Free Numerical Reasoning Practice Test: Questions, Answers & Explanations

A numerical reasoning test measures your ability to interpret numbers, solve practical math problems, analyze data, and make decisions using tables, charts, percentages, ratios, averages, and basic calculations.

Numerical reasoning tests are common in pre-employment assessments for roles that involve data, analysis, finance, operations, management, administration, sales, logistics, customer service, civil service, graduate programs, and technical work.

You may see numerical reasoning questions in:

aptitude tests;
cognitive ability tests;
SHL assessments;
CCAT-style tests;
PI Cognitive Assessment;
Wonderlic-style tests;
civil service exams;
graduate assessments;
finance assessments;
management assessments;
analyst assessments;
Excel assessments;
employer-specific hiring tests.

Aptitude test practice can supplement numerical prep with free mixed reasoning drills across math and data interpretation.

This free numerical reasoning practice test includes sample questions, answers, and explanations across the most common numerical test topics.

These questions are not official questions from SHL, Criteria, CCAT, PI, Wonderlic, Aon, Saville, Korn Ferry, JobTestPrep, or any employer. They are practice-style examples designed to help you understand common numerical reasoning formats.

Numerical reasoning test practice can help you rehearse percentages, tables, and word problems under timed conditions.

What Is a Numerical Reasoning Test?

A numerical reasoning test is an assessment that measures your ability to work with numerical information.

Unlike a basic arithmetic quiz, numerical reasoning often requires you to:

understand the question;
identify the relevant data;
choose the right calculation;
interpret tables or charts;
compare values;
calculate percentages;
calculate averages;
estimate quickly;
make logical conclusions from numbers.

The difficulty usually comes from time pressure, data interpretation, and choosing the right method quickly.

You may not need advanced math, but you do need strong accuracy and speed.

What Does a Numerical Reasoning Test Measure?

Numerical reasoning tests may measure:

basic arithmetic;
percentages;
percentage increase and decrease;
ratios and proportions;
fractions and decimals;
averages;
rates;
time calculations;
currency calculations;
table interpretation;
chart interpretation;
data comparison;
number series;
business math;
financial reasoning;
estimation;
problem-solving under time pressure.

The exact content depends on the employer, role, test provider, and difficulty level.

Common Numerical Reasoning Test Providers

Numerical reasoning questions may appear in many provider-specific assessments, including:

SHL numerical reasoning;
Aon numerical reasoning;
Saville numerical analysis;
Korn Ferry numerical reasoning;
Criteria/CCAT numerical questions;
PI Cognitive numerical questions;
Wonderlic numerical questions;
civil service numerical reasoning;
employer-specific numerical assessments.

If your test invitation names a provider, prepare for that provider’s format.

How to Use This Free Numerical Reasoning Practice Test

Use this page as a diagnostic practice test.

For best results:

Answer each question before reading the explanation.
Use a calculator only if your real test allows one.
Use scratch paper if your real test allows it.
Time yourself if you want realistic practice.
Track which topics are slow or difficult.
Review every explanation.
Practice weak topics separately.

Suggested timing:

Beginner: 60 minutes.
Intermediate: 45 minutes.
Advanced: 35 minutes.

If your real test is tightly timed, reduce the time limit gradually.

Free Numerical Reasoning Practice Test Format

This free practice test includes 45 questions across:

basic arithmetic;
percentages;
percentage change;
fractions and decimals;
ratios and proportions;
averages;
rates and productivity;
tables;
charts;
word problems;
number series;
financial reasoning;
data interpretation;
estimation.

Not every numerical reasoning test includes all these topics.

Use the sections that match your actual assessment.

Section 1: Basic Arithmetic and Practical Calculation

These questions test core calculation accuracy.

Question 1

What is 18 × 7?

A. 116
B. 126
C. 136
D. 146

Correct answer: B

Explanation: 18 × 7 = 126.

Question 2

What is 360 ÷ 12?

A. 20
B. 25
C. 30
D. 36

Correct answer: C

Explanation: 360 divided by 12 equals 30.

Question 3

A department processed 48 files in the morning and 67 files in the afternoon.

How many files were processed in total?

