Guide to Numerical Reasoning Tests

Table of Contents

Introduction

This page will guide you through the most common numerical reasoning tests used during candidate selection processes.

Below, you’ll find a series of numerical reasoning questions, each with its correct answer and a clear explanation of how to solve it. This will help you get familiar—completely free—with the typical question formats, learn how to approach and solve them, and better manage pressure and uncertainty. 

If you’re looking for a broader overview of the different types of aptitude tests used by companies and public institutions during recruitment, check out our Practical Guide to Aptitude Tests: A General Overview of all Test Types. You’ll find detailed explanations, examples, and strategies to solve the most common question types—including numerical, logical, abstract, and verbal reasoning. 

For additional practice, you can access our free test simulator anytime. It includes over 11,000 questions covering numerical, verbal, logical, and abstract reasoning—drawn from the most widely used aptitude tests by employers and institutions looking to hire new talent.

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What Is a Numerical Reasoning Test?

Numerical reasoning tests measure your math skills using a variety of question types involving tables and graphs. These tests typically include the following question formats:

  • Number Series – Common in many assessments such as the CCAT, PI Cognitive Assessment, McQuaig Mental Agility Test, and Cubiks Logiks Intermediate.
  • Word Problems (Story-Based) – Also found in many of the same tests, these questions present a short real-world scenario that requires mathematical or logical reasoning to solve.
  • Tables and Charts – These play a major role in numerical assessments like the SHL Numerical Test, Korn Ferry Numerical Test, cut-e Scales, Saville Swift, and Cubiks Logiks Advanced.
  • Arithmetic Calculations – A key part of almost all numerical ability tests, including addition, subtraction, multiplication, division, roots, powers, and more.
  • Basic and Advanced Math Skills – These cover essential topics such as ratios, percentages, averages, unit and currency conversions, and geometry, and are frequently tested across most major assessments.

Examples of Numerical Reasoning Questions

1) Number Series

Number series questions present a sequence of numbers—called terms—that follow a logical pattern based on arithmetic operations.

Your task is to identify the missing number in the sequence. These questions tend to increase in difficulty as the underlying logic becomes less obvious, requiring sharper focus and out-of-the-box thinking.

You’ll typically encounter number series questions on the following numerical reasoning assessments:

  • CCAT (Criteria Cognitive Aptitude Test)
  • PI Cognitive Assessment
  • McQuaig Mental Agility Test (MMAT)
  • Cubiks Logiks
  • Question 1 with solution

3  |  8  |  15  |  24  |  35  |  ?

A) 42
B) 36
C) 48
D) 46

Correct answer: C - The differences between terms increase by 2 each time: 5, 7, 9, 11… So the next difference is 13. Adding 13 to the last term: 35 + 13 = 48. Therefore, the correct answer is 48.
  • Question 2 with solution

3  |  3  |  3  |  6  |  3  |  9  |  3  |   ?

A) 3
B) 27
C) 12
D) 6

Correct answer: C - The numbers in the odd positions remain constant (always 3), while the even-position numbers increase by 3 each time: 3 → 6 → 9 → 12. Therefore, the correct answer is 12.
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2) Word Problems

A word problem consists of a few sentences that describe a scenario in which a mathematical calculation is required to find the solution.

Word problems vary in both difficulty and format. Some of the most common types involve work- or travel-related scenarios that require the use of algebraic expressions or arithmetic reasoning.

These types of problems frequently appear in the following tests:

  • CCAT (Criteria Cognitive Aptitude Test)
  • PI Cognitive Assesmen
  • McQuaig Mental Agility Test (MMA
  • Cubiks Logiks
  • Question 1 with solution

A post office receives one package every 3 minutes, and the mail carrier delivers 12 packages per hour. If the carrier starts work at 8:00 AM and there were no leftover packages from the day before, how long will it take before exactly 100 packages have accumulated at the post office?

A) 50 minutes
B) 3 hours and 20 minutes
C) 6 hours and 40 minutes
D) 10 hours and 50 minutes
E) 12 hours and 30 minutes

Correct answer: E - The post office receives 1 package every 3 minutes, which means 20 packages per hour. The number of undelivered packages added each hour is 20 - 12 = 8. So: 8T = 100 → T = 12.5 hours.
  • Question 2 with solution

Chiara and her parents are walking down the street. Her parents are walking at a pace of 80 steps per minute. Her father is 12 steps ahead of her mother. Chiara is walking behind them at a pace of 90 steps per minute. All family members have the same average step length. How many seconds would pass between the moment Chiara catches up to her mother and the moment she catches up to her father?

A) 8 seconds
B) 12 seconds
C) 28 seconds
D) 72 seconds
E) 82 seconds

Correct answer: D - Since everyone has the same average step length, we can associate steps with speed. Chiara walks 10 steps per minute faster than her parents, so she is closing the gap at 10 steps per minute. The parents move at the same speed, so the 12-step gap between them remains constant. We need to find out how long it takes Chiara to cover those 12 steps at her relative speed of 10 steps per minute. If we subtract the shared walking speed from everyone, Chiara effectively moves at 10 steps per minute while her parents are stationary. So: 12 ÷ 10 = 1.2 minutes, which equals 72 seconds.
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3) Tables and Charts

Numerical reasoning tests include a broad range of questions based on mathematical data. With these types of questions, employers are primarily looking to assess your ability to make logical deductions.

These questions aim to evaluate how well you understand numerical data, how effectively you can extract relevant information, and—most importantly—how accurately you use it to solve problems.

