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Worked Solutions – Test 5 2021-02-05T14:13:58+00:00

## Worked Solutions – Test 5

#### Question 1

As a percentage to the nearest whole number, how much more expensive is it to purchase a £180,000 property with a 5% deposit and having a 35 year mortgage (including the initial costs of the mortgage) compared to purchasing the property outright?

A: 65%

B: 72%

C: 88%

D: 105%

#### Written Solutions

If you are paying 5% on a £180,000 property for 35 years, you would end up paying:

($\pounds803 \times12 \times35) + \pounds1800 = \pounds339,060$

This would therefore cost $\pounds339,060 - \pounds180,000 = \pounds159,060$ more than buying the property outright.

We can calculate how much more expensive it is as a percentage as follows:

$\pounds159,060 \div \pounds180,000 \times100 = 88.36\%$ or $88\%$ to the nearest whole number.

#### Question 2

A buyer decides to opt for a 15% deposit on a £180,000 house instead of a 5% deposit. What is the percentage increase in the total initial cost to the nearest percentage point?

A: 163%

B: 165%

C: 167%

D: 169%

#### Written Solutions

With the 5% deposit mortgage, the deposit amount would be:

$\pounds180,000 \times0.05 = \pounds9000$

We also need to factor in the initial cost of £1800, so the total payable at the start of the mortgage would be:

$\pounds9000 + \pounds1800 = \pounds10,800$

With the 15% deposit mortgage, the deposit amount would be:

$\pounds180,000 \times0.15 = \pounds27,000$

We also need to factor in the initial cost of £2100, so the total payable at the start of the mortgage would be:

$\pounds27,000 + \pounds2100 = \pounds29,100$

The percentage increase can be calculated as follows:

$\dfrac{\pounds29,100 - \pounds10,800}{\pounds10,800} \times100 = 169.4\%$ or $169\%$ to the nearest percentage point.

#### Question 3

A first-time buyer earns £25,000 per year and saves 18% of this each year. How long will it take to save up the 15% deposit for a £240,000 property?

A: 6 years

B: 8 years

C: 9 years

D: 11 years

#### Written Solutions

If a first-time buyer manages to save 18% of £25,000 every year, then he would save:

$\pounds25,000 \times0.18 = \pounds4500$ per year

A 15% deposit for a £240,000 property would cost:

$\pounds240,000 \times0.15 = \pounds36,000$

Therefore, it would take the buyer the following number of years to save this deposit:

$\pounds36,000 \div \pounds4500 = 8$ years

#### Question 4

If monthly payments on a £300,000 property on a 25 year mortgage were to increase by 2%, what is the difference in cost of the overall mortgage repayments between a mortgage with a 5% deposit and a 15% deposit?

A: £108,687

B: £132,673

C: £145,985

D: £148,410

#### Written Solutions

Monthly payments on a 5% mortgage are £1574. If they were to increase by 2%, then they would become:

$\pounds1574 \times1.02 = \pounds1605.48$ per month

For the duration of the mortgage this would work out as:

$\pounds1605.48 \times12 \times25 = \pounds481,644$

Monthly payments on a 15% mortgage are £1089. If they were to increase by 2%, then they would become:

$\pounds1089 \times1.02 = \pounds1110.78$ per month

For the duration of the mortgage this would work out as:

$\pounds1110.78 \times12 \times25 = \pounds333,234$

Therefore, the overall difference in monthly mortgage repayments is:

$\pounds481,644 - \pounds333,234 = \pounds148,410$

#### Question 5

Which country had the largest percentage increase in the production of cars between 2018 and 2019?

A: Japan

B: China

C: Germany

D: India

#### Written Solutions

Japan went from producing 7.34 (hundreds of thousands) to 8.35 (hundreds of thousands). As a percentage increase this is:

$\dfrac{8.35 - 7.34}{7.34} \times 100 = 13.7\%$ increase

China went from producing 22.19 (hundreds of thousand) to 24.81 (hundreds of thousands). As a percentage increase this is:

$\dfrac{24.81 – 22.19}{22.19} \times 100 = 11.8\%$ increase

Germany went from producing 4.92 (hundreds of thousand) to 5.65 (hundreds of thousands). As a percentage increase this is:

$\dfrac{5.65 - 4.92}{4.92} \times 100 = 14.83\%$ increase

India went from producing 3.61 (hundreds of thousand) to 3.95 (hundreds of thousands). As a percentage increase this is:

$\dfrac{3.95 - 3.61}{3.61} \times 100 = 9.4\%$ increase

Therefore Germany had the largest percentage increase.

