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Item X is the best-selling new sous vide circulator that every wannabe home-chef wishes to own. It has seven speeds and can be controlled from a mobile app. The product has received rave reviews – appearing in the QG magazine of ‘Top Ten Kitchen Items Any Gentleman Should Own’.
Sales of Item X in Shop A in 2018-19
| Quarter | Sales |
| Q1 | 75 |
| Q2 | 100 |
| Q3 | 250 |
| Q4 | 175 |
Explanation
Answer: A
Explanation: Without information on the total number of sales, we cannot compare the pie charts. Thus, the claim that the sales were higher in Shop A than Shop B cannot be supported as we only know that the sales were a higher proportion of the whole year in Q1 in Shop A rather than being a higher number sold.
Top Tip: Remember that pie charts cannot be compared if we do not know the total number of items sold. 33% of 2 is smaller than 20% of 2000.
Item X is the best-selling new sous vide circulator that every wannabe home-chef wishes to own. It has seven speeds and can be controlled from a mobile app. The product has received rave reviews – appearing in the QG magazine of ‘Top Ten Kitchen Items Any Gentleman Should Own’.
Sales of Item X in Shop A in 2018-19
| Quarter | Sales |
| Q1 | 75 |
| Q2 | 100 |
| Q3 | 250 |
| Q4 | 175 |
Explanation
Answer: E
Explanation:
1. Find the total sales in each quarter for B and compare
We are looking for 2018-19 so it is based on the information in the table:
For percentage difference:
New Value = Original Value x Multiplier
Top tip: For information on how to find a multiplier for a given percentage difference, look at the Medic Mind Lesson on the topic.
For Quarter 1: 33% higher so
New = 75 x 1.33
New = 100
Repeat these calculations for the figures for Q2 to Q4
Q2: 30% decrease – 100 x 0.7 = 70
Q3: 32% increase – 250 x 1.32 = 330
Q4: 44% decrease – 175 x 0.56 = 98
This gives a total of 100 + 70 + 330 + 98 = 598
For Shop A the total is:
75 + 100 + 250 + 175 = 600 – 2 more than in Shop B – answer option A.
Timing Tip: This question has differences in sales of one unit so it is important that you work precisely from the outset.
Item X is the best-selling new sous vide circulator that every wannabe home-chef wishes to own. It has seven speeds and can be controlled from a mobile app. The product has received rave reviews – appearing in the QG magazine of ‘Top Ten Kitchen Items Any Gentleman Should Own’.
Sales of Item X in Shop A in 2018-19
| Quarter | Sales |
| Q1 | 75 |
| Q2 | 100 |
| Q3 | 250 |
| Q4 | 175 |
Explanation
Answer: A
Explanation:
1. Identify the trend in size.
As it goes Q1 to Q4 in a clockwise direction, It has to go smallest, second smallest, biggest then smaller but not as small as the first 2.
From this fact alone, we know it must be one of A or C.
2. Find the total sales in each quarter for B and compare
The total sales are 600. The largest section of this is 250/600. This is less than half the total.
This means that C cannot be correct as it has a segment which is half of the total of the pie.
Therefore, A is the only possible correct answer.
Top Tip: Selecting Pie Charts may need some calculation – this required you to notice that there are 600 total sales and so the largest segment couldn’t be half the pie.
Common Trap: It might be tempting to go for Option D – it has the right size of segments but fails to take into account the fact that the question states that the pies go from Q1 to Q4 in a clockwise direction.
Item X is the best-selling new sous vide circulator that every wannabe home-chef wishes to own. It has seven speeds and can be controlled from a mobile app. The product has received rave reviews – appearing in the QG magazine of ‘Top Ten Kitchen Items Any Gentleman Should Own’.
Sales of Item X in Shop A in 2018-19
| Quarter | Sales |
| Q1 | 75 |
| Q2 | 100 |
| Q3 | 250 |
| Q4 | 175 |
Explanation
Answer: D
Explanation:
1. Find the number they have of each in stock and set up the ratio
They sell 50% of their blue Item Qs:
250 x 0.5 = 125 left
They then order 100 so:
125 + 100 = 225
They sell 75 of their red Item Qs but order 75 so there is no net change.
They therefore have 200 red Item Qs
This gives the ratio
225:200
2. Simplify the ratio
To simplify a ratio, divide by the highest common factor for the two sides. This is the largest number which both can be divided by.
For 225 and 200, this is 25.
225 / 25 = 9
200 / 25 = 8
This makes the simplified ratio 9:8.