A. 105
B. 115
C. 125
D. 135

Correct answer: B

Explanation: 48 + 67 = 115.

Question 4

A box contains 24 items. How many items are in 15 boxes?

A. 240
B. 300
C. 330
D. 360

Correct answer: D

Explanation: 24 × 15 = 360.

Question 5

A report contains 144 pages. It is divided equally into 8 sections.

How many pages are in each section?

A. 16
B. 18
C. 20
D. 24

Correct answer: B

Explanation: 144 ÷ 8 = 18.

Section 2: Percentages

Percentage questions are very common in numerical reasoning tests.

Useful shortcuts:

10% = divide by 10;
20% = one fifth;
25% = one quarter;
50% = one half;
75% = three quarters.

Question 6

What is 20% of 350?

A. 35
B. 50
C. 70
D. 90

Correct answer: C

Explanation: 20% is one fifth.

350 ÷ 5 = 70.

Question 7

What is 15% of 240?

A. 24
B. 30
C. 36
D. 48

Correct answer: C

Explanation: 10% of 240 is 24.

5% of 240 is 12.

15% = 24 + 12 = 36.

Question 8

A company has 800 employees. If 30% work remotely, how many employees work remotely?

A. 180
B. 210
C. 240
D. 300

Correct answer: C

Explanation: 10% of 800 is 80.

30% is 80 × 3 = 240.

Question 9

A product costs $120. It is discounted by 25%.

What is the discount amount?

A. $20
B. $25
C. $30
D. $40

Correct answer: C

Explanation: 25% is one quarter.

120 ÷ 4 = 30.

The discount is $30.

Question 10

A survey had 500 respondents. 62% selected “Yes.”

How many respondents selected “Yes”?

A. 280
B. 300
C. 310
D. 320

Correct answer: C

Explanation: 62% of 500 = 0.62 × 500 = 310.

Section 3: Percentage Increase and Decrease

For percentage change, use:

Percentage change = change ÷ original value × 100

Always divide by the original value, not the new value.

Question 11

A team completed 160 tasks in March and 200 tasks in April.

What was the percentage increase?

A. 20%
B. 25%
C. 30%
D. 40%

Correct answer: B

Explanation: The increase is:

200 - 160 = 40.

40 ÷ 160 = 0.25.

0.25 = 25%.

Question 12

Sales decreased from $90,000 to $72,000.

What was the percentage decrease?

A. 10%
B. 15%
C. 20%
D. 25%

Correct answer: C

Explanation: The decrease is:

90,000 - 72,000 = 18,000.

18,000 ÷ 90,000 = 0.20.

0.20 = 20%.

Question 13

A product costs $80 after a 20% discount.

What was the original price?

A. $90
B. $96
C. $100
D. $120

Correct answer: C

Explanation: After a 20% discount, the sale price is 80% of the original price.

80 ÷ 0.80 = 100.

The original price was $100.

Question 14

A website had 12,000 visitors last month and 15,000 visitors this month.

What was the percentage increase?

A. 20%
B. 25%
C. 30%
D. 35%

Correct answer: B

Explanation: The increase is:

15,000 - 12,000 = 3,000.

3,000 ÷ 12,000 = 0.25.

0.25 = 25%.

Question 15

A budget was reduced from $50,000 to $42,500.

What was the percentage decrease?

A. 10%
B. 12.5%
C. 15%
D. 20%

Correct answer: C

Explanation: The decrease is:

50,000 - 42,500 = 7,500.

7,500 ÷ 50,000 = 0.15.

0.15 = 15%.

Section 4: Fractions, Decimals, and Ratios

These questions test conversion, proportion, and comparison.

Question 16

What is 3/4 of 200?

A. 50
B. 100
C. 150
D. 175

Correct answer: C

Explanation: One quarter of 200 is 50.

Three quarters is 50 × 3 = 150.

Question 17

Which decimal is equal to 3/5?

A. 0.3
B. 0.5
C. 0.6
D. 0.75

Correct answer: C

Explanation: 3 ÷ 5 = 0.6.

Question 18

The ratio of managers to analysts is 2:5.

If there are 14 managers, how many analysts are there?

