Numerical Reasoning Test: Free Practice Questions, Answers and Tips

A numerical reasoning test measures your ability to understand, interpret and solve problems using numbers.

These tests are common in cognitive aptitude tests, pre-employment tests, psychometric tests and graduate hiring processes. They may include percentages, ratios, averages, rates, number series, word problems, tables, charts and data interpretation.

Numerical reasoning is often used in assessments such as:

• CCAT;
• PI Cognitive Assessment practice Assessment practice Assessment practice Assessment;
• Wonderlic;
• SHL numerical reasoning;
• Aon / cut-e assessments;
• Korn Ferry assessments;
• general cognitive ability tests;
• general aptitude tests.

For free mixed aptitude drills, aptitude test practice can complement employer-specific numerical prep.

These are original practice questions for study purposes. They are not official questions from SHL, Aon, Korn Ferry, Criteria, Predictive Index, Wonderlic practice or any other test provider.

What Is a Numerical Reasoning Test?

A numerical reasoning test assesses how well you can work with numerical information.

You may need to:

• calculate percentages;
• compare ratios;
• find averages;
• solve word problems;
• interpret tables;
• read charts;
• identify number patterns;
• estimate quickly;
• make decisions from numerical data.

Most employment numerical reasoning tests do not require advanced mathematics. They usually test practical quantitative reasoning under time pressure.

Numerical reasoning test practice can help candidates become familiar with percentages, ratios, tables and timed data interpretation before assessment day.

What Does Numerical Reasoning Measure?

Numerical reasoning tests may measure:

• arithmetic accuracy;
• mental math;
• percentage calculation;
• ratio and proportion reasoning;
• data interpretation;
• number pattern recognition;
• speed under pressure;
• ability to extract relevant information;
• decision-making using numbers.

Employers use these tests to assess whether candidates can handle numerical information accurately and efficiently.

Numerical Reasoning vs Math Test

A numerical reasoning test is not exactly the same as a school math test.

Numerical Reasoning Test	Math Test
Focuses on practical number reasoning	May test formal math knowledge
Often used in hiring	Often used in education
Usually time-pressured	Timing varies
Uses workplace-style problems, tables and charts	May include algebra, geometry or formulas
Tests decision-making with numbers	Tests mathematical curriculum knowledge

You usually do not need advanced math for employment numerical reasoning tests. You need fast, accurate reasoning.

Numerical Reasoning vs Cognitive Aptitude Test

Numerical reasoning can be one section of a broader cognitive aptitude test.

Cognitive Aptitude Test	Numerical Reasoning Test
May include numerical, verbal, abstract, logical and spatial reasoning	Focuses mainly on numbers and data
Broader assessment	Specific quantitative reasoning section
Example: CCAT, PI Cognitive, Wonderlic	Example: SHL numerical reasoning
Tests general learning and problem solving	Tests numerical interpretation and calculation

Related guide:

• Cognitive Ability Test

When numerical reasoning appears inside a broader assessment, cognitive ability test practice can support mixed timed review across question types.

Common Numerical Reasoning Question Types

Question Type	What You Need to Do
Percentages	Calculate discounts, increases, decreases and proportions
Ratios	Compare quantities or split totals
Averages	Find mean values or missing values
Rates	Work with speed, output, productivity or time
Fractions	Convert and compare parts of a whole
Word problems	Translate text into calculations
Number series	Identify numerical patterns
Tables	Extract and compare data
Charts	Interpret graphs, bar charts or line charts
Estimation	Approximate quickly to eliminate wrong answers

Key Numerical Reasoning Formulas

Topic	Formula / Rule
Percentage	part ÷ whole × 100
Percentage of a number	percentage × number
Percentage increase	difference ÷ original × 100
Percentage decrease	difference ÷ original × 100
Discounted price	original price × remaining percentage
Original price after discount	sale price ÷ remaining percentage
Average	total ÷ number of values
Rate	total ÷ time
Distance	speed × time
Ratio share	total × part ÷ total ratio parts
Fraction to percentage	fraction × 100
Percentage to decimal	divide by 100

Useful Percentage Shortcuts

Percentage	Fraction	Example
10%	1/10	10% of 80 = 8
20%	1/5	20% of 80 = 16
25%	1/4	25% of 80 = 20
50%	1/2	50% of 80 = 40
75%	3/4	75% of 80 = 60
5%	half of 10%	5% of 80 = 4
15%	10% + 5%	15% of 80 = 12

These shortcuts are useful when calculators are not allowed.