Common Trap: Make sure to keep a track of the sales and restocking of the items. Answers A and B are variants to the ratio for the initial number of each and Answer E is the situation before restocking. Use the whiteboard to keep a track of the changes in stock levels – all the calculations are possible to do on it.
A university has researched all the 12 species of birds which are endemic to an island group in the Pacific Ocean. The project required the monitoring of the birds resting heart rate measured using trackers over a period of 72 hours. This chart shows the comparison of a resting heart rate of birds in comparison to their wingspan in metres.
Explanation
Answer: C
Explanation:
1. Find the number of birds in the chart and thus the ‘middle’ number.
To find the median add one to the number of birds and divide by 2 to find the middle number.
There are 12 birds so the median wingspan is: 12 + 1 = 13 / 2 = 6.5
The median is therefore halfway between the 6th and 7th number.
The sixth is at 0.50m and the seventh is at 0.60m. 0.55 Is halfway between these.
Top Tip: Remember that when there are an even number of values in a data set, the median is the average of the two ‘middle’ numbers.
A university has researched all the 12 species of birds which are endemic to an island group in the Pacific Ocean. The project required the monitoring of the birds resting heart rate measured using trackers over a period of 72 hours. This chart shows the comparison of a resting heart rate of birds in comparison to their wingspan in metres.
Explanation
Answer: C
Explanation:
1. Identify the number with a heart rate below the median and those which don’t but do have an above average wingspan
There are six birds below the median heart rate.
There is one more bird which doesn’t have a low heart rate but does have an above average wingspan.
This means there are 7 meeting the criteria out of 12 birds total so the fraction is 7/12ths – C.
Timing Tip: Use knowledge of median as a concept to answer by inspection. You do not need to find the exact value but rather to rank the answers in order visually.
Common Trap: Remember that the fact that the median is the average of the two middle numbers, half the values will be above it and half below – this will include the two numbers which are averaged to find the median value.
- Here is information about the number of English counties pupils in two classes at a primary school had visited.
- The class size for each was 30.
Explanation
Answer: B
Explanation:
1. Find where the cumulative frequency reaches the total class size:
There are 30 in the class so this happens at 8 counties for class 1 – B
Common Trap:Remember that this is a cumulative frequency graph not a line chart. This means that you are looking for the number of the x axis when you reach 30 on the y axis.
John Paul Medicmind Tutor Fri, 14 Aug 2020 12:31:57
why not 9 counties?
- Here is information about the number of English counties pupils in two classes at a primary school had visited.
- The class size for each was 30.
Explanation
Answer: B
Explanation:
1. Find the number who have been to four counties as a proportion of the total.
Remember that a proportion considers one value as a percentage of the total value.
Exactly four counties is the increase from the value for 3 or fewer (12) to the value for 4 or fewer (15).
15 – 12 = 3
There are 30 in the class so:
3/30 = 10%
Common Trap: Remember that it is not a case of simply reading off the graph – the value at four is 15 which means that 15 have been to 4 or fewer counties rather than exactly four.
- Here is information about the number of English counties pupils in two classes at a primary school had visited.
- The class size for each was 30.
Explanation
Answer: E
Explanation:
1. Find the greatest increase.
The increase in cumulative frequency highlights the number who have been to a specific number.
This happens for Class 2 between 6 and 7 so the largest number had been to 7 counties
Timing Tip: This question can be answered by inspection – the largest increase will be shown by the steepest gradient and this is clearly between six and seven.
- Here is information about the number of English counties pupils in two classes at a primary school had visited.
- The class size for each was 30.
Explanation
Answer: A
Explanation:
1. Find the number of students who have been to four or more counties
The easiest way is to find the number who have been to 3 or fewer and take it away from 60 (the size of the classes combined):
Originally this would be: 60 – 12 – 8 = 40.
Now add in the people who have now been to four or more following the summer:
60% of 5 = 3
50% of 4 = 2
40 + 3 + 2 = 45
2. Find this as a proportion of the total
Proportions consider one value in a set as a percentage of the total.
Here the value is the number who have been to four counties or more and the total is all the students in the two classes:
45/60 = 75%
Common Trap: Remember to consider the new students who have been to four or more, without these, the fraction would be two-thirds and thus the proportion 66.6%.
The following graph shows the sales data from R Toys We, showing the units sold for the four most popular items in a single store in a year.
Item W is an electric plane.
Item X is a toy car racing set.
Item Y is a toy phone
Item Z is an electronic cash register toy.
Item W had the lowest returns rate at 0.5% whilst Item Z was returned at double this rate.
Q1 is January to March, Q2 is April to June, Q3 is July to September and Q4 is October to December.