A. 28
B. 30
C. 35
D. 40

Correct answer: C

Explanation: The ratio 2:5 means 2 manager parts correspond to 5 analyst parts.

If 2 parts = 14, then 1 part = 7.

5 parts = 35.

Question 19

A team has 45 employees. The ratio of full-time to part-time employees is 4:1.

How many full-time employees are there?

A. 30
B. 32
C. 36
D. 40

Correct answer: C

Explanation: The total ratio parts are 4 + 1 = 5.

45 ÷ 5 = 9 per part.

Full-time employees = 4 × 9 = 36.

Question 20

Which is greater?

A. 0.65
B. 2/3
C. 60%
D. 0.6

Correct answer: B

Explanation: 2/3 is approximately 0.667.

0.667 is greater than 0.65, 0.60, and 0.6.

Section 5: Averages

Average questions are common in business and employment tests.

Average = total ÷ number of values.

Question 21

Four employees processed 18, 24, 20, and 22 files.

What is the average number of files processed?

A. 20
B. 21
C. 22
D. 24

Correct answer: B

Explanation: 18 + 24 + 20 + 22 = 84.

84 ÷ 4 = 21.

Question 22

A store made sales of $1,200, $1,500, $1,800, and $1,900 over four days.

What was the average daily sales amount?

A. $1,500
B. $1,600
C. $1,700
D. $1,800

Correct answer: B

Explanation: 1,200 + 1,500 + 1,800 + 1,900 = 6,400.

6,400 ÷ 4 = 1,600.

Question 23

The average of five numbers is 12.

What is the total of the five numbers?

A. 48
B. 50
C. 60
D. 72

Correct answer: C

Explanation: Average × number of values = total.

12 × 5 = 60.

Question 24

A team averaged 75 calls per hour over 6 hours.

How many calls did the team handle in total?

A. 375
B. 400
C. 450
D. 500

Correct answer: C

Explanation: 75 × 6 = 450.

Question 25

A candidate scored 70, 80, and 90 on three practice tests.

What was the average score?

A. 75
B. 80
C. 85
D. 90

Correct answer: B

Explanation: 70 + 80 + 90 = 240.

240 ÷ 3 = 80.

Section 6: Rates, Productivity, and Time

Rate questions involve work per hour, speed, time, or output.

Question 26

A worker completes 12 tasks per hour.

How many tasks are completed in 7 hours?

A. 72
B. 78
C. 84
D. 96

Correct answer: C

Explanation: 12 × 7 = 84.

Question 27

A machine produces 450 units in 9 hours.

How many units does it produce per hour?

A. 40
B. 45
C. 50
D. 55

Correct answer: C

Explanation: 450 ÷ 9 = 50.

Question 28

A car travels 180 miles in 3 hours.

What is the average speed?

A. 45 mph
B. 50 mph
C. 60 mph
D. 70 mph

Correct answer: C

Explanation: 180 ÷ 3 = 60 miles per hour.

Question 29

A task takes 18 minutes. How many full tasks can be completed in 2 hours?

A. 5
B. 6
C. 7
D. 8

Correct answer: B

Explanation: 2 hours = 120 minutes.

120 ÷ 18 = 6.66.

Only 6 full tasks can be completed.

Question 30

A project starts at 9:15 AM and ends at 11:45 AM.

How long does it last?

A. 1 hour 30 minutes
B. 2 hours
C. 2 hours 30 minutes
D. 3 hours

Correct answer: C

Explanation: From 9:15 AM to 11:45 AM is 2 hours and 30 minutes.

Section 7: Tables and Data Interpretation

Numerical reasoning tests often use tables.

Answer using only the data provided.

Table 1: Monthly Sales by Region

Region	January	February	March
North	120	150	180
South	200	220	210
East	160	170	190
West	140	130	160

Question 31

Which region had the highest sales in February?

A. North
B. South
C. East
D. West

Correct answer: B

Explanation: February sales:

North: 150
South: 220
East: 170
West: 130

South had the highest sales.

Question 32

What was the total March sales across all regions?

A. 680
B. 720
C. 740
D. 760

Correct answer: C

Explanation: March sales:

180 + 210 + 190 + 160 = 740.

