cities combined, then we need to work out what the total (100%) would be.

If $948.094875 \text{ billion} = 18\%$

then $1\% = \948.094875 \text{ billion} \div 18$

so $100\% = \948.094875 \text{ billion} \div 18 \times 100 = \5267.19375 \text{ billion or } \5267 \text{ billion to the nearest billion.}$