UCAT Quantitative Reasoning Practice Test 2022 Question Bank

UCAT Quantitative Reasoning Practice Test 2022 Question Bank: You can also download UCAT Quantitative Reasoning Question Bank in PDF format. Try our free original University Clinical Aptitude Test (UCAT) exam test prep for the UK, Australia and New Zealand.

The Quantitative Reasoning subtest tests your ability to quickly interpret data and perform relevant calculations upon them. Section 3 contains 36 questions and you have 24 minutes to answer them, giving a total of 40 seconds per question – slightly more generous than the verbal reasoning section. As with all UKCAT sections, you have one additional minute to read the instructions at the start.

UCAT Quantitative Reasoning Practice Test 2022 Question Bank

UCAT Quantitative Reasoning Practice Test

There is an on-screen calculator – a basic calculator for performing arithmetic. You should ideally practice with a non-scientific calculator when working through this book, as that will give the closest simulation to what you will get on the day. When you move on to trying the online UKCAT practice papers, the calculator is available on screen as you will see it in the test. 

In addition to using it to solve questions, practice different calculations to build your speed using it – though this sounds boring, it will save you valuable time on the day. Something many candidates do not realise is that the calculator can be operated using keyboard controls. Try this out for yourself in practice, and if it works for you it is yet another way to boost your speed when you come to the UCAT for real.

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UCAT Quantitative Reasoning Practice Test

Quantitative Reasoning Practice Test

Total Questions: 36
Time Limit: 25 minutes

 INSTRUCTIONS

You will be presented with questions that most often refer to charts and graphs containing data. Additional information may also be found within the question itself. Most questions will be shown as sets of four questions each connected to the same data. There are some questions that standalone and do not share data. Each question has five answer options. Your task is to choose the best option.

An onscreen calculator is available to assist you with these questions – you can access this by clicking on the button at the top left of the screen.

tail spin

1 / 36


A zoo vet needs to sedate his elephants. To do this, he will use the special sedative jumbodiaz- epane. In elephants, the effective dose of jumbodiazepane is one microgram per kilogram of bodyweight (a microgram is one thousandth of a milligram), and the lethal dose is one and a half micrograms per kilogram of bodyweight.

An average male (bull) elephant weighs 3 tonnes (a tonne is 1,000 kilograms), a female weighs two-thirds of this, and a new-born calf weighs a quarter of its mother’s weight.

An average zoo-vet weighs 80 kilograms.


Veterinary scientists have discovered that a compound found in peanuts lowers the tolerance thresholds of elephants to jumbodiazepane by one third. What is the largest weight of a peanut-eating elephant, in kilograms, that could be killed by 2.5 milligrams of jumbodiazepane?

 

2 / 36


A zoo vet needs to sedate his elephants. To do this, he will use the special sedative jumbodiaz- epane. In elephants, the effective dose of jumbodiazepane is one microgram per kilogram of bodyweight (a microgram is one thousandth of a milligram), and the lethal dose is one and a half micrograms per kilogram of bodyweight.

An average male (bull) elephant weighs 3 tonnes (a tonne is 1,000 kilograms), a female weighs two-thirds of this, and a new-born calf weighs a quarter of its mother’s weight.

An average zoo-vet weighs 80 kilograms.


 

If the lethal dose of jumbodiazepane for a human is a tenth of a microgram per kilogram of body weight, how many zoo vets could be killed by the sedative by the amount needed to send to sleep a female elephant?

 

3 / 36


A zoo vet needs to sedate his elephants. To do this, he will use the special sedative jumbodiaz- epane. In elephants, the effective dose of jumbodiazepane is one microgram per kilogram of bodyweight (a microgram is one thousandth of a milligram), and the lethal dose is one and a half micrograms per kilogram of bodyweight.

An average male (bull) elephant weighs 3 tonnes (a tonne is 1,000 kilograms), a female weighs two-thirds of this, and a new-born calf weighs a quarter of its mother’s weight.

An average zoo-vet weighs 80 kilograms.


 

The vet gives each elephant an injection of 10 millilitres. If he first prepares the sedation mixture in batches of one litre, how much pure jumbodiazepane, in grams, does he need to put into a batch to produce injections that will sedate elephants weighing one and a half tonnes?