#### Question 6

In 2019, 60% of Japan’s cars are produced by Ichiban.  An Ichiban car costs on average £9,385 to produce and is sold on average for £13,965.  How much profit did Ichiban make in 2019?

A: £826,000,500

B: £932,768,000

C: £2,294,580,000

D: £3,565,465,000

#### Written Solutions

In 2019, Japan produced 8.35 hundreds of thousands of cars. If 60% were from the manufacturer Ichiban, that means that the following number of cars were produced by Ichiban:

$8.35 \times0.6 = 5.01$ hundreds of thousands of cars produced

The profit per car can be calculated as follows:

$\pounds13,965 - \pounds9,385 = \pounds4,580$

Therefore the total profit on all the cars they produced was:

$\pounds4580 \times 5.01 = \pounds22,945.8$ (hundreds of thousands)

$\pounds22,945.8 \times100,000 = \pounds2,294,580,000$

(Of course you could multiply the 5.01 by 100,000 prior to this final calculation if this seems more logical to you.)

#### Question 7

In 2019, 32% of China’s cars and 46% of Japan’s cars were exported to Europe.  If on average each car generates a profit of £4,625, what is the total profit of Japan and China’s exports in euros if there is an exchange rate of €1.18 = £1?  Give your answer to one decimal place.

A: €3.2 billion

B: €5.1 billion

C: €4.5 billion

D: €6.4 billion

#### Written Solutions

In 2019, China produced 24.81 hundreds of thousands of cars. If 32% of these were exported, we can work out exactly how many cars this is:

$24.81 \times0.32 = 7.9392$ (hundreds of thousands)

In 2019, Japan produced 8.35 hundreds of thousands of cars. If 46% of these were exported, we can work out exactly how many cars this is:

$8.35 \times0.46 = 3.841$ (hundreds of thousands)

The total number of cars exported by both countries combined is:

$3.841 + 7.9392 = 11.7802$ (hundreds of thousands)

If the average profit per car is £4,625, then the total profit is:

$11.7802 \times100,000 \times\pounds4,625 = \pounds5,448,342,500$

In euros, this can be calculated as follows:

$\pounds5,448,342,500 \times €1.18 = € 6,429,044,150$ or $€6.4$ billion to one decimal place.

#### Question 8

Germany intends to continue its car production growth by ensuring that the growth between 2019 and 2020 increases by the same percentage (rounded to the nearest percentage point) as the increase between 2018 and 2019.  How many cars will Germany produce in 2020?

A: 649,750

B: 975,632

C: 6,497,500

D: 9,756,320

#### Written Solutions

In 2018, Germany produced 4.92 hundreds of thousands of cars and 5.65 in 2019.

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

$\dfrac{5.65 - 4.92}{4.92} \times100 = 14.83\%$ increase or $15\%$ rounded to the nearest percentage point (we have already worked this out in question 5 incidentally)

If Germany produces 5.65 hundreds of thousands of cars in 2019 and produces 15% more the following year, then the number of cars it produces in 2020 can be calculated as follows:

$5.65 \times1.15 \times100,000 = 649,750$

#### Question 9

To the nearest percentage point, what was Real Madrid’s percentage of overall transfer spending of all 5 teams in this 2 year period?

A: 23%

B: 24%

C: 29%

D: 32%

#### Written Solutions

Real Madrid’s transfer spending was $\pounds2100 + \pounds2350 = \pounds4450$ (since this question is about proportion / percentages, it will be easier to ignore the fact that these figures are in hundreds of thousands of pounds).

The total spending of all 5 clubs was $\pounds4450 + \pounds1850 + \pounds1900 + \pounds1950 + \pounds2250 + \pounds1400 + \pounds1500 + \pounds1300 + \pounds1600 = \pounds18,200$

Real Madrid’s percentage can be calculated as follows:

$\pounds4450 \div \pounds18,200 \times 100 = 24\%$ (to the nearest whole number)

#### Question 10

Barcelona plan to drastically reduce their transfer policy and hope to reduce 2019 transfer fees by 35% in 2020.  If they purchase 5 players in 2020, what is the average player transfer fee in 2020?

