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Test: Charts & Graphs - 2 - UCAT MCQ


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10 Questions MCQ Test Quantitative Reasoning for UCAT - Test: Charts & Graphs - 2

Test: Charts & Graphs - 2 for UCAT 2024 is part of Quantitative Reasoning for UCAT preparation. The Test: Charts & Graphs - 2 questions and answers have been prepared according to the UCAT exam syllabus.The Test: Charts & Graphs - 2 MCQs are made for UCAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Charts & Graphs - 2 below.
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Test: Charts & Graphs - 2 - Question 1

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.

Q. What was the approximate average sales for the four items in the first six months?

Detailed Solution for Test: Charts & Graphs - 2 - Question 1

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.

Test: Charts & Graphs - 2 - Question 2

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.

Q. Sales of Item W in Q1 of the following year declined by 20% from Q4. Sales of Item X increased by 10% in the same period. Comparing the difference between sales of Item W and sales of Item X in the two periods, by how many units did the difference in sales change?

Detailed Solution for Test: Charts & Graphs - 2 - Question 2

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

2. Find the change in difference:

For the old values: 150 – 100 = 50
For the new values: 165 – 80 = 85

85 – 50 = 35 – option C.

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Test: Charts & Graphs - 2 - Question 3

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.

Q. Which item has the second highest percentage change in units sold between Q1 and Q4?

Detailed Solution for Test: Charts & Graphs - 2 - Question 3

We are looking for the second highest difference in height.

Item Z is the highest change – the second bar is around 2.5 times the height of the first.

Item X is the second largest change – it has 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.

Test: Charts & Graphs - 2 - Question 4

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.

Q. For Item Z, half of the sales from Q4 were in December and the rest were split evenly between the other two months. The price of Item Z in December was £140 – a reduction of 20% on the price for the previous two months. What proportion of the revenue from sales of Item Z in Q4 came in December?

Detailed Solution for Test: Charts & Graphs - 2 - Question 4

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

Old Value = New Valur / Multiplier

Test: Charts & Graphs - 2 - Question 5

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.

Q. What is the largest fluctuation in the value of the company across the period of an hour?

Detailed Solution for Test: Charts & Graphs - 2 - Question 5

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.

Test: Charts & Graphs - 2 - Question 6

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.

Q. What would the purchase price be for 150 shares at 13:00?

Detailed Solution for Test: Charts & Graphs - 2 - Question 6

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

Test: Charts & Graphs - 2 - Question 7

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.

Q. A broker holds 105,000 shares. The stock’s Q1 dividend is 1% of the value of the shares at 1700 on the day shown above. The Q2 dividend is 3% higher than this. The Q3 dividend is 5% higher than the Q2 dividend. The Q4 dividend is half that of the Q1. Assuming the broker maintained the same number of shares for the whole year, to the nearest pound, what would the annual dividend be?

Detailed Solution for Test: Charts & Graphs - 2 - Question 7

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.

Test: Charts & Graphs - 2 - Question 8

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.

Q. Jeremy bought 5000 shares at 12:00 and sold them five hours later. To the nearest pound, how much profit did he make?

Detailed Solution for Test: Charts & Graphs - 2 - Question 8

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.

Test: Charts & Graphs - 2 - Question 9

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.

Q. In his fifth innings, Keaton scored 10 runs. By how many runs did his average runs scored fall?

Detailed Solution for Test: Charts & Graphs - 2 - Question 9

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

Test: Charts & Graphs - 2 - Question 10

Here is the graph about the number of English counties pupils in two classes at a primary school had visited.


The class size for each was 30.

Q. In the summer holidays, 50% of Class 1 students who had previously been to one county and 60% of Class 2 students who had previously been to one county visited three more counties each. Those who had previously been to two or more counties did not visit any more. What is the new proportion of the two classes who have been to four or more counties?

Detailed Solution for Test: Charts & Graphs - 2 - Question 10

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%

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