Table and chart-based questions are commonly found in the following numerical reasoning tests:

  • SHL Numerical Reasoning Test
  • Talent-Q (Korn Ferry) Numerical Test
  • Cut-e (AON) Numerical Aptitude Test
  • Saville Scales Test
  • Cubiks Logiks Test

Tables present data in rows and columns, often packed with large amounts of numerical information. You’ll need to learn how to identify and focus only on the data needed to answer the question.

Charts are used to illustrate relationships between different elements or variables. To solve these efficiently, you’ll need to understand common types of relationships and recognize them quickly.

Question and Answer

  • Question 1 with solution

By looking at the chart above showing annual revenue (in millions of dollars) by type of business, which group of businesses together account for 50% of total annual revenue?

A) Restaurants, ice cream shops, and clubs
B) Clubs and cafés
C) Restaurants, ice cream shops, and cafés
D) Restaurants and cinemas
E) Clubs and cinemas

La risposta esatta è D - 50% of the annual revenue means half of the total revenue generated by all business types. The total annual revenue is $46M (restaurants) + $70M (cafés) + $104M (cinemas) + $20M (ice cream shops) + $60M (clubs) = $300 million. Half of that is $300M ÷ 2 = $150 million. Among the options, only restaurants and cinemas together total exactly $150M ($46M + $104M), so they account for 50% of the annual revenue.
  • Question 2 with solution

Looking at the chart above showing the amount spent on computer imports, how much more did Germany spend than Italy in Year 3?


A) 650 million
B) 700 million
C) 750 million
D) 800 million
E) 850 million

Correct answer: B - To answer this question, you need to compare the figures for Germany and Italy in Year 3 from the chart. Germany spent $1,400 million, while Italy spent $700 million. The extra amount spent by Germany compared to Italy is calculated by subtracting these two figures (1,400 million – 700 million). Since the result is $700 million, the correct answer is B.
  • Question 3 with solution

Looking at the chart above showing the amount spent on computer imports, if the amount spent by the United Kingdom in Year 5 was 20% less than in Year 4, how much was spent in Year 5?


A) 1,080 million
B) 1,120 million
C) 1,160 million
D) 1,220 million
E) 1,300 million

Correct answer: B - To answer this, examine the UK data for Year 4 in the chart. It shows that the UK spent $1,400 million. To calculate the amount spent in Year 5, compute 20% of $1,400 million: 1,400 × 0.20 = 280 million. Subtracting this from 1,400 million gives: 1,400 – 280 = 1,120 million. The correct answer is B.
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4) Arithmetic Calculations

Arithmetic operations are the foundation of nearly every math question and appear in virtually all numerical aptitude tests.

It’s essential to master these operations so they don’t become a stumbling block during the actual test or cause you to lose points due to simple calculation errors. Arithmetic calculations primarily include:

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Fractions
  • Powers
  • Roots and radicals
  • Question 1 with solution (no calculator allowed)

4186 / 0.001 = ?

A) 4186000
B) 41860
C) 41.86
D) 418600
E) 4.186

Correct answer: A -The decimal point moves as many places as there are digits to the right of the quotient -> 4186/0,001 = 41860/0,01 = 418600/0,1 = 4186000/1 = 4186000
  • Question 2 with solution (no calculator allowed)

Convert 0.11111111 into a fraction.

A) 1/10
B) 1/11
C) 11/100
D) 1/9
E) 101/1000

Correct answer: D - Since 1/10 = 0.1, 11/100 = 0.11, and 101/1000 = 0.101, the only plausible options are B) and D). However, because 0.11111111 is greater than 0.1—and knowing that 1/11 is smaller than 1/10—it follows that the only fraction matching this value is 1/9, which is exactly equal to 0.111... (repeating).
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5) Math Skills

Beyond basic arithmetic, you’ll need to master more advanced topics that are commonly featured in numerical reasoning tests. These subjects include:

  • Ratios
  • Percentages
  • Averages
  • Unit and currency conversions
  • Geometry
  • Question 1 with solution

Due to a VAT increase on electronic devices, the price of a 46-inch LED TV has risen to $845—30% more than the original price. What was the TV’s price before the increase?

A) $515.45
B) $591.50
C) $650
D) $676
E) $768.95

Correct answer: C - If the final price equals 130% of the original price, divide the final price by 130 to find the value of 1%, then multiply that by 100. So: $845 ÷ 130 = $6.5 → $6.5 × 100 = $650
  • Question 2 with solution

Mark and Sarah are passionate car collectors. All the cars they own are either German-made or Japanese-made. In Mark’s collection, the ratio of German to Japanese cars is 5:2 in favor of German. In Sarah’s collection, the ratio is 4:3, also in favor of German cars. The number of Japanese cars in each collection is exactly the same. What is the ratio between the total number of cars (German + Japanese) in Mark’s collection and the total number in Sarah’s?

A) 15:8
B) 9:7
C) 1:1
D) 3:2

Correct answer: D - Mark has 5 German cars for every 2 Japanese cars. Sarah has 4 German cars for every 3 Japanese cars. Since both have the same number of Japanese cars, we find the least common multiple of 2 and 3 to match the Japanese count. Mark: 15 German and 6 Japanese (ratio 5:2 scaled ×3); Sarah: 8 German and 6 Japanese (ratio 4:3 scaled ×2). So, total cars: Mark: 15 + 6 = 21; Sarah: 8 + 6 = 14. The ratio is 21:14, which simplifies to 3:2.
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One Last Tip

For a full overview of the different types of aptitude tests that companies and institutions use during the hiring process, check out our Practical Guide to Aptitude Tests: A General Overview of all Test Types. You’ll find detailed information, examples, and step-by-step instructions for solving the most common question types—numerical, logical, abstract, and verbal.