# UCAT Quantitative Reasoning

Learn about the key skills tested in the Quantitative Reasoning subtest. Can you beat the clock and complete each question in 40 seconds?

## The UCAT Quantitative Reasoning Subtest

In this article, we explain what the UCAT Quantitative Reasoning subtest is and give you the strategies to ace it.

## What is it?

The Quantitative Reasoning subtest examines your ability to solve numerical problems. You will be required to interpret tables, read graphs and extract key information from long passages of text.

While the section assumes familiarity with simple numerical operations such as addition / subtraction, multiplication / division, percentages and ratios, questions are less to do with numerical facility and more to do with problem-solving.

## What is the structure of this subtest?

The Quantitative Reasoning subtest consists of 36 questions to be completed in 24 minutes.

 No. of questions 36 questions Time limit 24 minutes Time per question 40 seconds Time pressure score 9/10

The Quantitative Reasoning subtest contains 9 data sets, each with 4 attached questions. There may be one set of four questions which are standalone and unrelated to each other.

## What is the UCAT Quantitative Reasoning question format?

You will be given a table, graph or passage and will need to answer the following four questions using this information. Each question has five answer options and there is only one correct answer. All the questions in this section are equally weighted and worth 1 mark each.

Occasionally, the fifth answer option, (E), will be ‘Can’t tell’, which should be selected if there is not enough information to answer the question.

## What are the skills tested?

The level of math required for the UCAT Quantitative Reasoning subtest is approximately Year 7 or Year 8.

While the questions themselves are not particularly difficult, the challenge is completing them in a short period of time.

You will need to practice your mental arithmetic and exam strategy. Sometimes it is more efficient to eliminate incorrect answer options and make a guess than try to calculate the correct answer option.

The questions in this section involve:

• Percentages
• Averages: means, modes and medians
• Ratios and proportionality
• Rates and converting rates
• Perimeters, areas and volumes

## Example of a Quantitative Reasoning question

Christine’s swimming pool has a length of 12 metres, width of 5 metres and depth of 2 metres.

Question 1

What is the volume of the swimming pool in litres?

1. 120 L
2. 1,200 L
3. 12,000 L
4. 120,000 L
5. 1,200,000 L

Correct response: D

The volume of the swimming pool is 12 x 5 x 2 = 120 m3 = 120,000 L (1 m3 = 1,000 L).

Question 2

To maintain the hygiene of her pool, Christine needs to add 250 grams of chlorine for every 10,000 litres of pool water. How much chlorine needs to be added if the pool contains 90 m3 of water?

(A) 1.125 kg
(B) 2.250 kg
(C) 11.250 kg
(D) 22.500 kg
(E) 112.500 kg

Correct response: B

250g / 10,000 L is equivalent to 25 / m3 of cycling aid solution. Therefore, 25 x 90 = 2,250 g = 2.250 kg of chlorine needs to be added.

Question 3

The water is filled to 10cm below the brim of the pool. Christine thinks the water in the pool is too deep and removes 8 m3 of water from the pool. What is the percentage change in the depth of the water?

(A) 6 %
(B) 7 %
(C) 8 %
(D) 9 %
(E) 10 %

Correct response: B

The width and length of the pool do not change. Therefore, the change in the depth of the pool is the same as the change in volume which is 22 / (12 x 5 x 1.9) = 7.02%  7%.

Question 4

Christine’s outstretched body has a length of 2 metres. If she swims from one end of the swimming pool to the other at 140 centimetres per second, how long does she take to reach the other side of the pool (to the nearest second)?

(A) 8 seconds
(B) 9 seconds
(C) 10 seconds
(D) 11 seconds
(E) 12 seconds 