Question 33

Which region increased every month from January to March?

A. North only
B. North and East
C. South and West
D. All regions

Correct answer: B

Explanation: North: 120, 150, 180 = increases each month.

East: 160, 170, 190 = increases each month.

South decreases from February to March.

West decreases from January to February.

Question 34

What was the percentage increase for North from January to March?

A. 25%
B. 40%
C. 50%
D. 60%

Correct answer: C

Explanation: North increased from 120 to 180.

Increase = 60.

60 ÷ 120 = 0.50.

0.50 = 50%.

Question 35

Which region had the lowest total sales across the three months?

A. North
B. South
C. East
D. West

Correct answer: D

Explanation: Totals:

North: 120 + 150 + 180 = 450
South: 200 + 220 + 210 = 630
East: 160 + 170 + 190 = 520
West: 140 + 130 + 160 = 430

West had the lowest total.

Section 8: Charts and Graph-Style Questions

Some numerical reasoning tests use charts rather than tables.

For this free practice test, the chart information is written in text form.

Chart 1: Department Budget Allocation

A company budget is divided as follows:

Operations: 40%
Marketing: 25%
Technology: 20%
Training: 10%
Other: 5%

Total budget: $500,000

Question 36

How much is allocated to Operations?

A. $150,000
B. $180,000
C. $200,000
D. $250,000

Correct answer: C

Explanation: Operations receives 40% of $500,000.

0.40 × 500,000 = 200,000.

Question 37

How much is allocated to Training?

A. $25,000
B. $50,000
C. $75,000
D. $100,000

Correct answer: B

Explanation: Training receives 10% of $500,000.

0.10 × 500,000 = 50,000.

Question 38

How much more is allocated to Marketing than Technology?

A. $10,000
B. $15,000
C. $20,000
D. $25,000

Correct answer: D

Explanation: Marketing = 25% of $500,000 = $125,000.

Technology = 20% of $500,000 = $100,000.

Difference = $25,000.

Question 39

What is the combined allocation for Technology and Training?

A. $100,000
B. $125,000
C. $150,000
D. $175,000

Correct answer: C

Explanation: Technology = 20%.

Training = 10%.

Combined = 30% of $500,000.

0.30 × 500,000 = $150,000.

Question 40

Which category receives the smallest allocation?

A. Marketing
B. Technology
C. Training
D. Other

Correct answer: D

Explanation: Other receives 5%, which is the smallest percentage listed.

Section 9: Number Series

Some numerical reasoning or cognitive tests include number series.

Look for the rule before calculating.

Question 41

2, 4, 8, 16, ?

A. 20
B. 24
C. 32
D. 64

Correct answer: C

Explanation: Each number is multiplied by 2.

16 × 2 = 32.

Question 42

5, 10, 15, 20, ?

A. 22
B. 24
C. 25
D. 30

Correct answer: C

Explanation: The pattern adds 5 each time.

20 + 5 = 25.

Question 43

100, 50, 25, 12.5, ?

A. 5
B. 6.25
C. 7.5
D. 10

Correct answer: B

Explanation: Each number is divided by 2.

12.5 ÷ 2 = 6.25.

Question 44

1, 4, 9, 16, 25, ?

A. 30
B. 36
C. 40
D. 49

Correct answer: B

Explanation: These are square numbers:

1², 2², 3², 4², 5².

The next is 6² = 36.

Question 45

2, 5, 10, 17, 26, ?

A. 35
B. 36
C. 37
D. 38

Correct answer: C

Explanation: The differences increase by 2:

+3, +5, +7, +9.

The next difference is +11.

26 + 11 = 37.

Answer Key

How to Score Your Numerical Reasoning Practice Test

Use this practice score guide:

40-45 correct: Strong numerical reasoning baseline. Continue with timed simulations and provider-specific practice.
34-39 correct: Good performance. Review weaker topics and improve speed.
27-33 correct: Moderate readiness. Practice percentages, tables, charts, ratios, and averages separately.
20-26 correct: Needs improvement. Build core calculation accuracy before strict timing.
19 or fewer correct: Start with untimed numerical reasoning lessons and explanations before taking full tests.

