Doc 2: Practice Questions for Quantitative Reasoning | Quantitative Reasoning for UCAT PDF Download

Quantitative Reasoning Practice Questions

• You are presented with questions that most often refer to charts and graphs containing data.
• Most questions are shown as sets of four questions each connected to the same data. There are some questions that are standalone and do not share data.
• Each question has five answer options. You are only able to select one response.

Q.1. The table shows the viewership of five prime time programmes on a weekday

Q. What is the total number of audience who tuned in to Programme 3?
(a) 1,161
(b) 1,350
(c) 1,520
(d) 1,728
(e) 1,844

Correct Answer is Option (d)
Total number of audience who turned in to Programme 3 = number of audience who tuned in through network services + number of audience who tuned in through cable services + number of audience who tuned in through syndies + number of audience who tuned in through other networks = 567 + 594 + (2 x 13, 500 / 100) + (2.2 x 13,500 /100) = 567 + 594 + 270 + 297 = 1,728.

Q.2. The table shows the viewership of five prime time programmes on a weekday

Q. If about 33.33% of the audience who tuned in to Programme 1 through the syndies services switched to Programme 4 through the syndies, what would be the number of audience who tuned in to Programme 4 through the syndies? Assume the base audience population remains unchanged.
(a) 50
(b) 90
(c) 146
(d) 210
(e) 434

Correct Answer is Option (c)
Number of audience who tuned in to Programme 1 through the syndies services = rate x base audience population / 100 = 1.6 x 10,500 / 100 = 168

33.33% of this audience is = 56

Number of audience who tuned in to Programme 4 through the syndies = number of audience who switched to Programme 4 + number of audience who tuned in through the syndies originally = 56 + (rate x base population of Programme 4 / 100) = 56 + (3.6 x 2, 500 / 100) = 56 + 90 = 146

Q.3. The table shows the viewership of five prime time programmes on a weekday

Q. Approximately 24.8% of the audience who tuned in through the Syndies services for Programme 2 were female. What number of the audience who tuned in through the Syndies services for Programme 2 were male?
(a) 70
(b) 92
(c) 132
(d) 168
(e) 212

Correct Answer is Option (e)
Number of audience who tuned in through the syndies services for Programme 2 = rating x base audience population / 100= 3 x 9,400/ 100 = 282

24.8% of this 282 audience was female and the remaining, (100 – 24.8=)75.2%, was male. 

Number of audience who tuned in through the syndies services for Programme 2 that were male = 282 x 0.752 = 212 

Q.4. The table shows the viewership of five prime time programmes on a weekday

Q. What is the difference in the overall rating of Programme 2 and that of Programme 1?
(a) 0.25
(b) 0.48
(c) 1.00
(d) 1.62
(e) 2.00

Correct Answer is Option (e)
The overall rating of each programme is the total rating of people who tuned in through network, cable, syndies and others. As the information for syndies and others is already presented as a rating, the calculation needs to be made for network and cable services.

Programme 1 Network services rating = 756 / 10500 x 100 = 7.2

Programme 1 Cable services rating = 399 / 10500 x 100 = 3.8

The overall rating of Programme 1 is therefore: 7.2 + 3.8 + 1.6 + 0.4 = 13

Programme 2 Network services rating = 611 / 9400 x 100 = 6.5

Programme 2 Cable services rating = 423 / 9400 x 100 = 4.5

The overall rating of Programme 2 is therefore: 6.5 + 4.5 + 3 + 1 = 15

The difference between overall rating of the 2 programmes is 15 - 13 = 2

Q.5. The temperature on Venus is halfway between the temperature on Earth and the temperature on Mercury. What is the temperature on Mercury?

(a) 230 °C
(b) 240 °C
(c) 250 °C
(d) 460 °C
(e) 940 °C

Correct Answer is Option (e)
480 + (480 – 20) = 940.

Q.6. What is the correct rule for changing a temperature in °F to a temperature in °C?

(a) Temperature in °C = Temperature in °F multiplied by 1.8, then add 32
(b) Temperature in °C = Temperature in °F divided by 1.8, then add 32
(c) Temperature in °C = Temperature in °F multiplied by 1.8, then subtract 32
(d) Temperature in °C = Temperature in °F plus 32, then multiply by 1.8
(e) Temperature in °C = Temperature in °F minus 32, then divide by 1.8

Correct Answer is Option (e)
Option E is correct because the operators and the numbers are in the correct order.

Option A is incorrect because F must be divided by 1.8, not multiplied; 32 must be subtracted, not added.

Option B is incorrect because 32 must be subtracted, not added.