Explanation
Answer: D
Explanation:
1. Identify that this can be answered by inspection.
The question has asked for the average for the first six months of the year – quarters one and two.
There are three at 75, two at 50, two at 100 and one at 150. This means that the average of the first 7 is 75 and then one more at 150.
This means that the average must be above 75 but won’t be as high as 100 so option D or E. As 150 is much higher, the new average will be more than 0.4 above 75 so the answer must be D not E.
Timing Tip: As this question has asked for an average of 8 values, you may find it possible to add the numbers together and divide by 8. However, for questions with more values (such as for the four items for the whole year) estimation by eyeballing graphs will save time.
The following graph shows the sales data from R Toys We, showing the units sold for the four most popular items in a single store in a year.
Item W is an electric plane.
Item X is a toy car racing set.
Item Y is a toy phone
Item Z is an electronic cash register toy.
Item W had the lowest returns rate at 0.5% whilst Item Z was returned at double this rate.
Q1 is January to March, Q2 is April to June, Q3 is July to September and Q4 is October to December.
Explanation
Answer: D
Explanation:
1. This again can be answered by inspection.
We are looking for the second highest difference in height.
Item X is the highest change – the second bar is three times the height of the first.
Item Z is the second largest change – it has more than doubled in height and so must be the second largest percentage change – this is the answer we are looking for so D is the answer.
Common trap: Note that it is asking for the second highest figure – this means that the answer is Item Z not Item X.
The following graph shows the sales data from R Toys We, showing the units sold for the four most popular items in a single store in a year.
Item W is an electric plane.
Item X is a toy car racing set.
Item Y is a toy phone
Item Z is an electronic cash register toy.
Item W had the lowest returns rate at 0.5% whilst Item Z was returned at double this rate.
Q1 is January to March, Q2 is April to June, Q3 is July to September and Q4 is October to December.
Explanation
Answer: D
Explanation:
1. Find the new sales of each.
New value = Multiplier x Old value.
For Item W: New sales = 0.8 x 100 = 80
For Item X: New sales = 1.1 x 150 = 165
1. Find the change in difference:
For the old values: 150 – 100 = 50
For the new values: 165 – 80 = 85
85 – 50 = 35 – option C.
Common trap:The question has asked for the change in difference not the new difference – this means the answer is 35 not 85
The following graph shows the sales data from R Toys We, showing the units sold for the four most popular items in a single store in a year.
Item W is an electric plane.
Item X is a toy car racing set.
Item Y is a toy phone
Item Z is an electronic cash register toy.
Item W had the lowest returns rate at 0.5% whilst Item Z was returned at double this rate.
Q1 is January to March, Q2 is April to June, Q3 is July to September and Q4 is October to December.
Explanation
Answer: D
Explanation:
1. Find the revenue for December as a percentage of the Q4 revenue.
Proportions compare one variable in comparison to the total.
Half of the sales came in December, but they were at a decreased price.
0.5 x £200 = £100
These were sold at £140:
100 x 140 = £14,000.
This price was a 20% reduction. To find the original price use the formula
The multiplier for a 20% reduction is 0.8
Therefore, the calculation is:
The sales were the same so:
£175 x 100 = £17,500
To find the proportion of revenue earned in December use the equation:
The December revenue was £14000, and the total is £14000 + £17500:
This means the answer is D.
Common trap: Note that the fact that half the sales occurred in December does not mean that half the revenue was from that month. The price was lower, so the amount of revenue generated for the same number of units sold was also lower.
- The stock price for a listed company is given over a single day.
- The price is given in pence per share.
- To buy shares a broker will pay an ‘offer’ price of 2p more per share than the price shown, with an additional price of £5 for stock purchases of 5000 or fewer shares. Above this level, there is a charge of 0.5%.
- To sell shares a broker will be paid a ‘bid’ price 2p less than the price shown
- There is a 2.5% deduction on any profit gained by buying and selling shares.
- A company’s value is considered to be the price at which all the shares could be sold.
- There are a total 500,000 shares in the company.
- A dividend is an amount of money paid to shareholders quarterly according to how many stocks they hold.
Explanation
Answer: B
Explanation:
1. Find when the largest change in price occurs:
This comes between 10:00 and 11:00.
The change is 176p to 174p – 2p.
2. Work out what impact this makes on the company’s value.
There are 500,000 shares in the company so:
0.02 x 500,000 = £10,000 – C.
Common trap:It has asked for the largest hourly fluctuation rather than the largest fluctuation across the day or the increase across the day.
Timing Tip: The price of a company is found using the bid price. However, this doesn’t affect the change in price so you can read the change shown on the graph with no further calculation.
- The stock price for a listed company is given over a single day.
