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Time to put your knowledge about proportion questions to the test!

This is the daily schedule that Harry has stuck to on Monday to Friday for the past six weeks whilst working from home. He has always taken Saturdays and Sundays off from work.

1. He leaves the house at 7 am and returns at exactly 8 am. To the nearest 0.1 m/s, what is his average speed during his 10 km run?

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**Answer**: D

**Explanation**:

**1. Convert the units into metres and seconds and find the average speed.**

1 hour = 60 minutes = 60 x 60 seconds = 3600 s

10 km = 10,000 m

So in metres per second:

10000 / 3600 = 2.777… = 2.8 m/s

**Common trap: **Notice that the answers are all in m/s. He has run at 10 km/h so make sure that you don’t slip up and pick answer E without thinking.

Post Comment

This is the daily schedule that Harry has stuck to on Monday to Friday for the past six weeks whilst working from home. He has always taken Saturdays and Sundays off from work.

2. On days when he worked in the office, Harry purchased a Tescbury’s meal deal for £3.00 for lunch and drank a £2.75 latte on his way in. These were his only costs. He now has no morning coffee and estimates that his homemade lunch costs £1.50 a portion. Across a working week, what is his percentage decrease in costs?

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**Answer**: C

**Explanation**:

**1. Work out his old cost and his new cost and find the percentage difference**

His old costs were the meal deal and coffee:

2.75 + 3.00 = £5.75

His new costs are:

1.50

Use the formula:

Multiplier = New Value / Old Value

Multiplier = 1.50 / 5.75 = 0.26….

0.26… = 74% percentage decrease – Option C.

**Timing Tip: **Percentage decrease is one of the most commonly tested skills in UCAT Quantitative Reasoning. Get to grips with the multiplier method to save precious time.

**Timing Tip: **Note that the percentage difference will be same for one day as for 5 – there is no need to work out the values for 5 days’ worth of purchases.

Post Comment

This is the daily schedule that Harry has stuck to on Monday to Friday for the past six weeks whilst working from home. He has always taken Saturdays and Sundays off from work.

3. Harry’s job involves typing out long documents. His maximum speed when typing is 80 words per minute. In his Monday pre-lunch break work session, he types at an average of 67.5% of his maximum speed for the periods he was typing. He spent all of the morning typing apart from when he took two five-minute toilet breaks and had a half-an-hour Zoom meeting with his line manager. How many words did he type in that time?

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**Answer**: C

**Explanation**:

**1. Find the speed at which he is typing and the time he is typing for.**

He is working at 67.5% of his maximum of 80 words per minute.

67.5% of 80 = 54 words per minute.

He is typing for 4 and a half hours apart from a half-an-hour zoom call and 10 minutes total in breaks.

This means that, in minutes, he was working for 270 – 30 – 10 = 230 minutes.

This means he typed:

230 x 54 = 12,420 words in his pre-lunch session.

**Common Trap: **Note that he does not type at his maximum speed in this work session – if he did then the answer would be E.

Post Comment

4. When Harry showers, he does so for half the time between arriving home and starting work. The shower he uses is an eco-friendly one which advertises itself as using 20% less water than other models. During Harry’s typical shower, the eco model uses 25ml per second. In litres, how much water would the other non-eco-friendly models of shower use?

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**Answer**: D

**Explanation**:

**1. Find the eco-shower’s water use and thus the other showers’ use.**

The eco shower uses 25 ml per second.

If Harry showers for half the time between arriving home and starting work, he showers for 15 minutes.

15 x 60 x 25 = 22,500 ml.

This is 20% less than other models:

Use the formula:

New Value / Multiplier = Old Value

The multiplier for a 20% decrease is 0.8:

22500 / 0.8 = Old Value

28125ml = Old Value

In litres:

28125 / 1000 = 28.125L – answer D.

**Common Trap: **Remember when working out a percentage decrease to divide by the percentage decrease as a multiplier rather than by multiplying by the same percentage as a percentage increase. Using a multiplier of 1.2 would give 27L – lower than the true original value.

Post Comment

5. A city hosts a comedy festival annually. The festival lasted five weeks in Year 1 and the total number of tickets sold was 123,545. The festival ran for 8 weeks in Year 2 and the average weekly ticket sales were 25% higher. How many tickets were sold in year 2?