This score is for practice only.

It is not an official numerical reasoning score, SHL score, employer benchmark, JobTestPrep score, or passing score.

Real numerical reasoning scoring depends on the test provider, employer, role, norm group, difficulty level, and time limit.

What Your Score Means by Topic

Basic Arithmetic

If you missed basic arithmetic questions, practice:

multiplication;
division;
addition;
subtraction;
mental math;
estimating answers.

Core arithmetic speed helps with every numerical test section.

Percentages

If you missed percentage questions, review:

10%;
20%;
25%;
50%;
75%;
percentage of a number;
percentage increase;
percentage decrease;
reverse percentage calculations.

Ratios and Fractions

If you missed ratio or fraction questions, practice:

simplifying fractions;
converting fractions to decimals;
comparing fractions;
ratio parts;
proportional reasoning.

Averages

If you missed average questions, remember:

Average = total ÷ number of values.

Also practice reverse average questions where you are given the average and number of values.

Rates and Time

If you missed rate questions, practice:

tasks per hour;
units per hour;
average speed;
time conversion;
full task completion;
start and end time calculations.

Tables

If you missed table questions, practice:

locating the correct row and column;
adding totals;
comparing values;
identifying increases;
calculating percentage change;
avoiding wrong-month or wrong-region errors.

Charts

If you missed chart questions, practice converting percentages into amounts and comparing categories.

Number Series

If you missed number series questions, practice:

addition patterns;
multiplication patterns;
division patterns;
squares;
alternating sequences;
increasing differences.

How to Prepare for a Numerical Reasoning Test

1. Identify the Test Provider

Start by checking your assessment invitation.

Look for provider names such as:

SHL;
Aon;
Saville;
Korn Ferry;
Criteria;
CCAT;
PI;
Wonderlic;
Talent Q;
employer-specific assessment.

If you know the provider, prepare for that format.

Numerical reasoning test practice can help you build familiarity with common question formats before full timed simulations. Verify product fit on the vendor site before purchasing.

2. Learn the Core Math Topics

Most numerical reasoning tests rely on a small set of recurring topics:

percentages;
ratios;
averages;
fractions;
decimals;
rates;
tables;
charts;
word problems.

You usually do not need advanced math.

You need quick, accurate practical calculation.

Cognitive ability test practice can support broader reasoning review when your invitation covers several cognitive sections beyond numerical items alone.

3. Practice Table and Chart Questions

Many employment numerical tests use business-style data.

Practice extracting information from:

tables;
bar charts;
line graphs;
pie charts;
financial summaries;
sales reports;
productivity data;
budget allocations.

4. Build Percentage Speed

Percentages appear constantly.

Practice:

percentage of a value;
percentage change;
reverse percentages;
discount questions;
budget percentages;
sales increases;
productivity changes.

A common error is dividing by the new value instead of the original value. Numerical reasoning test practice with answer explanations can help you review formula choices after each timed set.

5. Add Timed Practice

Numerical reasoning tests are often timed.

Use this progression:

Learn the question type untimed.
Practice short sets.
Review mistakes.
Add timing.
Take mixed timed tests.
Take full simulations.

Pre-employment assessment practice can support mixed review when your hiring process includes several assessment steps.

6. Review Every Mistake

After each practice set, classify your errors:

calculation error;
wrong formula;
wrong row or column;
percentage base error;
misunderstood question;
time pressure;
careless copying;
calculator entry error;
estimation error.

Then practice similar questions.

7. Know Calculator Rules

Some numerical reasoning tests allow calculators.

Others do not.

Some online tests include an on-screen calculator.

Some assessment centers provide a standard calculator.

Always follow the instructions in your test invitation.

If calculators are allowed, practice with the type of calculator you will use.

8. Use Estimation

Estimation helps you eliminate unreasonable answers.

For example, if a question asks for 25% of 240, the answer should be about one quarter of 240, or 60.

If an answer choice is 240 or 12, you can eliminate it quickly.

9. Do Not Overcalculate

Some numerical reasoning questions can be solved faster by:

estimating;
comparing ratios;
eliminating impossible answers;
rounding carefully;
using percentage shortcuts;
simplifying numbers.