 

4 / 36


A zoo vet needs to sedate his elephants. To do this, he will use the special sedative jumbodiaz- epane. In elephants, the effective dose of jumbodiazepane is one microgram per kilogram of bodyweight (a microgram is one thousandth of a milligram), and the lethal dose is one and a half micrograms per kilogram of bodyweight.

An average male (bull) elephant weighs 3 tonnes (a tonne is 1,000 kilograms), a female weighs two-thirds of this, and a new-born calf weighs a quarter of its mother’s weight.

An average zoo-vet weighs 80 kilograms.


The vet has to sedate one bull elephant, two female elephants and three calves. What is the minimum weight of pure jumbodiazepane he needs to order?

 

5 / 36


The Republic of Francissia has recently introduced a new tax system. Citizens have an income allowance before they have to pay income tax. After that, they pay tax as a percentage of their income over a given amount. At higher threshold levels of income there are higher rates of income tax. Certain members of society receive tax perks, for example, nurses only start paying income tax on earnings over FR$ 1,600. The tax system is summarised in the following table (the currency is the Francissian dollar, FR$):

table


If a person earned FR$ 5,000 in 2017 and 2016, what is the percentage reduction in the amount of tax paid in 2017 compared to 2016?

6 / 36


The Republic of Francissia has recently introduced a new tax system. Citizens have an income allowance before they have to pay income tax. After that, they pay tax as a percentage of their income over a given amount. At higher threshold levels of income there are higher rates of income tax. Certain members of society receive tax perks, for example, nurses only start paying income tax on earnings over FR$ 1,600. The tax system is summarised in the following table (the currency is the Francissian dollar, FR$):

table


What did a nurse earning FR$ 8,000 receive in take-home pay in 2017, assuming income tax is the only deduction?

 

7 / 36


The Republic of Francissia has recently introduced a new tax system. Citizens have an income allowance before they have to pay income tax. After that, they pay tax as a percentage of their income over a given amount. At higher threshold levels of income there are higher rates of income tax. Certain members of society receive tax perks, for example, nurses only start paying income tax on earnings over FR$ 1,600. The tax system is summarised in the following table (the currency is the Francissian dollar, FR$):

table


 

What did a worker earning FR$ 12,250 receive in take-home pay in 2016, assuming income tax is the only deduction?

8 / 36


The Republic of Francissia has recently introduced a new tax system. Citizens have an income allowance before they have to pay income tax. After that, they pay tax as a percentage of their income over a given amount. At higher threshold levels of income there are higher rates of income tax. Certain members of society receive tax perks, for example, nurses only start paying income tax on earnings over FR$ 1,600. The tax system is summarised in the following table (the currency is the Francissian dollar, FR$):

table


 

If a worker earned FR$ 1,300 in gross income 2016. What would their pay be after tax deduc- tions if their wages in 2017 rose in line with an inflation figure of 1.5%, assuming they only pay income tax?

 

9 / 36


A renowned design company is in the process of bringing out a new range of furniture. The furniture is to be made of moulded plastic.

The plastic has a density of 2 g/cm 3 . It costs £100 per metric tonne (1,000 kilograms).

When it arrives at the furniture factory, the plastic is in the form of small pellets which measure 3 centimetres in length. Their height is a third of their length, and their width is double their height. These pellets need to be melted down to be moulded.

The factory plans to produce chairs with odd-shaped legs. One chair leg can be regarded as
a triangular prism, with a cross section shown in the following

Verbal Reasoning 2


 

The factory also makes cabinets. However, the machine that makes cabinets is faulty, and 12.5% of the plastic that enters it is accidentally destroyed. If a cabinet should have a final weight 10.5 kilograms, what is the minimum number of pellets that are needed to ensure that one cabinet can be correctly made?

 

10 / 36


A renowned design company is in the process of bringing out a new range of furniture. The furniture is to be made of moulded plastic.

The plastic has a density of 2 g/cm 3 . It costs £100 per metric tonne (1,000 kilograms).

When it arrives at the furniture factory, the plastic is in the form of small pellets which measure 3 centimetres in length. Their height is a third of their length, and their width is double their height. These pellets need to be melted down to be moulded.

