PrepForDoc

UCAT Quantitative Reasoning

Year 10 maths at speed. The numbers are not hard; finding the right ones in a table and getting through the calculation in 43 seconds is.

Facts checked against official sources on 3 October 2026.

Questions
36
Time
26 minutes
Per question
About 43 seconds
Answer format
Five options

What it tests

Whether you can use numbers to solve practical problems. Most questions refer to a table, chart or short description, such as a price list, a timetable or survey results. Often four questions share one set of data; some questions stand alone. Every question has five options.

The maths you need

  • Percentages: a percentage of an amount, percentage change, and working back to the original after a rise or a discount
  • Ratio and proportion: sharing in a ratio, scaling a recipe or a map
  • Rates: speed, distance and time; cost per unit; pay per hour; converting currency and units
  • Averages: mean, median, mode and range, including the effect of adding a value
  • Money: tax, simple and compound interest, profit and loss
  • Shape: perimeter, area and volume of simple figures
  • Reading data: tables, bar charts, line graphs, pie charts and graphs with two scales

There is no algebra beyond rearranging a simple formula, and no trigonometry.

A worked example

Original example: data

Harlow Community Pool: entry prices
TicketPrice
Adult$7.50
Child$4.20
Family (2 adults and 2 children)$19.00
Adult ten-visit pass$63.00

Question 1

Two adults and three children visit the pool together. What is the least they can pay?

  • A.$21.80
  • B.$23.20
  • C.$23.40
  • D.$26.50
  • E.$27.60

Answer: B, $23.20

A family ticket covers two adults and two children for $19.00, and the third child pays $4.20: $23.20. Buying five separate tickets costs $15.00 + $12.60 = $27.60, which is option E and is there for anyone who misses the family ticket.

Question 2

An adult buys a ten-visit pass. By what percentage is each visit cheaper than the standard adult price?

  • A.12%
  • B.14%
  • C.16%
  • D.19%
  • E.84%

Answer: C, 16%

Each visit on the pass costs $63.00 ÷ 10 = $6.30, a saving of $1.20. As a share of the standard price, 1.20 ÷ 7.50 = 0.16. Option E, 84%, is the pass price as a percentage of the standard price: the right calculation for a different question.

How to approach it

  1. Read the question, then go to the data. Tables carry more than you need. Know what you are looking for before you look.
  2. Estimate first. If the options are far apart, rounding gets you there without the calculator.
  3. Learn the calculator. It is a basic one, driven fastest from the number pad, and it works through sums in the order you type them. See how it behaves.
  4. Check the units and what is asked. Per person or in total, per week or per year, the increase or the new amount.
  5. Know when to leave. A question with four steps is worth the same as one with a single step. Guess, flag it and move on.

Where marks are lost

  • Taking a percentage of the wrong base, such as the new price instead of the old one.
  • Answering a different question from the one asked. The wrong options are the answers to the likely mistakes.
  • Typing every sum into the calculator, including the ones that are quicker in your head.
  • Running out of time with a whole data set unread.

How to practise

First close any gaps in the maths, untimed. Then build speed: mental arithmetic, the number pad, and the habit of estimating. In your results, PrepForDoc shows the time you spent on every question beside the 43 seconds the test allows, so you can see which kinds of calculation are slow. How to prepare has the full plan.

Official sources

Dates, fees and entry rules change every year. Always confirm them on the official page before you act on them.

See it on the real screen

The free sample runs all four subtests on a screen that works like the one in the test centre.

Start the free sample

Next in the guide: Situational Judgement