- The price is given in pence per share.
- To buy shares a broker will pay an ‘offer’ price of 2p more per share than the price shown, with an additional price of £5 for stock purchases of 5000 or fewer shares. Above this level, there is a charge of 0.5%.
- To sell shares a broker will be paid a ‘bid’ price 2p less than the price shown
- There is a 2.5% deduction on any profit gained by buying and selling shares.
- A company’s value is considered to be the price at which all the shares could be sold.
- There are a total 500,000 shares in the company.
- A dividend is an amount of money paid to shareholders quarterly according to how many stocks they hold.
Explanation
Answer: E
Explanation:
1. Find the ‘buy’ price of these shares and any additional cost.
The buy price at 13:00 is 174.00 + 2 = 176p
Find the total price for 150 shares
176 x 150 = 26,400p
In pounds this is £264.
There is an additional charge – for this £5 is greater than 1%
264 + 5 = £269
Common trap: Remember that the purchase price is 2p more per share. Always remember to read the bullet points below data as they can change the answer.
- The stock price for a listed company is given over a single day.
- The price is given in pence per share.
- To buy shares a broker will pay an ‘offer’ price of 2p more per share than the price shown, with an additional price of £5 for stock purchases of 5000 or fewer shares. Above this level, there is a charge of 0.5%.
- To sell shares a broker will be paid a ‘bid’ price 2p less than the price shown
- There is a 2.5% deduction on any profit gained by buying and selling shares.
- A company’s value is considered to be the price at which all the shares could be sold.
- There are a total 500,000 shares in the company.
- A dividend is an amount of money paid to shareholders quarterly according to how many stocks they hold.
Explanation
Answer: E
Explanation:
1. Find the price at which he bought the shares.
The buy price is the listed price of 172p + 2p = 174p
174p x 5000 = 870,000p
Convert this to pounds and add on the purchase price of £5.
870000/100 = £8700
£8700 + £5 = £8705
2. Find the price at which he sells the shares.
Five hours later, it is 1700. The price listed is 178p so he must have sold them at 176p.
176 x 5000 = 8800
3. Find the profit and therefore the amount he will receive.
8800 – 8705 = £95.
He is charged 2.5% therefore it is a decrease of 2.5%.
95 x 0.975 = £92.625
This rounds to £93.
Common trap: Remember that the price of purchase and the price of sale are not the same as the one listed.
- The stock price for a listed company is given over a single day.
- The price is given in pence per share.
- To buy shares a broker will pay an ‘offer’ price of 2p more per share than the price shown, with an additional price of £5 for stock purchases of 5000 or fewer shares. Above this level, there is a charge of 0.5%.
- To sell shares a broker will be paid a ‘bid’ price 2p less than the price shown
- There is a 2.5% deduction on any profit gained by buying and selling shares.
- A company’s value is considered to be the price at which all the shares could be sold.
- There are a total 500,000 shares in the company.
- A dividend is an amount of money paid to shareholders quarterly according to how many stocks they hold.
Explanation
Answer: B
Explanation:
1. Work out the Q1 dividend for the broker:
1% of 178p = 1.78p
The broker has 105,000 shares so:
105,000 * 0.0178 = £1869
2. Find the dividend in the other quarters and the total:
Q2 is 3% higher than Q1.
Q2: £1869 x 1.03 = £1925.07
Q3 is 5% higher than Q2.
Q3: £1925.07 x 1.05 = £2021.3235
Q4 is 50% of Q1:
Q4: £1869 x 0.5 = £934.50
In total: £1869 + £1925.07 + £2021.3235 + £934.50 = £6749.80.. = £6750 to the nearest pound.
Top tip: Sometimes estimates will not be able to find the answer. Here, the £6749 and £6750 are so close together so any estimate would not get near enough to the answer.
- In the first four innings of the season, Keaton has scored the above number of runs for his school cricket team.
- His school measures success by the average number of runs scored per innings.
- His bowling is above average for his age group with 15 wickets in the first four games of the season at an average of 12.5 and an economy rate of 4.
Explanation
Answer: D
Explanation:
1. Find the average after four innings:
85 + 90 + 95 + 80 = 350
350 / 4 = 87.5
2. Find the average after five innings and thus the difference:
350 + 10 = 360
360/5 = 72
Find the difference:
87.5 – 72 = 15.5 runs
Timing tip: Try to do as many of the calculations in your head or on your whiteboard as you can. This will often be quicker than using the UCAT calculator.
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Fri, 19 Mar 2021 09:22:33
Could someone explain why D is incorrect? We don't know that the sales are higher w/o the total, but we can tell that the % of sales are higher?