The factory plans to produce chairs with odd-shaped legs. One chair leg can be regarded as
a triangular prism, with a cross section shown in the following

Verbal Reasoning 2


 

The plastic that is turned into chair legs is produced as long prisms with a triangular cross- section. These prisms are then cut into chair legs. If over the course of a single day the factory produces a prism that is 50 kilometres long in total, what would have been the cost of the plastic needed to produce it?

 

11 / 36


A renowned design company is in the process of bringing out a new range of furniture. The furniture is to be made of moulded plastic.

The plastic has a density of 2 g/cm 3 . It costs £100 per metric tonne (1,000 kilograms).

When it arrives at the furniture factory, the plastic is in the form of small pellets which measure 3 centimetres in length. Their height is a third of their length, and their width is double their height. These pellets need to be melted down to be moulded.

The factory plans to produce chairs with odd-shaped legs. One chair leg can be regarded as
a triangular prism, with a cross section shown in the following

Verbal Reasoning 2


 

The chairs that the company are designing will have four legs. If each chair leg is 40 cm in
length, what is the mass of plastic required to make the chair legs for a single chair?

 

12 / 36


A renowned design company is in the process of bringing out a new range of furniture. The furniture is to be made of moulded plastic.

The plastic has a density of 2 g/cm 3 . It costs £100 per metric tonne (1,000 kilograms).

When it arrives at the furniture factory, the plastic is in the form of small pellets which measure 3 centimetres in length. Their height is a third of their length, and their width is double their height. These pellets need to be melted down to be moulded.

The factory plans to produce chairs with odd-shaped legs. One chair leg can be regarded as
a triangular prism, with a cross section shown in the following

Verbal Reasoning 2


 

The furniture factory has a processing vat which melts the plastic. The vat has a volume of 150 metres 3 . What number of pellets would fill half a vat?

 

13 / 36


Mike and Sarah are buying a house together. On the ground floor there are two receptions rooms (3 × 6 metres) and (4 × 7 metres), a kitchen-diner (5 × 4 metres) and a hallway. The hall- way is a quarter of the size of the largest reception room.


 

Mike and Sarah’s friends, Archie and Abbey, are looking to buy their first house and are offered a mortgage allowing them to borrow four times their deposit. Archie has been saving 15% of his £60,000 per year salary as a chartered accountant for the last 5 years. They have put down a deposit on a £340,000 house. Abbey has only been saving for 2 years but contributed 25% of her salary annually. How much does Abbey earn per year?

 

14 / 36


Mike and Sarah are buying a house together. On the ground floor there are two receptions rooms (3 × 6 metres) and (4 × 7 metres), a kitchen-diner (5 × 4 metres) and a hallway. The hall- way is a quarter of the size of the largest reception room.


Mike and Sarah bought their first house in 2016 for £225,000. It has subsequently increased in value by 6%. What is the value of their house today?

 

15 / 36


Mike and Sarah are buying a house together. On the ground floor there are two receptions rooms (3 × 6 metres) and (4 × 7 metres), a kitchen-diner (5 × 4 metres) and a hallway. The hall- way is a quarter of the size of the largest reception room.


After buying the house, they build a semi-circular conservatory extension to the kitchen, increasing the overall area of the kitchen by 50%.To the nearest half metre, what is the diameter of the conservatory?

 

16 / 36


Mike and Sarah are buying a house together. On the ground floor there are two receptions rooms (3 × 6 metres) and (4 × 7 metres), a kitchen-diner (5 × 4 metres) and a hallway. The hall- way is a quarter of the size of the largest reception room.


What is the surface area of the ground floor?

 

17 / 36


White blood cells are produced to fight infections. There are five main types of white blood cell that collectively make up the total white blood cell count. These five cell types include: neutrophils, leucocytes, monocytes, eosinophils and basophils. The following is a table of blood results of three patients

Verbal Reasoning 1


Patient 2 is treated with the antibiotic Meropenem, costing £10 per half gram. He requires 0.5 grams of Meropenem, three times per day for 7 days. This 7-day course costs six times as much as a standard 5-day course of the antibiotic Erythromycin. How much does a stan- dard 5-day course of Erythromycin cost per day?