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**Answer**: D

**Explanation**:

**1. Find the average weekly sales in Year 1**

123,545 in 5 weeks

123,545/5 = 24709 a week

**2. Find the average weekly sales in Year 2 and thus the total:**

New Value = Old Value x Multiplier

24,709 x 1.25 = 30,886.25

The festival ran for 8 weeks so:

30,886.25 x 8 = 247,090 tickets total – option D.

Post Comment

● All figures in the table are in kilograms.

● 1 ml water = 1g

6. In 2013-14, what proportion of the total mass of coffee beans used in the country were used in cafés?

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**Answer**: C

**Explanation**:

**1. Find the coffee bean usage in cafés as a percentage of all the coffee beans used.**

Beans in cafés: 242,000

Beans in total: 242000 + 50300 + 28341 + 36324 = 356965

242000/356965 = 0.6779… = 69.8%

**Timing Tip: **For this question, you could round the values to 50,000, 28,000 and 36,000 and you would still get an answer (67.9%) which clearly indicates option C

**Timing Tip: **Using rounded numbers, you could do some of these additions in your head or with the help of the scratch pad: 242 + 50 + 28 + 36 will tell you the number of thousands without having to type each number out in full.

**Top Tip: **Make sure to familiarise yourself with the scratchpad and calculator using the UCAT official website. You don’t want the first time you are using it to be in the real exam.

Post Comment

● All figures in the table are in kilograms.

● 1 ml water = 1g

7. The country wants to know what the average use of coffee beans across all sectors per year is. To the nearest kg, what was the mean mass of coffee beans used per year in the time period given?

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**Answer**: C

**Explanation**:

**1. Find the sum of all the values in the table:**

40000 + 25550 + 180000 + 30000 + 45243 + 25043 + 200,000 + 33000 + 48500 + 26030 + 220000 + 35050 + 50300 + 28341 + 242000 + 36324 + 55320 + 30245 + 266200 + 37200 = 1654346 Kg

**2. Find the mean annual use:**

The mean use = Total use in the period/Number of years

1654346/5 = 330869.2 so 330869 to the nearest kilogram.

**Top Tip: **Identify early on that this question is asking for the mean of all the values. Furthermore, the answer options are close together so it is clear that precision will be required. The best candidates will spot this is a potential timing trap and be strict about keeping to the 40s limit.

Post Comment

● All figures in the table are in kilograms.

● 1 ml water = 1g

8. Which of the following statements is incorrect?

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**Answer**: A

**Explanation**:

A is incorrect. Between 2010-11 and 2011-12 the increase was 200,000/180,000 = 1.11 which is an 11% increase not 10%. The other values are 10% increases but not the first period.

B is true. It fell between 2010-11 and 2011-12 but rose every other year.

C is true. 50300/48500 = 1.0371… so a 3.7% increase

D is true. Only one value (restaurants in 2011-12) was lower than the year before. This decrease was more than compensated by the increases in values for the categories so this can be selected as true through inspection.

E is true. The percentage change is 10% in the first year, 6.2% in the second, 3.6% in the third and 2.4% in the final year.

**Timing Tip: **Options which only mention one of the categories should be targeted first – they only require the assessment of one subset of the data. This means D should be assessed last. From the others, it is clear that E would take the longest so should be a lower priority.

Post Comment

● All figures in the table are in kilograms.

● 1 ml water = 1g

9. When preparing a coffee, the ideal ratio for the mass of coffee beans to the mass of water is 1:18. In cafes in 2011-12, 90% of coffee beans consumed were used to prepare drinks in this ratio. The remainder had the ratio for the mass of coffee beans to the mass of water of 1:20. Assuming coffees consist of solely water and coffee, how many litres of coffee were served by cafés in 2011-12?

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**Answer**: D

**Explanation**:

**1. Find the mass of coffee used in each ratio:**

90% was used at a ratio of 1:18:

0.9 x 200,000 = 180,000

10% was used at a ratio of 1:20

0.1 x 200,000 = 20,000

**2. Find the volume of coffee produced:**

Find the volume of coffee made from this mass:

1g = 1ml

180,000 was used in the ratio 1:18 so:

180,000 x 18 = 3,240,000Kg so 3,240,000L

20,000 was used in the ratio 1:20 so:

20,000 x 20 = 400,000Kg so 400,000L

3,240,000 + 400,000 = 3,640,000L – D.

