Numerical Reasoning Test: Practice Questions With Solutions

Free Numerical Reasoning Practice Questions & Answers

1) Tables & Graphs

The numerical reasoning test introduces a large family of tables and graphs that represent maths data.

Tables and graphs questions assess your understanding of numerical data presented in them, along with your ability to extract relevant data sets and use it correctly.

From these Numerical Reasoning questions, your future employer wants to ascertain how you form logical deductions.

What to expect?

  • Tables display data in rows and columns, containing a lot of numerical information in a small space. You will need to learn how to extract only what is needed to come up with an answer.
  • Graphs mostly show the relation between a number of different items or variables. To solve them efficiently you will have to get to know the relationship types and learn how to spot them.

Tables & graphs questions appear in the following Numerical Reasoning tests:

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

Example Question 1

Numerical reasoning test sample question 1

How many more employed graduates were there in 1990 than in 2000?
A. 75
B. 360
C. 485 
D. 100
E. 135

Answer Explanation

The correct answer is C (485)

 

The number of employed in 2000 =

Private + State = 1250 + 1350 = 2600.

The number of employed in 1990 =

Private + State = 1475 + 1610 = 3085

The difference in the number of employed in 1990 and 2000 =

3085 - 2600 = 485.

Example Question 2

numerical reasoning test sample question 2

 What businesses combined contribute 50% of the annual income?

A. Restaurants, Bars & Clubs
B. Clubs & Coffee shops
C. Restaurants, Bars & Coffee shops
D. Restaurants & Cinemas 
E. Clubs & Cinemas 

Answer Explanation

The correct answer is D (Restaurants & Cinemas)

50% of the annual income is half of the annual income.

The annual income is: 46 + 70 + 104 + 20 + 60 = £300 million (the sum of incomes of all businesses.

Therefore, half of the annual income is £300/2 = £150 million.

Looking at the answer-options and summing the annual incomes distribution of the businesses accordingly, one can see that the annual income distribution by:

 

- Restaurants, Bars & Clubs = 46 + 20 + 60 = £126

- Clubs & Coffee shops = 60 + 70 = £130

- Restaurants, Bars & Coffee shops = 46 + 70 = £116

- Restaurants & Cinemas = 46 + 104 = £150

 

The businesses that contributed £150 million combined are:

Restaurants (£46 million) and Cinemas (£104 million).

Example Question 3

numerical reasoning sample question 3

If Chinese Insurance Stocks comprise 3.5% of all Insurance securities (globally), approximately how many Insurance bonds are Chinese?
A. 9,200,000
B. 9,500,000
C. 10,800,000
D. 910,000
E. 1,080,000

Answer Explanation

The correct answer is (B): 9,500,000.

Looking at the left chart’s title and key, you can infer it presents data about the number of securities (in thousands), which are comprised of bonds and stocks. You should note that the question considers only the insurance securities.

According to the left chart, the total number of insurance securities (insurance stocks + insurance bonds) is: 33,000,000 + 3,000,000 = 36,000,000.

According to the right chart, Chinese Insurance securities are 30% of total securities. Thus, the total number of Chinese insurance securities is: 36,000,000 x 0.3 = 10,800,000

The question states that Chinese insurance stocks comprise 3.5% of the global insurance securities. Thus, the number of Chinese insurance stocks is: 36,000,000 x 0.035 = 1,260,000

As the total number of Chinese insurance securities is comprised of Chinese insurance stocks and Chinese insurance bonds, to find the number of Chinese insurance bonds you simply need to calculate:

Chinese insurance securities - Chinese insurance stocks = 10,800,800 – 1,260,000 = 9,540,000

This equals approximately 9,500,000.


Another possible, slightly shorter, way of resolution is to calculate the percentage of Chinese insurance bonds out of the total insurance securities and multiply it by the total number of insurance securities (which, according to calculation is 36,000,000):

% of Chinese insurance bonds = % of Chinese insurance securities – % of Chinese insurance stocks = 30% – 3.5% = 26.5%

26.5% of 36,000,000 = 36,000,000 x 0.265 = 9,540,000 ≈ 9,500,000

To try additional questions, take our Free Table & Graphs Sample Test  >> 

 

The prep package includes 13 Tables & Graphs practice tests, as well as tailored practice simulations for assessments that are heavily based on this topic, such as the SHL Numerical Reasoning test, Korn Ferry/Talent-Q, cut-e (AON), and more.

 

2) Number Series

Number series questions present sequences of numbers called ‘terms’, each following logical arithmetic operation rules.

