Free · original questions · 26 minutes · calculator allowed

UCAT Quantitative Reasoning practice questions

9 data sets with 4 questions each: percentages, rates, conversions, averages and area — calculator allowed. Same number of questions and time limit as the real UCAT Quantitative Reasoning.

All questions are written by Keiko Study in the official format; they are not official UCAT papers.

Take the UCAT Quantitative Reasoning section

36 questions, 26 minutes. Start the timer for real exam conditions, or answer at your own pace. When you submit, you get your score, the correct answers and a worked solution for every question.

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Questions 1–4

Pellidol dosing and prices

The daily dose of the antibiotic Pellidol is 20 mg per kg of body weight, split into three equal doses given every 8 hours. A pharmacy stocks the three forms below and can only dispense whole packs.

Form	Strength	Pack size	Price per pack
Suspension A	125 mg per 5 mL	100 mL bottle	£4.60
Suspension B	250 mg per 5 mL	100 mL bottle	£6.90
Capsules	250 mg per capsule	21 capsules	£5.25

Question 1

Dosage calculations

A child weighing 18 kg is prescribed Pellidol as Suspension A. What volume of suspension should be given at each dose?

Question 2

Dosage and costs

An adult weighing 78 kg is prescribed a 7-day course of Pellidol capsules. Each dose is rounded to the nearest whole number of capsules. How much do the capsules for the full course cost?

Question 3

Unit costs

To the nearest whole per cent, by how much is the cost per milligram of Pellidol in Suspension A greater than the cost per milligram in Suspension B?

Question 4

Multi-step costing

A child weighing 24 kg is prescribed Pellidol for 10 days. The pharmacy always supplies 10% more than the prescribed volume to allow for spillage. What is the difference between the cost of supplying the course as Suspension A and the cost of supplying it as Suspension B?

Questions 5–8

Bureau de change rates

A bureau de change's rates on one day; no commission is charged. A customer buying currency receives the 'sells' number of units for every £1 paid, and a customer selling currency back must hand over the 'buys back' number of units for every £1 received.

Currency	Bureau sells (units per £1)	Bureau buys back (units per £1)
Euro (€)	1.15	1.21
Swiss franc (CHF)	1.08	1.14
Czech koruna (CZK)	28.40	30.10
Danish krone (DKK)	8.60	9.40

Question 5

Currency conversion

A traveller exchanges £450 for euros at the bureau. How many euros does she receive?

Question 6

Currency conversion

A traveller bought €600 before a holiday and spent €418.50 while away. On her return she sells all of her remaining euros back to the bureau. How much does she receive?

Question 7

Exchange rate spreads

A customer buys 540 Swiss francs. His trip is then cancelled, so he immediately sells all 540 francs back to the bureau. How much money has he lost, to the nearest penny?

Question 8

Cross-currency conversion

A traveller has CZK 5,000 left over from a trip and wants Danish krone for her next holiday. The bureau buys back her koruna for pounds and then sells her krone with all of those pounds. To the nearest krone, how many Danish krone does she receive?

Questions 9–12

Morning trains to City Central

Weekday morning trains on a commuter line, with each station's distance along the track from Ashford Road. Times are when each train calls at the station; a dash means the train passes through without stopping.

Station	Distance from Ashford Road (km)	Train 1	Train 2	Train 3	Train 4
Ashford Road	0	06:42	07:15	07:48	08:20
Bellmont	14	06:57	07:31	—	08:36
Carrow Junction	31	07:15	07:50	08:16	08:55
Denholm	45	07:31	08:07	08:31	09:12
City Central	66	07:53	08:30	08:52	09:36

Question 9

Reading timetables

A passenger arrives at Bellmont station at 07:35 and wants to travel to Denholm. If every train runs to time, at what time will she arrive at Denholm?

Question 10

Average speed

What is the average speed of Train 3 between Ashford Road and City Central, to the nearest km/h?

Question 11

Average speed

What is the highest average speed that Train 1 reaches between two consecutive stations, in km/h to 1 decimal place?

Question 12

Speed, distance and time

One morning Train 4 leaves Ashford Road 9 minutes late. To make up time, it travels 10% faster than its timetabled speed for the whole journey to City Central. If all of its timetabled journey time is spent moving, how late does it arrive at City Central, to the nearest minute?

Questions 13–16

Sports shop prices

Prices and offers at a sports shop. Members get a further 10% off their whole order after all offers have been applied, and home delivery costs £4.95 on orders under £75 (after all discounts) but is free otherwise.

Item	Price	Offer
Running shoes	£84.00	25% off
Waterproof jacket	£120.00	15% off
Sports socks (pack of 3 pairs)	£9.00	Buy 2 packs, get 1 free
Water bottle	£12.50	No offer
Gym bag	£36.00	£8 off when bought with running shoes

Question 13

Discounts

A customer who is not a member orders running shoes and a water bottle for home delivery. How much does she pay in total?

Question 14

Discounts and offers

A member buys 6 packs of sports socks and a waterproof jacket, collecting them in store. How much does he pay?

Question 15

Percentage savings

A member buys running shoes and a gym bag together, collecting them in store. To the nearest whole per cent, what percentage of the full price of the two items does she save?