**Common Trap: **Remember that not all of the coffee will be made in the 1:18 ideal ratio. If this were true, the answer would be C.

Post Comment

● All figures in the table are in kilograms.

● 1 ml water = 1g

10. In 2010-11, the model used to predict the country’s coffee bean usage was inaccurate. It underestimated the consumption of coffee beans by cafes by 11% and it overestimated the usage by private households by 15%. The other values were correct. What is the percentage change in the total mass of coffee beans consumed using the new model?

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**Answer**: D

**Explanation**:

**1. Find the total consumption from the old model:**

40,000 + 25,550 + 180,000 + 30,000 = 275,550

**2. Find the new values:**

New value / Multiplier = Old value:

For the private households:

30000/1.15 = 26,086.9…

For the cafés:

180000/0.89 = 202,247.191…

**3. Find the new total and percentage difference: **

40000 + 25550 + 202247… + 26086.9… = 293,883…

293883… /275,550 = 1.0665 = 6.7% increase

**Common Trap:**A 11% underestimate means that the value given is 89% of the true value (11% percentage decrease to reach it) so to calculate the true value, divide by 0.89 rather than multiply by 1.11.

Post Comment

The budget for the Hornets, a premiership rugby club.

11. What was the club’s budget in 2017/18?

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**Answer**: E

**Explanation**:

**1. Identify the data the question is asking for:**

It has asked for the 2017/18 budget – this is not given directly in the question.

We are given the 2018/19 budget and how much more it is than the 2017/18 budget.

**2. Take away the increases to find the previous budget:**

17.9125 – 1.2 + 1.2 – 0.05 – 0.125 – 0.5 + 0.15 = 17.3875

**Common trap:** Remember to add on the values for when the budget has reduced from 2017/18 – two negatives make a positive.

Post Comment

zohra Medicmind Tutor

Tue, 18 Aug 2020 14:20:25

why is it -0.05 not +

The budget for the Hornets, a premiership rugby club.

12. To 0.1%, the proportion of the total budget that was spent on the playing staff in 2017/18 was:

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**Answer**: A

**Explanation**:

**1. Find the playing staff budget as a proportion of the known 2017/18 budget:**

Proportion for playing staff = Playing staff budget / Total budget

The total budget for 2017/18 was 17.3875

The playing staff budget was: 8.5 – 1.2 = 7.3

7.3/17.3875 = 0.4198… = 42.0%

Post Comment

The budget for the Hornets, a premiership rugby club.

13. Coaching staff wages in 2017/18 were 25% lower than in 2016-17. The coaching staff wages in 2016-17 were:

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**Answer**: D

**Explanation**:

**1. Find the wages in 2016/17**

There was a 25% percentage decrease between 2016/17 and 2017/8:

Original Value x Multiplier = New Value

So

Wages in 2016/17 x 0.75 = Wages in 2017/18

Wages in 2017/18:

3 – -1.2 = 4.2 million

New Value / Multiplier = Original Value

4.2/0.75 = 5.6 million

Therefore, the bill in 2016-17 was £5.6 million – D

**Common Trap:** To calculate the original before a 25% decrease, divide by 0.75 rather than multiplying by 1.25.

Post Comment

The budget for the Hornets, a premiership rugby club.

14. The total staff bill as a proportion of the total 2018/19 budget is:

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**Answer**: B

**Explanation**:

**1. Find the proportion of the budget spent on all types of staff:**

Proportion on staffing = Staffing costs / Total budget:

Staffing cost:

8.5 + 3 + 1.5 + 0.275 = 13.275 million

Total budget = 17.9125 million

13.275/17.9125 = 0.7411 = 74.1%

**Top Tip: **Remember that proportions compare a single value in comparison to the total. Here, the value is £13.275 million in comparison to the total of £17.9125 million

Post Comment

The budget for the Hornets, a premiership rugby club.

15. In the premiership, clubs are allowed to have two marquee players who command higher wages which do not count towards the league’s salary cap regulations. In 2018/19, all of the playing staff wage increase was due to the signing of a new marquee player. The second marquee player is paid approximately 12.7% of the 2018/19 playing budget. What is the approximate ratio for the 2 new marquee player : other player salaries?