Free Numerical Reasoning Practice Questions

Answer each question before reading the explanation.

Question 1: Percentage of a Number

What is 25% of 160?

• A. 30
• B. 35
• C. 40
• D. 45

Answer and Explanation

Correct answer: C. 40

25% is the same as one quarter.

160 ÷ 4 = 40

So 25% of 160 is 40.

Question 2: Discount

A product costs $80 after a 20% discount. What was the original price?

• A. $90
• B. $96
• C. $100
• D. $120

Answer and Explanation

Correct answer: C. $100

A 20% discount means the customer paid 80% of the original price.

80 = 0.80 × original price
80 ÷ 0.80 = 100

The original price was $100.

Question 3: Percentage Increase

A department had 60 employees. The number increased by 25%. How many employees are there now?

• A. 70
• B. 72
• C. 75
• D. 80

Answer and Explanation

Correct answer: C. 75

25% of 60 is:

60 ÷ 4 = 15

Add the increase:

60 + 15 = 75

There are now 75 employees.

Question 4: Rate

A team completes 72 reports in 9 hours. At the same rate, how many reports can the team complete in 5 hours?

• A. 35
• B. 40
• C. 45
• D. 50

Answer and Explanation

Correct answer: B. 40

First find the hourly rate:

72 ÷ 9 = 8 reports per hour

Then multiply by 5 hours:

8 × 5 = 40

The team can complete 40 reports.

Question 5: Average

The scores of four candidates are 18, 22, 24 and 28. What is the average score?

• A. 21
• B. 22
• C. 23
• D. 24

Answer and Explanation

Correct answer: C. 23

Add the scores:

18 + 22 + 24 + 28 = 92

Divide by 4:

92 ÷ 4 = 23

The average score is 23.

Question 6: Ratio

A team has 3 analysts for every 2 managers. If the team has 20 people total, how many are analysts?

• A. 8
• B. 10
• C. 12
• D. 15

Answer and Explanation

Correct answer: C. 12

The ratio is:

3 analysts : 2 managers

Total ratio parts:

3 + 2 = 5

Each part is:

20 ÷ 5 = 4

Analysts:

3 × 4 = 12

There are 12 analysts.

Question 7: Fraction

What is 3/5 of 200?

• A. 80
• B. 100
• C. 120
• D. 150

Answer and Explanation

Correct answer: C. 120

Calculate:

200 ÷ 5 = 40
40 × 3 = 120

So 3/5 of 200 is 120.

Question 8: Number Series

Find the next number:

4, 8, 16, 32, ?

• A. 40
• B. 48
• C. 60
• D. 64

Answer and Explanation

Correct answer: D. 64

Each number doubles:

4 × 2 = 8
8 × 2 = 16
16 × 2 = 32
32 × 2 = 64

The next number is 64.

Question 9: Increasing Difference

Find the next number:

5, 9, 17, 33, ?

• A. 49
• B. 57
• C. 65
• D. 71

Answer and Explanation

Correct answer: C. 65

The differences double:

5 to 9 = +4
9 to 17 = +8
17 to 33 = +16
33 to 65 = +32

The next number is 65.

Question 10: Word Problem

A machine produces 210 parts in 7 hours. How many parts does it produce per hour?

• A. 25
• B. 28
• C. 30
• D. 35

Answer and Explanation

Correct answer: C. 30

Use the rate formula:

rate = total ÷ time
210 ÷ 7 = 30

The machine produces 30 parts per hour.

Question 11: Table Interpretation

A store sold the following units:

Monday: 120
Tuesday: 150
Wednesday: 180
Thursday: 150

What was the average number of units sold per day?

• A. 140
• B. 145
• C. 150
• D. 155

Answer and Explanation

Correct answer: C. 150

Add the units:

120 + 150 + 180 + 150 = 600

Divide by 4 days:

600 ÷ 4 = 150

The average is 150 units per day.

Question 12: Chart-Style Comparison

Product A increased from 200 sales to 250 sales. What was the percentage increase?

• A. 20%
• B. 25%
• C. 30%
• D. 50%

Answer and Explanation

Correct answer: B. 25%

Find the difference:

250 - 200 = 50

Divide by the original value:

50 ÷ 200 = 0.25

Convert to percentage:

0.25 × 100 = 25%

The percentage increase is 25%.

Numerical Reasoning Answer Key

Question	Skill Tested	Correct Answer
1	Percentage	C
2	Discount	C
3	Percentage increase	C
4	Rate	B
5	Average	C
6	Ratio	C
7	Fraction	C
8	Number series	D
9	Increasing difference	C
10	Word problem	C
11	Table interpretation	C
12	Percentage increase	B

How to Solve Numerical Reasoning Questions

Use this process.