Your task is to find the missing number in the sequence. The difficulty level of these questions tends to increase as the logic behind the sequences becomes less trivial, thereby demanding attention and creativity.

Number sequence questions appear in the following Numerical Reasoning tests:

  • CCAT
  • PI Cognitive Assessment
  • McQuaig Mental Agility Test (MMAT)
  • Cubiks Logiks

Example Question 1

3 | 8 | 15 | 24 | 35 | ?

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

Answer Explanation

The correct answer is (48)

 

The value of the differences increases by 2 each time. 

Therefore 13 (11 + 2) should be added to the last term in the series.
35 + 13 = 48

The answer is 48.

Example Question 2

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

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

Answer Explanation

The correct answer is C (12)

 

There are two ways to look at this series:

1) There are two inner series. each following a different rule:

Odd terms- remain constant: 3.

Even terms- increase by 3: 

3+3=6, 6+3=9, 9+3=12.


2) Another point of view:

The series in this question follows two rules:

1) The mathematical operations between the terms change in a specific order, x, : and so forth.

2) Every two steps the number by which the terms are multiplied or divided increases by 1.

 

The test preparation pack includes 9 Number Series practice tests in three levels (basic, intermediate, and advanced). This way, you'll build strong foundations and improve your skills as you progress through the levels.

 

3) Word Problems

A word problem is a few sentences describing a scenario where a problem needs to be solved by way of a mathematical calculation.

Word problems vary in their difficulty and include several types, when the most common ones are Work Rate and Travel word problems.

Word problems appear in the following tests:

  • CCAT
  • PI Cognitive Assessment
  • McQuaig Mental Agility Test (MMAT)
  • Cubiks Logiks

Work Rate Example Question

The post office receives a package every 3 minutes, and the mail man delivers 12 packages an hour. If the mail man start working at 08:00, and there are no packages left from the previous day, how long will it take until there will be exactly 100 undelivered packages in 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

Answer Explanation

The correct answer is E.

1 package every 3 minutes = 20 packages an hour. The amount of undelivered packages in the post office every hour is 20-12=8. Therefore:
8T=100 >> T = 12.5 hours

Travel Example Question

Hanna and her parents are walking in the street. Her parents walk at a rate of 80 steps per minute. The father precedes the mother by 12 steps. Hanna walks behind her parents at a rate of 90 steps per minute. The average length of a step is equal among all family members.

How many seconds would pass from the moment she passes her mother until the moment she passes her father?

A. 8
B. 12
C. 1.2
D. 72
E. 80

Answer Explanation
The correct answer is (D), 72 seconds.
Since the average length of a step is equal, you can view step per minute as velocity.

Hanna walks 10 steps per minute faster than her parents, so this is the rate by which she closes the distance to them, as both parents move at the same velocity. You can visualize it as both parents are standing, 12 steps from one another, and Hanna walking at 10 steps per hour, since we only care about her velocity's ratio to theirs.

You need to find out then, how many steps (=how much time) would it take her to close the 12 step distance at her respective walking velocity of 10 steps per minute.

Hanna's velocity is 10 steps per minute. Therefore, 12 steps would take 1.2 minutes, which is in seconds: 1.2x60 = 72


 

The prep package includes 19 Word Problem practice tests that cover the most commonly used problem types - Percentages, Work Rate, Travel, Probablity & Combinatorics, and Equations.

 

4) Arithmetic Calculations

Arithmetic calculations, or operations, are the foundations of any math question and therefore appear in any Numerical Aptitude test.

It's essential to master these operations so that they won't become a hurdle in the real test and cause you to lose points over calculation mistakes.

Arithmetic calculations mainly include:

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Fractions
  • Powers
  • Roots and Square Roots

Example Questions (Without a Calculator)

4186 / 0.001 = ?

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

Answer Explanation

The correct answer is (A).

The decimal point can move an equal amount of places in each side of the quotient

4186 / 0.001
= 41860 / 0.01
= 418600 / 0.1
= 4186000 / 1
= 4186000

Convert 0.111 to a fraction

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

Answer Explanation

The correct answer is (D).

The places to the right of the decimal point correspond, in order from left to right, to these fractions: tenths, hundredths, thousandths, etc.

Therefore, the decimal 0.01 = 1/100, and the decimal 0.111= 111/1000.

0.111 is a customary expression of 1/9.

1/9 actually equals 0.1111111..., but it is abbreviated into 0.111.11

For those who don't remember the basic list of decimal-to-fraction conversions, the best way to answer this question is by the process of elimination, or by multiplying both the numerator and denominator by the same factor to reach the same denominator of the number in question.