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**Answer**: B

**Explanation**:

**1. Find the amount spent on marquee players and non-marquee players:**

1.2.+ 12.7% of 7.3 million = £2.1271 million

8.5 – 2.1271 = £6.3729 million

**2. Set up a ratio for the marquee players to non-marquee players:**

2.127: 6.3729

**3. Simplify this ratio:**

We know that one side is equal to one so divide through by 2.127 as it must be the highest common factor:

6.3729/2.127 = 2.99 = 3

Therefore, the simplified ratio is 1:3

Post Comment

This graph shows the average rent per calendar month (PCM) in a popular area of South London.

A year is made up of 12 calendar months.

16. Harry rents a one-bedroom flat in this area in 2015 at 75% of the average market rate. Between 2015-16 and 2016-17, the price increases at twice the rate that the price of the average property increases. What is the difference between his new rent and the new 2016-17 market average?

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**Answer**: B

**Explanation**:

**1. Work out his rent in each of the years.**

He paid 75% of the market average (which was £1000 PCM).

0.75 x 1000 = 750

The average price increased from 1000 to 1250.

To find the percentage increase use the formula:

New Value / Old Value = Multiplier

1250/1000 = 1.25 = 25%

His rent increased at double this rate so 50%.

For a percentage increase:

New value = Old value x multiplier

50% increase = multiplier of 1.5

New rent = 750 x 1.5

New rent = £1125

**2. Find the difference from the market rent**

The graph shows that the new average rent is £1250.

£1250 – £1125 = £125 so he pays £125 below the market rate.

**Top Tip: **Look over the Multiplier Method lesson on the Online Portal – getting to grips with it will save you time.

Post Comment

This graph shows the average rent per calendar month (PCM) in a popular area of South London.

A year is made up of 12 calendar months.

17. Ben is a landlord who owns a 3-bedroom property in the area. At the start of the year 2015-16 he charged the market average for his tenants. He kept it at the same rate for a second year. When the first tenants left, he charged the new tenants the new market average and kept the same price for the second year of their lease. Assuming that there is no gap in the tenancy, how much does he earn in these four years?

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**Answer**: B

**Explanation**:

**1. Work out the price he charges each tenant and so the income**

The first tenants, he charges at the rate for 2015-16 – £2000 PCM

He does this for 24 months so: 2000 x 24 = £48,000

The second tenants, he charges at the new average rate for 2017-18 – £2250

Again, he does this for 24 months: 2250 x 24 = £54,000

54,000 + 48,000 = £102,000 – B.

**Timing Tip: **When adding numbers in the thousands, remember that you don’t have to write out every digit. 54 + 48 = 102 and is easier to do as mental maths or on the whiteboard.

Post Comment

This graph shows the average rent per calendar month (PCM) in a popular area of South London.

A year is made up of 12 calendar months.

18. A buy-to-let property’s RTV is the fraction of the value of the property which is paid as rent in a month. For example, a house valued at £100,000 which had a monthly rental value of £1,000 would have an RTV of 1,000 / 100,000 = 1%. In 2017-18, a property developer bought a 4-bed property in this area with a value of £600,000. He paid one fifth of this up front with a loan for the rest. As it is within the catchment area for the best local school and has superb period features, it had a rental value which was twice the going rate. The rental market collapsed and his tenants left. He has had to rent it out at 60% of the value he was renting it to the original tenants. The property value remained the same. What is the RTV now?

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**Answer**: C

**Explanation**:

**1. Find the new rent**

The initial rent was double the average market rate in 2017-18.

2500 x 2 = 5000.

He now charges 60% of that:

0.6 x 5000 = £3000.

**2. Find the RTV**

RTV = Monthly Rental Income / Property Value

RTV = 3000 / 600,000

RTV = 0.005 = 0.5% – option C.

**Common Trap: **Watch out when there are values which are different by a factor of 10 – it could be a sign that there is a common conversion error.

Post Comment

This graph shows the average rent per calendar month (PCM) in a popular area of South London.

A year is made up of 12 calendar months.

19. For all of 2015-16, Genevieve lived in a two-bedroom flat with a friend. In 2018-19, she lived with her partner in a one-bedroom and they paid half the rent each. Which year did she pay more rent in and by how much?

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**Answer**: C

**Explanation**:

**1. Find the monthly rent of each and answer by inspection:**

In both years, she was paying half the rent.