 

18 / 36


White blood cells are produced to fight infections. There are five main types of white blood cell that collectively make up the total white blood cell count. These five cell types include: neutrophils, leucocytes, monocytes, eosinophils and basophils. The following is a table of blood results of three patients

Verbal Reasoning 1


The estimated blood volume of patient 1 is 6 litres. How many grams of haemoglobin does his blood contain?

19 / 36


White blood cells are produced to fight infections. There are five main types of white blood cell that collectively make up the total white blood cell count. These five cell types include: neutrophils, leucocytes, monocytes, eosinophils and basophils. The following is a table of blood results of three patients

Verbal Reasoning 1


When they repeated the blood tests the next day, the platelet count of Patient 3 had decreased by 20%. What was his platelet count the next day?

 

20 / 36


White blood cells are produced to fight infections. There are five main types of white blood cell that collectively make up the total white blood cell count. These five cell types include: neutrophils, leucocytes, monocytes, eosinophils and basophils. The following is a table of blood results of three patients

Verbal Reasoning 1


What proportion of the white blood cells are made up by cells other than neutrophils and leucocytes in Patient 2?

21 / 36

At another point, Point F, water flows at a rate of 30 m 3/s in the summer. By examining trends on the graph, what can we estimate the flow rate in the winter to be?

22 / 36


The following graph shows the average rates of water flow at various points along a river in both summer and winter for this year.

Verbal Reasoning


A cubic metre of water weighs one metric tonne. How many tonnes of water flow past Point C in the summer over the course of a two- and three-quarter-hour period?

23 / 36


The following graph shows the average rates of water flow at various points along a river in both summer and winter for this year.

Verbal Reasoning


Last year, the average flow-rate at Point B in winter was 40 m 3/s. What has been the percent- age change in flow-rate since then?

 

24 / 36


The following graph shows the average rates of water flow at various points along a river in both summer and winter for this year.

Verbal Reasoning


What was the average flow rate along the whole river in the summer?

25 / 36


Noradrenaline is a drug used in critical care units to increase the blood pressure of sick patients in shock. It has to be given as a continuous infusion, the strength of which varies as standard strength (4 milligrams of Noradrenaline diluted in 50 millilitres of saline), double strength (8 milligrams of Noradrenaline diluted in 50 millilitres saline) and quadruple strength (16 milligrams Noradrenaline diluted in 50 millilitres saline).


The average cost per night for a patient staying in an intensive care unit is £1,500. The intensive care unit at a district general hospital has eight beds, and runs at an average occupancy of 75% throughout the year. What is the annual cost of patients staying in the intensive care unit?

26 / 36


Two friends, Matthew and John, have decided to race each other on bikes around the woods. They have set up three checkpoints: A, B and C. They both start at point A, with Matthew cycling from A to B to C then back to A. John, however is cycling from A to C to B to A. The distance from A to B is 4 miles and from B to C is 6 miles. It takes Matthew 20 minutes to cycle from A to B. He com- pletes the entire course in 90 minutes. Matthew arrives back at point A half an hour before John.


 

How much faster did Matthew cycle compared to John?

 

27 / 36


Two friends, Matthew and John, have decided to race each other on bikes around the woods. They have set up three checkpoints: A, B and C. They both start at point A, with Matthew cycling from A to B to C then back to A. John, however is cycling from A to C to B to A. The distance from A to B is 4 miles and from B to C is 6 miles. It takes Matthew 20 minutes to cycle from A to B. He com- pletes the entire course in 90 minutes. Matthew arrives back at point A half an hour before John.


 

Assuming Matthew cycles at a constant speed throughout, how far is it between points C and A?

 

28 / 36


Two friends, Matthew and John, have decided to race each other on bikes around the woods. They have set up three checkpoints: A, B and C. They both start at point A, with Matthew cycling from A to B to C then back to A. John, however is cycling from A to C to B to A. The distance from A to B is 4 miles and from B to C is 6 miles. It takes Matthew 20 minutes to cycle from A to B. He com- pletes the entire course in 90 minutes. Matthew arrives back at point A half an hour before John.