Looking at 1/10, multiply the denominator and numerator by 100 to get 100/1000, which is of course not equal to 111/1000.

Using the same method, it can't be 1/11 either, nor is it 101/1000.

 

The practice pack includes 8 arithmetic calculation practice tests, to ensure you dominate these foundational skills. Additionally, you'll receive 5 study guides to brush up on your basic computation skills.

 

5) Basic & Advanced Maths Skills

In addition to basic arithmetic calculations, you'll need to master more advanced subjects that are part of many questions on common Numerical assessment tests.

These subjects include:

  • Ratios
  • Percentages
  • Averages
  • Unit and Currency Conversion
  • Geometry

Example Question 1 - Percentages

Due to an increase in taxes on electronic devices, the price of a 46” LED flat TV screen has increased to £845, which is 30% increase of the original price.

What was the original price of the TV prior to the increase?
A. £515.45
B. £591.50
C. £650
D. £676
E. £768.95

Answer Explanation

The correct answer is (£650)

In this question the 100% is the original price.
A good way to tackle this type of questions is by writing down the information you have in a table:

% Value
   
   

You can use the 'triangle trick' in order to calculate the missing data:

Multiply along the diagonal and then divide by the remaining number.
Applying this method to this question:

In order to find the missing data we will multiply the numbers connected by the diagonal (the hypotenuse).

Then divide by the number located on the remaining vertex: X = (845*100)/130 = £650.


Another approach to this type of questions requires an understanding of the relation between a given percentage and the proportion it represents (and vice versa).

This relation is represented by the following formula: 

total = the value of the 100%.

We can isolate the part we are interested in

Total = (Value*100)/%

And insert the data: 

Value = (£845*100)/130 = £650.


Another way to tackle this question:

If you start with 130%, divide the number by 130 to get 1%.

Then, simply multiply the value you have received by 100.

Example Question 2 - Ratios

Scott and Rachel are enthusiastic car collectors. The cars they own are either German or Japanese made cars.

The German to Japanese ratio in Scott's collection is 5:2 in favour of the Germans. 
The German to Japanese ratio in Rachel's collection is 4:3 in favour of the Germans
The number of Japanese cars Scott owns is identical to the number of Japanese cars Rachel owns.

What is the ratio between the total amount of cars (German and Japanese) Scott has and the total amount of cars Rachel has?

A. 15:8

B. 9:7

C. 1:1

D. 3:2

Answer Explanation

The correct answer is D (3:2)

 

A good way to tackle this question will be to use a ratio table:

  German Japanese
Scott 5 2
Rachel 4 3

In the question we are given 2 sets of ratios between German and Japanese cars in each collection. Each collection has its own row in the table.

Since we know the number of Japanese cars is identical in both collections we will modify the table so it will indicate this equality in a manner that is easier to manipulate and preferably using the minimum common product.

 

We will expand Scott's ratio by 3 and Rachel's ratio by 2:

  German Japanese
Scott 15 6
Rachel 8 6

Thus, we can see that the ratio between Scott's total amount of cars and Rachel's total amount of cars is 21:14.

Simplify the ratio, dividing it by 7 → 3:2.

 

Shortcut:

Rachel =R
Scott = S

For Japanese cars: 2S=3R

Remember, you are told that the number of Scott's Japanese cars equals to the number of Rachel's Japanese cars.

So, the Scott to Rachel Japanese cars ratio also represents the ratio between Scott's total number of cars and Rachel's total number of cars:

Therefore: S/R=3/2

 

The prep package includes 14 practice tests to sharpen your basic and more advanced math skills (Ratios, Percentages, Averages, Conversions & Finance, and Geometry). Additionally, you'll find 8 video tutorials to brush up on the foundations, in case you haven't touched maths for years.


Get to Know the Most Common Numerical Reasoning Tests Used by Top Employers

Huge employers such as Amazon, Vista Equity, banks, accounting and consulting firms, and hundreds of others use Numerical Reasoning tests as part of their selection process. Here's a list of the most commonly used numerical assessments:

SHL Numerical Reasoning

The SHL Numerical test is one of the most widely used numerical psychometric tests. It's unique in that most questions will come in the form of data-based tables or graphs along with multiple-choice format of Numerical Reasoning questions and will include five distractors. 