The rent in 2015-16 for a two-bedroom was £1500 PCM – the same as for a

one-bedroom flat in 2018-19 so, with no further calculation, we can say she paid the same in both years.

**Top Tip: **Identifying questions which can be answered by inspection will save precious time by avoiding completely unnecessary calculations.

Post Comment

A village Post Office offers small parcel and large parcel delivery. Letters are classed as small parcels.

In the month of January, the same total number of small and large parcels were paid for and posted. The frequency of each is provided in the pie charts.

The pricing for large parcels is given in the table below:

Size
| Price for Standard Delivery ($) | Price for Recorded Delivery ($) |

1 – 1.25 | 7.25 | 14.25 |

1.25 – 1.5 | 8.25 | 15.50 |

1.5 – 2.5 | 9.50 | 17.00 |

2.5 – 5 | 10 | 18.50 |

5+ | 12.50 + 0.10 per additional 100g above 5 kg | 20.00 + 0.12 per additional 100g above 5kg |

20. Harry has a 1.45 kg box of parts and wants to send it with standard delivery. What is the percentage increase in price if he adds a 100g component and decides to go for recorded delivery instead?

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**Answer**: C

**Explanation**:

**1. Find the percentage increase.**

A percentage increase can be found using the formula:

He initially would have gone for a 1.45kg package (in the 1.25-1.5kg band) at standard delivery – $8.25.

He is now going for a 1.55kg package (in the 1.5-2.5kg band) with recorded delivery ($17.00)

This means that the percentage increase is 106%.

**Top Tip: **It is worth spending the time getting used to the multiplier method. Our research shows that it does save time

Post Comment

A village Post Office offers small parcel and large parcel delivery. Letters are classed as small parcels.

In the month of January, the same total number of small and large parcels were paid for and posted. The frequency of each is provided in the pie charts.

The pricing for large parcels is given in the table below:

Size
| Price for Standard Delivery ($) | Price for Recorded Delivery ($) |

1 – 1.25 | 7.25 | 14.25 |

1.25 – 1.5 | 8.25 | 15.50 |

1.5 – 2.5 | 9.50 | 17.00 |

2.5 – 5 | 10 | 18.50 |

5+ | 12.50 + 0.10 per additional 100g above 5 kg | 20.00 + 0.12 per additional 100g above 5kg |

21. What percentage of all parcels sold weighed less than 1.25kg?

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**Answer**: B

**Explanation**:

**1. Find the percentage of parcels below 1.25kg.**

The question information states that there were an equal number of small and large parcels. All of the small parcels (50% of the total) were less than 1.25kg.

From the large parcels – 14% were 1 – 1.25kg. This means that 14% of the 50% that were large were less than 1.25kg.

This can be calculated using decimals:

50% of 14% = 7%

The total which are less than 1.25kg is therefore:

50% + 7% = 57%.

**Common Trap: **It is important to see that the 14% of parcels between 1 – 1.25kg represent 14% of the 50% that are large parcels. Therefore, it only represents 7% of the total of parcels.

Post Comment

A village Post Office offers small parcel and large parcel delivery. Letters are classed as small parcels.

In the month of January, the same total number of small and large parcels were paid for and posted. The frequency of each is provided in the pie charts.

The pricing for large parcels is given in the table below:

Size
| Price for Standard Delivery ($) | Price for Recorded Delivery ($) |

1 – 1.25 | 7.25 | 14.25 |

1.25 – 1.5 | 8.25 | 15.50 |

1.5 – 2.5 | 9.50 | 17.00 |

2.5 – 5 | 10 | 18.50 |

5+ | 12.50 + 0.10 per additional 100g above 5 kg | 20.00 + 0.12 per additional 100g above 5kg |

22. The price of the standard 1.5-2.5 kg parcel delivery increases by 38%. The price of the recorded delivery for the same category increases by the same amount. By how much does the difference in price increase?

