# UCAT Quantitative Reasoning Test #6

#### This is the income for a medium-to-large Australian company.

All figures are reported in Australian dollars.

What was the percentage drop in Teaching revenue for this company between February and March, to the closest 0.1 percent?

Explanation:

Find the multiplier:

130/145 = 0.89655… = 10.345 % percentage decrease

To the nearest 0.1%, this is 10.3%

#### A poll found that 43% of people can snowboard and 34% can ski. 30% of people were unable to perform both. 7 percent of those who have gone skiing or snowboarding for a total of more than 28 days in their lives have needed hospital care due to an accident or injury. How many people can ski and snowboard at the same time?

Explanation:

The best approach is to use a value of 100 people because it makes it simple to calculate percentages.

Draw a Venn Diagram to represent the situation.

A + B + C + 30 = 100

A + B + C = 70

Create equations for the number of people who can perform each activity, then solve them to obtain C and 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.

#### This is the income for a medium-to-large Australian company.

All figures are reported in Australian dollars.

The business wishes to evaluate its mean monthly revenue across all three of its revenue sources. What is the average monthly revenue for the three months listed in the table, to the closest $250?

Explanation:

Find the average monthly income and the total amount of the incomes:

(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.

#### One-day-only savings are available on Hispanlearn's online Spanish course. They are providing a 40% discount. You would save an additional 10% off the revised pricing if you paid in full up advance. What portion of the original price would you pay today if you paid everything up front?

Explanation:

Find the first discount.

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

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 54%

#### The Hornets' budget, a premiership rugby team.

Premiership clubs are permitted to employ two marquee players with higher salaries who are exempt from the salary cap rules of the league. The hiring of a new marquee player was the sole cause of the playing staff's compensation hike in 2018–19. About 12.7% of the playing budget for 2018–19 goes to the other star player. What is the approximate ratio of the two star players' salary to that of the other players?

Explanation:

Calculate the difference between the money spent on marquee and non-marquee players:

1.2.+ 12.7% of 8.5 million = £2.2795 million

8.5 – 2.1271 = £6.2205 million

Establish a ratio between the marquee and non-marquee players:

2.2795: 6.2205

Simplify this ratio:

Since we already know that one side equals one, we can divide by 2.2795 to find the largest common factor:
6.2205/2.2795 = 2.73 = 3

Therefore, the simplified ratio is 1:3

#### The Hornets' budget, a premiership rugby team.

How much money did the club spend in 2017–18?

Explanation:

Identify the information that the query is seeking:

The budget for 2017–18 has been requested, but it is not stated explicitly in the question.

We are informed of the budget for 2018–19 and how much higher it is than the budget for 2017–18.

To determine the prior budget, subtract the increases:

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

#### The Hornets' budget, a premiership rugby team.

The percentage of the overall budget spent on the playing staff in 2017/18, which came to 0.1 percent, was as follows:

Explanation:

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

The 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%

#### Every year, a city hosts a comedy festival. In Year 1, the festival lasted five weeks and 123,545 tickets were sold in total. In Year 2, the event lasted for 8 weeks, and the average weekly ticket sales were 25% higher. In year two, how many tickets were sold?

Explanation:

Find the average weekly sales in Year 1

123,545 in 5 weeks

123,545/5 = 24709 a week

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

#### The units sold for the four most popular items at a single store over the course of a year are represented in the following graph using sales data from R Toys We.

An electric plane is Item W.

A set of toy race cars is Item X.

It is a toy phone, item Y.

An electronic cash register toy is item Z.

While Item Z was returned at twice the rate of Item W, Item W had the lowest return rate at 0.5 percent.

January through March is considered Q1, April through June, July through September, and October through December.

What was the four goods' approximative average sales throughout the first six months?

Explanation:

The average for the first six months of the year, or quarters one and two, was requested in the question.

At 75, two are at 50, two are at 100, and one is at 150. Accordingly, the average of the first seven is 75, followed by one more at 150.

#### The units sold for the four most popular items at a single store over the course of a year are represented in the following graph using sales data from R Toys We.

An electric plane is Item W.

A set of toy race cars is Item X.

It is a toy phone, item Y.

An electronic cash register toy is item Z.

While Item Z was returned at twice the rate of Item W, Item W had the lowest return rate at 0.5 percent.

January through March is considered Q1, April through June, July through September, and October through December.

Which product's percentage change in units sold between Q1 and Q4 is second highest?

Explanation:

The second-highest height difference is what we're looking for.

The second bar is around 2.5 times as tall as the first in Item Z, which has undergone the greatest modification.

The answer is Item X since it has undergone the second-largest alteration and has doubled in height, making it the second-largest percentage change.

#### The units sold for the four most popular items at a single store over the course of a year are represented in the following graph using sales data from R Toys We.

An electric plane is Item W.

A set of toy race cars is Item X.

It is a toy phone, item Y.

An electronic cash register toy is item Z.

While Item Z was returned at twice the rate of Item W, Item W had the lowest return rate at 0.5 percent.

January through March is considered Q1, April through June, July through September, and October through December.

Item W sales in the first quarter of the next year fell by 20% from the previous quarter. Item X's sales rose by 10% during the same time frame. How many units did the sales difference vary when comparing the difference between the sales of Item W and Item X in the two periods?

Explanation:

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

Find the change in difference:

For the old values: 150 – 100 = 50

For the new values: 165 – 80 = 85

85 – 50 = 35

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