Step 1: Identify What Is Being Asked

Before calculating, ask:

What value do I need to find?

Examples:

• original price;
• final price;
• percentage increase;
• average;
• rate per hour;
• missing number;
• ratio share.

Many mistakes happen because candidates calculate the wrong thing.

Step 2: Extract the Relevant Numbers

Ignore unnecessary wording.

Example:

A team completes 72 reports in 9 hours. At the same rate, how many in 5 hours?

Relevant numbers:

72 reports
9 hours
5 hours

Step 3: Choose the Formula

Match the question type to the formula.

Question Type	Formula
Average	total ÷ number of values
Rate	total ÷ time
Percentage increase	difference ÷ original × 100
Discount original price	sale price ÷ remaining percentage
Ratio share	total × part ÷ total ratio parts

Step 4: Estimate Before Calculating

Estimation helps you eliminate impossible answers.

Example:

25% of 160

Since 25% is one quarter, the answer should be around:

160 ÷ 4 = 40

If an answer choice is 90, it is clearly too high.

Step 5: Check Units and Direction

Watch for:

• per hour vs total;
• increase by vs increase to;
• discount price vs original price;
• percentage of vs percentage increase;
• monthly vs annual;
• units sold vs revenue.

Small wording differences change the calculation.

Numerical Reasoning Strategies by Topic

Percentages

For percentages:

percentage = part ÷ whole × 100

Example:

30 out of 120 = 30 ÷ 120 × 100 = 25%

Common shortcut:

10% = divide by 10
5% = half of 10%
25% = divide by 4
50% = divide by 2

Discounts

For discounts, calculate what remains.

Example:

20% discount means 80% remains.

If the sale price is $80:

80 ÷ 0.80 = 100

Original price is $100.

Percentage Increase

Use:

increase ÷ original × 100

Example:

200 to 250
increase = 50
50 ÷ 200 × 100 = 25%

Averages

Use:

average = total ÷ number of values

Example:

10, 20, 30
total = 60
average = 60 ÷ 3 = 20

Ratios

For ratios:

1. Add the ratio parts.
2. Divide the total by total parts.
3. Multiply by the relevant part.

Example:

3:2 ratio, total 20
parts = 3 + 2 = 5
one part = 20 ÷ 5 = 4
3 parts = 12

Rates

Use:

rate = total ÷ time

Example:

210 parts in 7 hours
210 ÷ 7 = 30 parts per hour

Number Series

Check common patterns:

1. Add or subtract a fixed number.
2. Multiply or divide.
3. Use increasing differences.
4. Alternate between two rules.
5. Use squares or cubes.
6. Combine operations.

Example:

3, 6, 12, 24, ?

Rule:

×2

Answer:

48

Tables and Charts

For table and chart questions:

1. Read the title.
2. Check units.
3. Identify rows and columns.
4. Find the exact numbers needed.
5. Calculate only what is asked.
6. Check whether the answer is total, difference, average or percentage.

Do not calculate extra values unless needed.

Common Numerical Reasoning Mistakes

Mistake 1: Using the Wrong Percentage Base

Percentage change is based on the original value, not the final value.

Example:

Sales increase from 200 to 250.

Correct calculation:

50 ÷ 200 × 100 = 25%

Wrong calculation:

50 ÷ 250 × 100 = 20%

Mistake 2: Confusing Discount and Original Price

If a price is after a discount, you often need to work backward.

Example:

$80 after 20% discount

$80 is 80% of the original price.

80 ÷ 0.80 = 100

Mistake 3: Overcalculating

Some questions can be solved with shortcuts or estimation.

Do not waste time doing long calculations when answer choices are far apart.

Mistake 4: Ignoring Units

Watch for:

• hours vs minutes;
• monthly vs yearly;
• units vs dollars;
• total vs per person;
• percentage points vs percent.

Mistake 5: Practicing With a Calculator When It Is Not Allowed

Some cognitive aptitude tests do not allow calculators.

If your test does not allow one, practice mental math and estimation.

Mistake 6: Spending Too Long on One Question

Numerical questions can become time traps.

If the calculation is too long, skip and return if the test allows.

Logical reasoning practice can help when your numerical section also includes short rule-based or sequence questions.