A: £2.925 million

B: £4.278 million

C: £29.25 million

D: £42.78 million

#### Written Solutions

Barcelona’s transfer fees in 2019 were £2250 (hundreds of thousands). If they wish to reduce this by 35% for 2020, this can be calculated as follows:

$\pounds2250 \times0.65 = \pounds1462.5$ (hundreds of thousands)

If they purchase 5 players for this amount, then the price of one player is:

$\pounds1462.5 \div 5 \times 100,000 = \pounds29,250,000 = \pounds29.25$ million

#### Question 11

One football agent, Agent A, received 65% of all fees that AC Milan paid to agents in 2019.  If a football club pays 18% of a transfer fee to an agent, how much did Agent A receive in 2019?

A: £9.53 million

B: £18.72 million

C: £23.75 million

D: £44.31 million

#### Written Solutions

If a club pays 18% of a transfer fee to an agent, that means that AC Milan paid 18% of £1600 (hundreds of thousands) to agents in 2019.

$\pounds1600 \times0.18 = \pounds288$ (hundreds of thousands)

If Agent A received 65% of this sum, this his share can be calculated as follows:

$\pounds288 \times0.65 \times100,000 = \pounds18,720,000$ or $\pounds18.72$ million

#### Question 12

In 2018, the 5 clubs signed 28 players in total and 31 players in total in 2019.  What was the approximate difference in average player cost between 2018 and 2019 to the nearest €100,000?

A: €200,000

B: €300,000

C: €400,000

D: €500,000

#### Written Solutions

In 2018, the 5 clubs spent $\pounds1850 + \pounds2100 + \pounds1950 + \pounds1400 + \pounds1300 = \pounds8600$ (hundreds of thousands) on players.

If this was spent on 28 players, then the average cost of a player was:

$\pounds8600 \div 28 \times 100,000 = \pounds30,714,285.71$

In 2019, the 5 clubs spent $\pounds1900 + \pounds2350 + \pounds2250 + \pounds1500 + \pounds1600 = \pounds9600$ (hundreds of thousands)

If this was spent on 31 players, then the average cost of a player was:

$\pounds9600 \div 31 \times 100,000 = \pounds30,967,741.94$

Therefore the difference in average player cost from 2018 – 2019 is:

$\pounds30,967,741.94 - \pounds30,714,285.71 = \pounds253,456.22$

In euros, this would be:

$\pounds253,456.22 \div \pounds0.84 = €301,733.60$ or $€300,000$ approximately.

#### Question 13

What was the total profit of the 5 companies combined in 2018?

A: £6,585,620

B: £7,811,250

C: £8,975,500

D: £9,423,480

#### Written Solutions

The profit of Company A was $38 + 36 + 38 + 44 \times1000 \times\pounds10.65 = \pounds1,661,400$

The profit of Company B was $34 + 36 + 32 + 37 \times1000 \times\pounds9.80 = \pounds1,362,200$

The profit of Company C was $42 + 42 + 41 + 44 \times1000 \times\pounds11.25 = \pounds1,901,250$

The profit of Company D was $26 + 22 + 24 + 29 \times1000 \times\pounds12.40 = \pounds1,252,400$

The profit of Company E was $46 + 44 + 48 + 52 \times1000 \times\pounds8.60 = \pounds1,634,000$

The total profit of all 5 companies was $\pounds1,661,400 + \pounds1,362,200 + \pounds1,901,250 + \pounds1,252,400 + \pounds1,634,000 = \pounds7,811,250$

#### Question 14

Which company showed the biggest percentage increase in sales between quarter 1 and quarter 4?

A: Company A

B: Company B

C: Company C

D: Company D

#### Written Solutions

The percentage increase for Company A from quarter 1 to quarter 4 is:

$\dfrac {44 - 38}{38} \times 100 = 15.79\%$

The percentage increase for Company B from quarter 1 to quarter 4 is:

$\dfrac {37 - 34}{34} \times 100 = 8.82\%$

The percentage increase for Company C from quarter 1 to quarter 4 is:

$\dfrac {44 - 42}{42} \times 100 = 4.76\%$

The percentage increase for Company D from quarter 1 to quarter 4 is:

$\dfrac {52 - 46}{46} \times 100 = 13.04\%$

Therefore the answer is Company A

I would also say that for Company B and Company C, the jumps are relatively small, so can probably be discounted without the need for the above calculations.