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**Answer**: D

**Explanation**:

**1. Find the new prices for each:**

The new price can be found using the formula:

NewValue=OldValue×Multiplier

The percentage increase of 38% gives a multiplier 1.38:

For the standard postage:

9.50 x 1.38 = $13.11

For the recorded postage:

17.00 x 1.38 = $23.46

**2. Find the difference for the old and the new prices**

Old: 17.00 – 9.50 = $7.50

New: 23.46 – 13.11 = $10.35

Difference: 10.35 – 7.50 = $2.85 – option D

Post Comment

The pricing for large parcels is given in the table below:

Size
| Price for Standard Delivery ($) | Price for Recorded Delivery ($) |

1 – 1.25 | 7.25 | 14.25 |

1.25 – 1.5 | 8.25 | 15.50 |

1.5 – 2.5 | 9.50 | 17.00 |

2.5 – 5 | 10 | 18.50 |

5+ | 12.50 + 0.10 per additional 100g above 5 kg | 20.00 + 0.12 per additional 100g above 5kg |

23. In December 50% of the packages in the range 1 – 1.25 kg were sent by recorded delivery and the rest were sent by standard delivery. The Post Office made $752.50 from the sales of these parcels. How many parcels in the range 500 – 1 kg were sold?

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**Answer**: B

**Explanation**:

**1. Find the number of parcels sold in the 1 – 1.25kg range.**

X is the number of parcels sold which were in the 1 – 1.25kg range.

They sold 0.5X of these recorded.

They sold 0.5X of these standard.

752.50 = 0.5X x 14.25 + 0.5X x 7.25

752.50 = 10.75X

X = 752.50 / 10.75

X = 70 – this is 14% of the number of large parcels

**2. Find the number in the range 500g – 1kg.**

Let us call the total number of large parcels Y:

14% of Y = 70

0.14Y = 70

Y = 70/0.14

Y = 500

The question information states that there are an equal number of large and small parcels.

Therefore, there are 500 small parcels. 10% of small parcels are 500g – 1 kg.

1. x 500 = 50 – B

**Common Trap: **This question relied on noticing that the number of large parcels is equal to the number of small parcels. Always read the bullet points below tables in the scenario.

Post Comment

24. Hispanlearn are offering a one-day-only discount on their online Spanish course. They are offering a 40% discount. If you pay up front you would receive an additional 10% discount on the new price. What is the price for paying up front today as a percentage of the original price?

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**Answer**: B

**Explanation**:

**1. Find the first discount.**

It is a 40% discount, so the new price is 0.6 times the full price.

**2 Find the second discount.**

It is a 10% discount so the price for paying upfront is 0.9 times the discounted price.

0.9 x 0.6 = 0.54 – 54%.

This means that the answer is B

Common trap: Note that the 10% discount is on the new price. This means the calculation is 0.6 x 0.9 rather than 0.6 – 0.1 = 0.5 or 50% discount.

Post Comment

- Eastern Perks is a café selling coffee and ice cream.
- The graph shows the number of each product sold in each month of the year.
- Their year is split into four quarters: Q1: January to March, Q2: April to June, Q3: July to September and Q4: October to December.
- The cafe offers a rewards card where customers’ 7th coffee is free. They offer the opportunity to “pay this forward” where the customer donates it to the Eastern Perks Foundation which provides free coffee to those on the margins of society.

25. What was the approximate value of June sales of ice cream as a percentage of ice cream sales in May?

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**Answer**: D

**Explanation**: The question has asked for the June value *as a percentage of *the May value.

**1. Find the May and June values:**

June: From the graph, this is roughly 1500.

May: From the graph, this is roughly 1000.

**2. Find 1500 as a percentage of 1000.**

New value / Old value = Multiplier.

1500/1000 = 1.5 = 150%.

Common Trap: Notice this has asked for the June value as a percentage of May rather than asking for the percentage increase.

Post Comment

Roha Alam Medicmind Tutor

Fri, 25 Sep 2020 16:16:11

the graph doesnt load

- Eastern Perks is a café selling coffee and ice cream.
- The graph shows the number of each product sold in each month of the year.
- Their year is split into four quarters: Q1: January to March, Q2: April to June, Q3: July to September and Q4: October to December.
- The cafe offers a rewards card where customers’ 7th coffee is free. They offer the opportunity to “pay this forward” where the customer donates it to the Eastern Perks Foundation which provides free coffee to those on the margins of society.

26. In 2018, by approximately how units was the difference in average sales of ice cream between Q1 and Q4 greater than the difference in average sales of coffee between Q1 and Q4?

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**Answer**: B

**Explanation**:

**1. Find the average for each for the first quarter.**

For many questions, this could be done by estimation through eyeballing the graphs to save time. However, this one has a scale which has too wide a margin of error for this.