Question 16

Reverse percentages

In a sale, the jacket's 15% offer is replaced by a larger percentage discount. A member who buys only the jacket in the sale, collecting it in store, pays £86.40. What is the sale discount on the jacket?

Questions 17–20

Cricket club batting records

Season batting records for five players at a cricket club. A player's batting average is runs ÷ (innings − not outs), and strike rate is the number of runs scored per 100 balls faced.

Player	Innings	Not outs	Runs	Balls faced	Highest score
Ahmed	18	2	712	1,036	121
Brennan	20	1	655	802	88
Clarke	15	4	418	590	74
Doyle	12	3	297	455	61
Evans	19	0	593	711	96

Question 17

Averages

What is Clarke's batting average?

Question 18

Rates

Which player has the highest strike rate?

Question 19

Averages

Brennan is out in his next innings. What is the smallest number of runs he must score in that innings to raise his batting average to at least 36.00?

Question 20

Percentages

To 1 decimal place, what percentage of the five players' total runs was scored by players with a strike rate below 70?

Questions 21–24

How students travel to campus

A university surveyed 1,200 students about their main way of travelling to campus. The table shows the percentage of each year group choosing each option; every student chose exactly one.

Main mode of travel	Year 1 (500 students)	Year 2 (400 students)	Year 3 (300 students)
Walk	38%	31%	22%
Bus	24%	19%	14%
Cycle	17%	23%	29%
Car	9%	14%	21%
Train	12%	13%	14%

Question 21

Percentages of amounts

How many more Year 1 students than Year 3 students walk to campus?

Question 22

Weighted percentages

To 1 decimal place, what percentage of all 1,200 students cycle to campus?

Question 23

Proportions

Of all the students whose main mode of travel is by car, what percentage are in Year 3, to the nearest whole per cent?

Question 24

Percentage change

Suppose the Year 1 group were 20% larger, the Year 2 and Year 3 groups stayed the same size, and every group kept the same travel percentages. What percentage of all students would walk to campus, to 1 decimal place?

Questions 25–28

Electricity tariffs

Three electricity tariffs from one supplier. A bill is the standing charge for each day of the billing period plus the unit rate for each kWh used, with VAT at 5% added to the total; an exit fee is charged only to a customer who leaves that tariff.

Tariff	Standing charge (pence per day)	Unit rate (pence per kWh)	Exit fee
Fixed Saver	53.2	24.5	£75
Flex Standard	48.6	27.1	None
Green Plus	61.0	22.8	£50

Question 25

Bills and VAT

A household on Flex Standard uses 820 kWh in a 91-day billing period. What is its bill, including VAT, to the nearest penny?

Question 26

Break-even

Ignoring exit fees, at what yearly electricity use would a 365-day year on Fixed Saver cost exactly the same as a 365-day year on Green Plus? Give your answer to the nearest kWh.

Question 27

Comparing costs

A household on Flex Standard uses 3,100 kWh a year. If it switched to Green Plus, how much would it save over a 365-day year, including VAT and after paying any exit fee?

Question 28

Reverse calculations

A household on Fixed Saver receives a bill of £231.42, including VAT, for a 91-day period. How much electricity did it use, to the nearest kWh?

Questions 29–32

Flat renovation

Floor dimensions of the rooms in a flat; every room is a rectangle with a ceiling height of 2.6 m. Laminate flooring is sold in packs covering 2.2 m² at £34.10 a pack, and one litre of paint covers 12 m² per coat.

Room	Length (m)	Width (m)
Living room	6.4	4.5
Bedroom	4.2	3.6
Kitchen	3.8	3.0
Hallway	5.0	1.2

Question 29

Area

What is the combined floor area of the living room and the bedroom?

Question 30

Area and costs

Laminate is to be laid in the kitchen and the hallway. The fitter buys 10% more than the floor area to allow for cutting waste, in whole packs. How much does the laminate cost?

Question 31

Surface area

The four walls of the bedroom are to be given two coats of paint. The door and window take up 3.4 m² of wall in total and will not be painted. How many litres of paint are needed, to 1 decimal place?

Question 32

Scale and area

A floor plan of the flat is drawn to a scale of 1:50. What is the area of the living room on the plan?

Questions 33–36

Delivery round

A van driver's delivery round, which starts and ends at the depot. The driver leaves at 08:15 and spends 20 minutes at each of the three stops; the van does 38 miles per gallon (1 gallon = 4.546 litres) and diesel costs £1.46 per litre.

Leg	Distance (miles)	Average speed (mph)
Depot to Ashworth	18	45
Ashworth to Brindle	12	30
Brindle to Calder	27	54
Calder to depot	33	60

Question 33

Speed, distance and time

At what time does the driver arrive at Brindle?

Question 34

Average speed

What is the driver's average speed for the whole round, from leaving the depot to getting back, including the time spent at stops? Give your answer to the nearest mph.

Question 35

Unit conversion

How much does the diesel for the whole round cost, to the nearest penny?

Question 36

Speed, distance and time

On another day, roadworks cut the average speed between Brindle and Calder to 36 mph, but the driver shortens each stop to 12 minutes. All other speeds are unchanged and the driver still leaves at 08:15. At what time does the driver get back to the depot?

0 of 36 answered