UCAT Quantitative Reasoning Test #6

Question 1

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?

Accepted Answer

10.30%

Answer

Explanation:
Find the multiplier:
130/145 = 0.89655… = 10.345 % percentage decrease
To the nearest 0.1%, this is 10.3%

Question 2

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?

Accepted Answer

7%

Answer

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.

Question 3

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?

Accepted Answer

$239,250

Answer

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.

Question 4

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?

Accepted Answer

54%

Answer

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%

Question 5

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?

Accepted Answer

1:3

Answer

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

UCAT Practice Test

UCAT Practice Test

UCAT Quantitative Reasoning Test #6