For Coffee: (1000 + 1250 + 1750) / 3 = 4000/3

For Ice cream: (250 + 500 + 750) / 3 = 500

**2. Find the average for each for the final quarter:**

For Coffee: (1250 + 1500 + 1500) / 3 = 4250/3

For Ice cream: (750 + 250 + 100) / 3 = 1100/3

**3. Find the difference in averages:**

C: 4250/3 – 4000/3 = 83.3

I: 500 – 1100/3 = 133.3

133.3 – 83.3 = 50.

Timing Tip: Some QR questions would take longer than 40s to answer. Try to identify these and learn to be disciplined so that you are not spending 120s making sure that you get the answer right.

Post Comment

- Eastern Perks is a café selling coffee and ice cream.
- The graph shows the number of each product sold in each month of the year.
- Their year is split into four quarters: Q1: January to March, Q2: April to June, Q3: July to September and Q4: October to December.
- The cafe offers a rewards card where customers’ 7th coffee is free. They offer the opportunity to “pay this forward” where the customer donates it to the Eastern Perks Foundation which provides free coffee to those on the margins of society.

27. Standard ice creams are sold at a price of £2.00 and large are sold at a price of £2.75. In June and July, two-fifths of the ice creams sold were large. In this period was more income earned from sales of large ice creams or sales of small ice creams and by how much?

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**Answer**: D

**Explanation**:

**1. Find the number of each type of ice cream sold:**

1500 + 2000 = 3500 ice creams.

2/5ths are large so 0.4 x 3500 = 1400

3/5ths are small so 0.6 x 3500 = 2100

Top tip: This method is known as calculation by proportions – these come up in Lesson 6.

**2. Find the revenue from each type of ice cream and thus the difference:**

The large ice creams are £2.75:

1400 x 2.75 = £3850

The small ice creams are £2:

2100 x 2 = £4100

Find the difference between the two:

4100 – 3850 = £350

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- Eastern Perks is a café selling coffee and ice cream.
- The graph shows the number of each product sold in each month of the year.

28. The Eastern Perks manager desires an annual coffee sales growth of 5%. This is measured at the end of each quarter. Approximately what would the sales have had to be in March 2019 to hit this target if sales growth in January and February had been only 2%?

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**Answer**: B

**Explanation**:

**1. Find the approximate coffee sales in the first quarter in 2018 and therefore the 2019 target.**

1000+1250+1750 = 4000

The manager wants 5% growth.

4000 x 1.05 = 4200

**2. Find the sales in January and February.**

In 2018: 1000 + 1250 = 2250

In 2019: 2250 x 1.02 = 2295

**3. Find the necessary number for March:**

The cafe need to meet the target of 4200 so:

4200 – 2295 = 1905.

**Top Tip:** Graphs often have far more information than will be required to answer the question. Here, focus on the three bars which represent coffee sales in the first quarter.

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● This survey shows the preferred foot of a number of playground footballers.

● They were also asked about what hand they write with.

● There were no ambidextrous individuals in the group (i.e. those that could use both hands to write).

29. Five-sixths of those who prefer using their left foot, 16.7% of those who prefer to play with their right foot, and 90% of those who are equally comfortable with both feet are left-handed. What percentage of the group surveyed were right-handed?

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**Answer**: B

**Explanation**:

**1. Find the number of each group who are left handed.**

⅚ of the left-footed people are left-handed:

5/6 x 54 = 45

16.7% of the right-footed people are left-handed:

0.167 x 102 = 17

90% of those who expressed no preference are left-handed:

0.9 x 40 = 36

This means that the total is:

45+17+36 = 98

**2. Find the total interviewed and thus the percentage who are right-handed:**

40+54+102 = 196

If 98 are left handed:

196 – 98 = 98 right handed people

98/196 = 50%

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Dan Medicmind Tutor

Sun, 30 Aug 2020 15:59:02

"5/6 of the left-footed people are left-handed - 5/6 x 54 = 45. Could you please explain where the 54 is coming from.

lin Medicmind Tutor

Tue, 08 Sep 2020 16:16:55

where does the 54, 102 and 40 come from?

30. In a survey, 34% of individuals ski and 43% can snowboard. 30% of individuals could not do both. Of those who have been skiing and snowboarding for a total period of greater than 28 days over their lifetime, 7% have required hospital treatment for an accident or injury. What is the percentage of individuals who could both ski and snowboard?