#### Question 15

The combined yearly sales target for 2019 is 16% greater than 2018.  In 2019, company C would like to increase profit per sale by 5% and have a sales target of 22% of the combined yearly sale target.  How much profit should company C make to the nearest ten thousand pounds if it meets these targets?

A: £950,000

B: £1,450,000

C: £2, 260,000

D: £3,420,000

#### Written Solutions

The sales target for 2018 is $148 + 150 + 173 + 97 + 182 \times1000 = 750,000$

If the sales target for 2019 is 16% more than this, the sales target will be:

$750,000 \times1.16 = 870,000$

If Company C are striving for 22% of this target, then their target is:

$870,000 \times0.22 = 191,400$

Company C’s profit in 2018 was £11.25 per sale. If this increase by 5%, the new profit per sale will be:

$\pounds11.25 \times1.05 = \pounds11.81$

Therefore Company C should make:

$191,400 \times\pounds11.81 = \pounds2,260,000$ to the nearest £10,000.

#### Question 16

The sales target for company B in 2018 was 20% greater than the previous year.  If company B generated 20% of all sales in 2017, what was the total revenue generated in 2017 if the mean profit per sale was £11.50?

A: £4,560,000

B: £5,687,600

C: £7,187,500

D: £8,560,600

#### Written Solutions

The sales target for Company B in 2018 was 150,000.

If the target of 150,000 is 20% more than the previous year, then this means that 150,000 sales represents 120%.

If $150,000 = 120\%$

then

$150,000 \div 120 = 1\%$

so

$1\% = 1250$

Therefore $100\% = 1250 \times100 = 125,000$

If 125,000 sales represents 20% of all sales in 2017, then the total number of sales is $125,000 \times 5 = 625,000$

If the mean profit per sale is £11.50, then the total revenue generated is $\pounds11.50 \times 625,000 = \pounds7,187,500$

#### Question 17

What was the ratio of Company A to Company B’s sales for November and December combined?

A: 2 : 3

B: 3 : 2

C: 3 : 4

D: 4 : 3

#### Written Solutions

In November and December, Company A made $64 + 56 = 120$ sales (easier to not worry about the fact that these values need to be multiplied by £10,000 since this is a ratio / proportion question).

In November and December, Company B made $49 + 41 = 90$ sales

$\dfrac{120}{90}$ can be simplified to $\dfrac{12}{9}$ which can again be simplified to $\dfrac{4}{3}$

#### Question 18

If Company A continue to increase sales month on month at the same rate as the overall percentage increase in sales from August to December, what will be the value of their sales in February?

A: £103,356

B: £633,780

C: £702,464

D: £956,462

#### Written Solutions

Company A’s sales increased from 50 to 56. The percentage increase can be calculated as follows:

$\dfrac{56 - 50}{50} \times 100 = 12\%$ increase

If sales in December were £560,000, then in January they would be:

$\pounds560,000 \times1.12 = \pounds627,200$

Therefore in February they would be:

$\pounds627,000 \times1.12 = \pounds702,464$

#### Question 19

In which month were Company C’s sales exactly a quarter of overall sales?

A: September

B: October

C: November

D: December

#### Written Solutions

In September, the total sales were $40 + 45 + 49 = 134$

Company C’s sales were 49

$49 \div 134 = 0.36$ …. (this is not a quarter since a quarter is 0.25)

In October, the total sales were $57 + 42 + 33 = 132$

Company C’s sales were 33

$33 \div 132 = 0.25$

No need to continue with the November and December calculations since there can only be one correct answer to this question.

#### Question 20

What was Company B’s total sales from August to December in Australian dollars?

A: A$3,784,957 B: A$4,675,328

C: A$5,530,590 D: A$6,342,008

#### Written Solutions

Company B’s sales from August to December was $(42 + 45 + 57 + 49 + 41) \times\pounds10,000 = \pounds2,340,000$

In US dollars this would be $\pounds2,340,000 \times\1.63 = \3,814,200$

Now we need to convert from US dollars to Australian dollars:

$\3,814,200 \times \text{ AUS}\1.45 = \text{ AUS}\5,530,590$