Related guide:

• Time Management

Numerical Reasoning in Major Tests

Test / Provider	How Numerical Reasoning May Appear
CCAT	Math and logic questions, no calculator
PI Cognitive	Numerical reasoning and number patterns
Wonderlic	Arithmetic, word problems and number series
SHL	Numerical reasoning with data, tables and charts
Aon / cut-e	Numerical reasoning and short timed formats
Korn Ferry	Numerical or cognitive reasoning depending on role
General cognitive tests	Mixed arithmetic, rates, percentages and patterns

If your invitation names a provider, use provider-specific practice.

Before test day, pre-employment assessment practice can help you rehearse provider-style numerical formats under realistic time limits.

Best Numerical Reasoning Test Prep

For employment numerical reasoning and cognitive aptitude tests, JobTestPrep is a strong option because it provides practice across major test providers and reasoning formats.

Use JobTestPrep for:

• numerical reasoning;
• cognitive ability tests;
• CCAT;
• PI Cognitive;
• Wonderlic;
• SHL-style numerical reasoning;
• Aon-style assessments;
• Korn Ferry-style assessments;
• answer explanations;
• timed simulations.

Numerical reasoning test practice can highlight how percentages, rates and chart questions behave under timed conditions. Verify product fit on the vendor site before purchasing.

Free vs Paid Numerical Reasoning Practice

Prep Type	Best Use
Free numerical questions	Learn the basics
Free cognitive tests	Practice mixed reasoning
Official provider samples	Confirm assessment style
Answer explanations	Learn formulas and shortcuts
Paid JobTestPrep	More practice volume and simulations
Timed drills	Build speed
Provider-specific prep	Best if your invitation names SHL, Aon, CCAT, PI or Wonderlic

Free practice is useful for learning formulas. Paid prep is more useful when the assessment is high-stakes or provider-specific.

7-Day Numerical Reasoning Study Plan

Day	Study Focus
Day 1	Diagnostic numerical practice test
Day 2	Percentages, discounts and percentage change
Day 3	Ratios, fractions and averages; add verbal reasoning practice if your test is mixed
Day 4	Rates, word problems and unit conversion
Day 5	Number series and pattern recognition
Day 6	Tables, charts and timed mixed practice
Day 7	Review mistakes and repeat weakest topics

24-Hour Numerical Reasoning Study Plan

If your test is tomorrow:

1. Review percentage formulas.
2. Practice 10 percentage questions.
3. Practice 10 rate or average questions.
4. Practice 10 number series questions.
5. Review every wrong answer.
6. Memorize common shortcuts.
7. Complete one timed mixed set.
8. Stop heavy practice before you become fatigued.

If your invitation also includes visual reasoning, abstract reasoning practice can round out last-minute mixed review.

Related Cognitive Aptitude Test Guides

Use these related pages to continue preparing:

Guide	Best For
Cognitive Test Sample Questions	Mixed examples
Cognitive Test Answers Explained	Step-by-step explanations
Aptitude Test Practice	General practice
Free Cognitive Test With Answers	Free mixed test
Time Management	Pacing and skipping
Common Mistakes	Mistakes to avoid
Best Cognitive Test Prep	Prep resources
Verbal Reasoning	Word questions
Abstract Reasoning	Pattern questions
Logical Reasoning	Logic questions
How to Prepare in 7 Days	One-week plan
How to Prepare in 24 Hours	Last-minute plan

Sources / Information to Verify Before Publication

Before publication, verify numerical reasoning and provider-specific assessment details with current sources.

Use sources such as:

• JobTestPrep numerical reasoning resources;
• JobTestPrep cognitive ability test page;
• JobTestPrep free cognitive test page;
• JobTestPrep free aptitude test page;
• SHL numerical reasoning resources;
• AssessmentDay numerical reasoning resources;
• Aon talent assessment products and tools;
• Korn Ferry candidate assessment guide;
• Criteria CCAT official pages;
• Predictive Index Cognitive Assessment resources;
• Wonderlic official cognitive assessment resources;
• Aptitude-Test.com cognitive ability test;
• Practice Aptitude Tests cognitive ability test page;
• 12minprep free cognitive ability test practice;
• employer assessment invitation.

Verify:

• exact assessment name;
• exact test provider;
• whether numerical reasoning is tested directly;
• question types;
• current time limit;
• number of questions;
• calculator policy;
• whether guessing is penalized;
• whether tables or charts are included;
• whether full simulations are included;
• whether explanations are included;
• current JobTestPrep product contents;
• current JobTestPrep affiliate URL;
• access duration;
• refund or guarantee terms.

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