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**Answer**: A

**Explanation**:

**Top tip: **The best method is to use a value of 100 individuals – this allows easy calculations from percentages.

**1. Draw a Venn Diagram to represent the situation.**

A + B + C + 30 = 100

A + B + C = 70

**2. Form equations for the number who can do each of the activities and solve to find C then B.**

Snowboarding: A + B = 43

Skiing: B + C = 34

Substitute the equation for snowboarding into the first equation to find the

value of C.

A + B + C + 30 = 100

A + B = 43

43 + C + 30 = 100

C = 27

Thus find the value of B

We know from the skiing group that:

B + C = 34

B + 27 = 34

B = 7% – A.

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Revenue Stream | January Revenue (000s) | February Revenue (000s) | March Revenue (000s) |

Teaching | 120 | 145 | 130 |

Mentoring | 15 | 17.5 | 19 |

Writing | 80 | 90 | 101 |

- This is the revenue for a medium-to-large-sized business in Australia.
- All figures are given in AUD$

31. The company wants to assess its mean monthly income including all three of its revenue streams. To the nearest $250, what is the mean total revenue each month for the three months given in the table?

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**Answer**: B

**Explanation**:

**1. Find the sum of the incomes and find the monthly average:**

(120 + 145 + 130 + 15 +17.5 19 + 80 + 90 + 101) x 1000 = $717,500

Divide this by 3 to find the monthly average.

$717,500/3 = $239,166… = $239,250 to the nearest $250.

**Common Trap:** Remember that the question is looking for the average monthly income rather than the mean income from each revenue stream.

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Revenue Stream | January Revenue (000s) | February Revenue (000s) | March Revenue (000s) |

Teaching | 120 | 145 | 130 |

Mentoring | 15 | 17.5 | 19 |

Writing | 80 | 90 | 101 |

- This is the revenue for a medium-to-large-sized business in Australia.
- All figures are given in AUD$

32. To the nearest 0.1%, what was the percentage decrease in revenue from Teaching for this company between February and March?

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**Answer**: B

**Explanation**:

**1. Find the multiplier:**

130/145 = 0.89655… = 10.345 % percentage decrease

To the nearest 0.1%, this is 10.3%

**Top tip:** The answer options are 0.1% away so it will be necessary to work precisely.

**Top tip:** The multiplier method will save time – get to grips with it in practice and you will save precious seconds.

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Revenue Stream | January Revenue (000s) | February Revenue (000s) | March Revenue (000s) |

Teaching | 120 | 145 | 130 |

Mentoring | 15 | 17.5 | 19 |

Writing | 80 | 90 | 101 |

- This is the revenue for a medium-to-large-sized business in Australia.
- All figures are given in AUD$

33. Approximately what proportion of this company’s teaching revenue in the three months in the table was earned in February?

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**Answer**: C

**Explanation**:

**1. Find the total income from teaching:**

120 + 145 + 130 = 395

**2. Find the February revenue as a proportion of that:**

145/395 = 0.367… = 37% to the nearest percentage point

**Top tip:** Proportion is the comparison of one characteristic with the whole group.

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Revenue Stream | January Revenue (000s) | February Revenue (000s) | March Revenue (000s) |

Teaching | 120 | 145 | 130 |

Mentoring | 15 | 17.5 | 19 |

Writing | 80 | 90 | 101 |

- This is the revenue for a medium-to-large-sized business in Australia.
- All figures are given in AUD$

34. In March, teaching had a 40% profit margin and writing had a 52% profit margin. Based on the revenue from the table, which of teaching or writing generated a greater profit in March and by what percentage?

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**Answer**: D

**Explanation**:

**1. Find the profit for each:**

Teaching: 0.4 x 130,000 = $52,000

Writing: 0.52 x 101,000 = $52,520

**2. Find the percentage difference between the two:**

52,520/52000 = 1.01

Therefore, writing has a higher profit by 1%.

**Common trap:** The profit margin is different by 12% but this is not the same as the profit being different by 12%. The profit is also dependent on the level of revenue which is very different for the two revenue streams.

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Maria Medicmind Tutor

Sun, 07 Mar 2021 18:49:59

The wrong answer has been selected.

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