Option C is incorrect because F must be divided by 1.8, not multiplied.

Option D is incorrect because 32 must be subtracted, not added.

Q.7. How much higher is the temperature in °F on Earth than the temperature in °F on Mars?

(a) 68°F

(b) 72°F
(c) 104°F
(d) 144°F
(e) 176°F

Correct Answer is Option (d)
Earth (20 x 1.8) + 32 = 68

Mars (-60 x 1.8) + 32 = -76

-76 – 68 = -144

Q.8. When the numerical value of the temperature in °F is the same as the numerical value of the temperature in °C, what is the temperature in °F?
(a) -100°F
(b) -60°F
(c) -40°F
(d) 0°F
(e) 40°F

Correct Answer is Option (c)
If x is the numerical value that equals C and F then it can be put into the equation to solve x:

x = 1.8x + 32

0.8x = 32

x = 40

(-40 x 1.8) + 32 = -40

Q.9. The winner of a council election in April resigns in July and a new election is held in September. There are no changes in the number of people entitled to vote between April and September.

By reading across, you can see the number of voters supporting a party in April and how the same people voted in September. No one had died or left the district.
To learn how people who voted for a particular party in September had voted in April, read down the column - the total September vote is given at the bottom of each column, including any votes gained in September from people who had not voted in April.
Q. The percentage of people entitled to vote who actually did vote in April was:
(a) 45%
(b) 50%
(c) 55%
(d) 60%
(e) 65%

Correct Answer is Option (b)
This is because the total turnout is 540 + 520 + 440 which equals 1500.

The eligible voters for April is this figure plus 1500 which equals 3000.

The percentage of people entitled to vote is then (1,500 ÷ 3,000) x 100 which equals 50%.

Q.10. The winner of a council election in April resigns in July and a new election is held in September. There are no changes in the number of people entitled to vote between April and September.

By reading across, you can see the number of voters supporting a party in April and how the same people voted in September. No one had died or left the district.
To learn how people who voted for a particular party in September had voted in April, read down the column - the total September vote is given at the bottom of each column, including any votes gained in September from people who had not voted in April.
Q. Rounded to the nearest whole number, what percentage of all people eligible to vote acted in the same way in the two elections?
(a) 53%
(b) 54%
(c) 60%
(d) 61%
(e) 67%

Correct Answer is Option (c)
This is because the total number of people who voted the same way in both elections is 270 + 208 + 330 + 1,000 which equals 1,808. 

The total number of votes over two elections is 540 + 520 + 440 + 1,500 which equals 3,000 (or 494 + 382 + 711 + 1,413). 1,808 / 3,000 ≈ 60%.

Q.11. The winner of a council election in April resigns in July and a new election is held in September. There are no changes in the number of people entitled to vote between April and September.

By reading across, you can see the number of voters supporting a party in April and how the same people voted in September. No one had died or left the district.
To learn how people who voted for a particular party in September had voted in April, read down the column - the total September vote is given at the bottom of each column, including any votes gained in September from people who had not voted in April.
Q. What percentage of the people who voted for Party C in April voted for the party again in September?
(a) 50%
(b) 60%
(c) 65%
(d) 75%
(e) 100%

Correct Answer is Option (d)
This is because the number of people who voted for the party in both April and September is 330.

The total number of voters in April was 440. Therefore, 330/440 = 75%

Q.12. The winner of a council election in April resigns in July and a new election is held in September. There are no changes in the number of people entitled to vote between April and September.

By reading across, you can see the number of voters supporting a party in April and how the same people voted in September. No one had died or left the district.
To learn how people who voted for a particular party in September had voted in April, read down the column - the total September vote is given at the bottom of each column, including any votes gained in September from people who had not voted in April.
Q. Calculate the difference in votes between the first and second party in September.
(a) 20
(b) 100
(c) 112
(d) 217
(e) 702

Correct Answer is Option (d)
This is because the party with the most votes in September got 711 votes. The party in second place got 494 votes. 

The winning margin was then 711 – 494 = 217.

Q.13. The graph shows respondents’ responses when asked what finger they use to type the “Space” bar on the keyboard of a computer.