Secondly, SHL varies its Numerical Reasoning tests to fit various job descriptions and needs. Lastly, you will be given only 25-35 minutes to finish the test.

notePrep Tip - Calculators: 

There is no rule, sometime it will be allowed and sometimes not. In the event, calculators are permitted, make sure to practise using advanced functions like memory, factorial and exponents, among others. If calculators are not allowed, make sure to brush up on “mental arithmetic tips.” You can accomplish this by focusing on averages, square roots and ratios, among many other operations.

Revelian Numerical Reasoning 

The Revelian Numerical Reasoning Test has an even more strict time limit than the SHL Numerical Reasoning test variations with only 12 minutes. Additionally, while SHL is administered in a wide range of professions, the Revelian is primely used for numerical-based occupations. Lastly, most questions will come in the form of 3X3 tables or matrix’s, which are broken down into vertical and horizontal variations. 

note Prep Tip – Tricky Questions: 

The questions on the Revelian numerical reasoning test are difficult. One of the most frequent questions on the test is completing incomplete number sets. So, this is something that you should defiantly focus on.

Talent Q Elements Numerical Reasoning 

Talent Q Elements provides 12 questions in a 16-minute time frame on the numerical section of its test. What makes this test unique is that as you answer each question, the difficulty level increases. Receiving only 1 minute and 20 seconds to answer each question certainly increases the challenge. 

note Prep Tip – Memory Function: 

While calculators are allowed on this Numerical Reasoning test, we recommend staying clear of those built into your smartphone. Instead, get a useful handheld calculator with advanced functions and make sure you practice using the memory function, as this will give you a big advantage.

Cubiks Numerical Reasoning 

The Cubiks numerical test is part of a larger Logiks Test, which also includes sections on verbal and Diagrammatic/ Abstract. The numerical section contains 20 questions within a 25-minute time frame. Question formats will be in the form of several multiple-choice questions preceded by tables and graphs. 

note Prep Tip - Order Does Not Matter:

This Numerical Reasoning test allows you to answer questions in no particular order. We recommend first to find all the questions you are sure of and answer them and then move on to items you are unsure. Just remember that several questions will relate to a single table or graph, so don’t get confused.

cut-e Numerical Reasoning Test

cut-e, a huge test provider, administers three types of Numerical Reasoning tests:

  1. scales Numerical Ability, which itself is dived into three versions, including, consumer, finance and industrial. Each segment has the same level of complexity and do not require any specialized knowledge going into the text. 
  2. scales tmt - Applied Numeracy requires you to calculate spaces and areas, calculate percentages, unit translations and rule of three. 
  3. scales eql- Applied Numeracy version provides you with number series, which includes several empty spaces. You are tasked with filling in the blanks. 

note Prep Tip for scales eql: 

Due to the range of test variations within the cut-e, we will give you just a small taste. The eql variation will demand of you to apply BODMAS (Bracket, Of, Division, Multiplication, Addition and Subtraction.) We recommend to begin the process with division; afterwards, you will be able to determine better the numbers that will lead to the answer.

Saville

Saville aptitude tests try to mimic work-related tasks and challenges, utilizing a variety of tables, charts, and documents.

Saville's Numerical ability tests measure how you analyze and interpret statistical, graphical and numerical data, and how you draw conclusions from this data interpretation.

Saville offers 8 types of Numerical Reasoning Tests: Numerical Analysis Aptitude, Professional Numerical Analysis, Work Numerical Analysis, Numerical Comprehension Aptitude, Operational Numerical Comprehension, Commercial Numerical Comprehension, Customer Numerical Comprehension, and Administrative Numerical Comprehension.

McQuaig MMAT

The McQuaig Mental Agility Test (MMAT) is a 15-minute timed cognitive ability test measuring the speed of thought, consisting of 50 questions on math, verbal reasoning, and vocabulary.

The mathematical ability portion consists of multiple-step Word Problems and Number Series. For these questions, make sure you also practice decimals, ratios, Fibonacci numbers, percentages, and fractions.

CCAT

The Criteria Cognitive Aptitude Test includes 50 questions to complete in 15 minutes, when about 19 of the questions measure Numerical Reasoning.

You'll find the following numerical question types on the CCAT: Straightforward basic math questions (basic math skills), Math word problems, Number series, Graphs and tables, Ratio and proportions, Averages, Fraction value.

PI Cognitive Assessment

The PI Cognitive Assessment is a tough test with 50 questions to be completed in 12 minutes only. It measures your Numerical, Verbal, and Abstract reasoning, when the Numerical Reasoning portion has the following question types: Number Series, Math Problems, and Word Problems.


Top Numerical Reasoning Tips Video Tutorial

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