 

After the race, it transpired that John had gotten lost between points C and B, increasing his race distance. In total John cycled 22 miles. What was his average speed?

 

29 / 36


Two friends, Matthew and John, have decided to race each other on bikes around the woods. They have set up three checkpoints: A, B and C. They both start at point A, with Matthew cycling from A to B to C then back to A. John, however is cycling from A to C to B to A. The distance from A to B is 4 miles and from B to C is 6 miles. It takes Matthew 20 minutes to cycle from A to B. He com- pletes the entire course in 90 minutes. Matthew arrives back at point A half an hour before John.


 

The friends decide that as cycling is very good for keeping fit, by burning approximately 500 kilocalories per hour, they should do 2 hours a week for all but 4 weeks in the year. How many calories per year will they each burn as a result?

 

30 / 36


James is currently driving to and from his office every Monday to Friday but feels it’s time to upgrade
to a new car. He is undecided about which car to get so he has created the following table:


group 7

If James wishes to upgrade the sound system on the Audi A5, he needs to pay an additional £716.75. What is the percentage increase in total price?

 

31 / 36


James is currently driving to and from his office every Monday to Friday but feels it’s time to upgrade
to a new car. He is undecided about which car to get so he has created the following table:


group 7

To buy the Audi A4, James takes out a loan. The terms of the loan require him to pay a 25% deposit followed by 24 monthly payments of £800. How much extra will James have to pay the aforementioned list price?

 

32 / 36


James is currently driving to and from his office every Monday to Friday but feels it’s time to upgrade
to a new car. He is undecided about which car to get so he has created the following table:

group 7


The Mercedes C Class has a fuel tank size of 67.5 litres and a fuel economy of 40 miles per gallon. One gallon is approximately 4.5 litres. How far can the Mercedes C Class travel on a third of a tank of petrol?

 

33 / 36


James is currently driving to and from his office every Monday to Friday but feels it’s time to upgrade
to a new car. He is undecided about which car to get so he has created the following table:

group 7


James commutes 25 miles to work every day. If he bought the Audi A4, his fuel efficiency would be 10 miles per litre of petrol. Currently, petrol costs £1.40 per litre. How much would it cost him to commute to and from work every week?

 

34 / 36


Noradrenaline is a drug used in critical care units to increase the blood pressure of sick patients in shock. It has to be given as a continuous infusion, the strength of which varies as standard strength (4 milligrams of Noradrenaline diluted in 50 millilitres of saline), double strength (8 milligrams of Noradrenaline diluted in 50 millilitres saline) and quadruple strength (16 milligrams Noradrenaline diluted in 50 millilitres saline).


A patient is receiving an infusion of standard strength Noradrenaline at a rate of 0.5 micrograms per kilogram of body weight per minute. He weighs 70 kilograms. How much Noradrenaline is he receiving per hour?

35 / 36


Noradrenaline is a drug used in critical care units to increase the blood pressure of sick patients in shock. It has to be given as a continuous infusion, the strength of which varies as standard strength (4 milligrams of Noradrenaline diluted in 50 millilitres of saline), double strength (8 milligrams of Noradrenaline diluted in 50 millilitres saline) and quadruple strength (16 milligrams Noradrenaline diluted in 50 millilitres saline).


A 60 year old gentleman weighing 62.5 kilograms is requiring 3 milligrams Noradrenaline per hour. How many syringes of double strength Noradrenaline will he require per 24 hours?

36 / 36


Noradrenaline is a drug used in critical care units to increase the blood pressure of sick patients in shock. It has to be given as a continuous infusion, the strength of which varies as standard strength (4 milligrams of Noradrenaline diluted in 50 millilitres of saline), double strength (8 milligrams of Noradrenaline diluted in 50 millilitres saline) and quadruple strength (16 milligrams Noradrenaline diluted in 50 millilitres saline).


Noradrenaline is sold in vials containing 4 micrograms of powder each, costing £11.55 per vial. Saline costs £0.10 per 10 millilitres container. To draw up the solution, staff require a 50 millilitres syringe (costing £0.45) and a needle (costing £0.12). What is the cost of drawing up a quadru- ple strength Noradrenaline infusion?

 

 

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