Q. Among all the respondents, only 40% of those who said “Left thumb” and 50% of those who said “Alternating thumb” were self-taught typists. How many respondents were self-taught typists?
(a) 38
(b) 42
(c) 46
(d) 52
(e) 55

Correct Answer is Option (d)
The respondents who voted for “Left thumb” = 65

The respondents who voted for “Left thumb” and are self taught = 0.4 × 65 = 26 

The respondents who voted for “Alternating thumb” = 52

The respondents who voted for “Alternating thumb” and are self taught = 0.5 × 52 = 26 respondents

The number who are self taught = 26 + 26 = 52

Q.14. The snow leopard population in Country A is 40% of the snow leopard population in Country (b) The population of snow leopards in Country C is 50% of that in Country (a) If the snow leopard population in Country C is 520.
Q. What is the snow leopard population in Country B?
(a) 2,060
(b) 2,160
(c) 2,350
(d) 2,550
(e) 2,600

Correct Answer is Option (e)
Let the snow leopard population in Country A be x

Let the snow leopard population in Country B be y. x = 0.4y

Snow leopard population in Country C is 520, but this is 50% of x. So, 0.5x = 520, x = 1040

Since, x = 0.4y, y = 1040/0.4 = 2,600

Q.15.Government spending on “Health Services” and “Social Protection” was 120 billion dollars and 190 billion dollars respectively for the year 2010-2011. In the same year, government spending on “Debt Interests” was 33.33% of the spending on “Health Services”, and the spending on “Health Services”, “Social Protection” and “Debt Interests” constituted 50% of the total spending by the government.
Q. What was the government’s approximate total spending for the year 2010-11?
(a) 350 billion dollars
(b) 670 billion dollars
(c) 680 billion dollars
(d) 700 billion dollars
(e) 725 billion dollars

Correct Answer is Option (d)
The government spending on Health Services = 120 billion dollars

The government spending on Debt Interests = 0.3333 x 120 billion dollars = 39.996 billion dollars

The sum of spending on Health Services, Social Protection and Debt Interests = 120 + 190 + 39.996 = 349.996 billion dollars

The total government spending = 349.996 x 100/50 = 699.992 billion dollars

Q.16. The table shows the prices to place different sized advertisements in the main section of a newspaper.

Q. How much more does it cost a company to place two 24 x 10 mono advertisements and one 22 x 5 mono advertisement combined than four 8 x 10 colour advertisements?
(a) £56
(b) £78
(c) £3,758
(d) £5,510
(e) £9,485

Correct Answer is Options (b)
Cost of two mono 24 x 10 = 2 x 7533 = 15,066

Cost of one mono 22 x 5 = 3,836

Total cost = 18,902

Cost of 4 colour 8 x 10 = 4 x 4706 = 18,824

Difference = 18,902 – 18,824 = 78

Q.17. The table shows the billions of units of apps and songs downloaded from an Internet store, months after the store launch.

Q. If the numbers downloaded seen after 25 months continues to increase at an average rate, approximately how many more billions of apps than songs are likely to be downloaded 40 months after the launch?
(a) 3
(b) 7
(c) 9
(d) 10
(e) 12

Correct Answer is Options (e)

Number of apps downloaded at 25 months = 5.65 billion

Number of apps downloaded at 30 months = 9.15 billion

Number of apps downloaded at 35 months = 12.14 billion

Increase from 25 months to 30 months = 9.15 – 5.65 = 3.5 billion

Increase from 30 months to 35 months = 12.14 – 9.15 = 2.99 billion

So, the average increase is (3.5 + 2.99)/2 = 3.245 billion

The number expected to be downloaded at 40 months = 12.14 + 3.245 = 15.385

Number of songs downloaded at 25 months = 2.85 billion

Number of songs downloaded at 30 months = 2.94 billion

Number of songs downloaded at 35 months = 3.01 billion

Increase from 25 months to 30 months = 2.94 – 2.85 = 0.09 billion

Increase from 30 months to 35 months = 3.01 – 2.94 = 0.07 billion

So, the average increase is (0.09 + 0.07)/2 = 0.08 billion

The number expected to be downloaded at 40 months = 3.01 + 0.08 = 3.09

Difference = 15.385 – 3.09 = 12.295 billion

Q.18. The budget for a country council

Q. The total budget for 2005/6 was:
(a) $28m
(b) $528m
(c) $540m
(d) $568m
(e) $596m

Correct Answer is Options (c)
Sum the increase (28) and deduct from the total 568 - 28 = 540.

Q.19. The budget for a country council

Q. Waste management costs in 2005/6 were:
(a) $3m
(b) $39m
(c) $42m
(d) $45m
(e) $126m

Correct Answer is Options (b)
42 – 3 = 39m

Q.20. The budget for a country council

Q. The percentage of spending on Children's services in 2005/06 was (to the nearest whole percentage):
(a) 21%
(b) 23%
(c) 25%
(d) 27%
(e) 29%

Correct Answer is Options (b)
(130-6) =124. (124/540) x 100 = 22.96