Speed matters, but accuracy matters too.

Common Numerical Reasoning Test Mistakes

Mistake 1: Dividing by the Wrong Base

For percentage change, divide by the original value, not the new value.

Mistake 2: Misreading Tables

Check the row, column, month, region, and unit carefully.

Mistake 3: Ignoring Units

Watch for:

thousands;
millions;
dollars;
percentages;
hours;
minutes;
miles;
units;
per hour.

Mistake 4: Overusing the Calculator

A calculator can help, but entering too many unnecessary calculations wastes time.

Use mental shortcuts when possible.

Mistake 5: Not Practicing Under Timing

Numerical reasoning tests often feel harder because of the time limit.

Practice timed sets.

Mistake 6: Skipping Explanations

Reviewing explanations helps you learn faster methods.

Mistake 7: Rushing Easy Questions

Easy questions are valuable.

Do not lose points through careless mistakes.

Mistake 8: Spending Too Long on One Question

If a question becomes too complex, use elimination and move on if the test allows it.

Mistake 9: Forgetting Reverse Percentages

When a discounted price is given, remember that the sale price may be less than 100% of the original.

Mistake 10: Treating Number Series Like Table Questions

Number series questions require pattern recognition, not data interpretation.

Use different strategies for different formats.

Free vs Paid Numerical Reasoning Practice

Free practice is useful for:

learning the format;
reviewing basic math;
checking your baseline;
identifying weak topics;
practicing common calculations.

Paid preparation may be useful if:

your test is provider-specific;
the role is competitive;
you need full timed simulations;
you want detailed explanations;
you need table and graph practice;
you want score tracking;
you have failed before;
the job opportunity is important.

Verbal reasoning practice can help when your aptitude battery also includes verbal or data-interpretation sections alongside numerical reasoning.

Numerical Reasoning Test-Day Tips

Before the test:

identify the provider if possible;
review percentage formulas;
review averages and ratios;
practice table and chart questions;
confirm calculator rules;
prepare your device if online;
do a short warm-up;
sleep as well as possible.

During the test:

read the question carefully;
identify the relevant data;
check units;
use the original value for percentage change;
estimate before calculating;
use elimination;
avoid overchecking;
manage time;
do not panic after one difficult question.

After the test:

follow employer instructions;
prepare for the next hiring stage;
do not assume failure because some questions felt difficult.

Final Numerical Reasoning Practice Checklist

Before your numerical reasoning test, make sure you can:

calculate percentages quickly;
calculate percentage increase and decrease;
solve reverse percentage questions;
compare fractions and decimals;
solve ratio problems;
calculate averages;
solve rate and time questions;
read tables accurately;
interpret charts;
identify number series patterns;
estimate answers;
use a calculator efficiently if allowed;
manage time under pressure.

FAQ

What is a numerical reasoning test?

A numerical reasoning test is a pre-employment assessment that measures your ability to interpret numerical data, solve practical math problems, analyze tables and charts, and make decisions using numbers.

What questions are on a numerical reasoning test?

Numerical reasoning tests may include percentages, ratios, averages, fractions, decimals, rates, time, tables, charts, word problems, number series, and data interpretation.

Are numerical reasoning tests hard?

They can be challenging because of time pressure, data interpretation, and multi-step calculations. The math is often not advanced, but accuracy and speed are important.

Do I need advanced math for a numerical reasoning test?

Usually not. Most employment numerical reasoning tests focus on practical math such as percentages, ratios, averages, tables, charts, and basic arithmetic.

Can I use a calculator on numerical reasoning tests?

It depends on the test provider and employer. Some tests allow calculators, some provide an on-screen calculator, and some do not allow calculators. Always check your test instructions.

How do I prepare for a numerical reasoning test?

Review core math topics, practice percentages and ratios, work through table and chart questions, take timed practice tests, and review every mistake. Numerical reasoning test practice can offer timed simulations when you need more than the samples on this page.

What is the best strategy for numerical reasoning tests?

Read the question carefully, identify the required data, check units, estimate the answer, calculate efficiently, use elimination, and manage time.

How do I improve numerical reasoning speed?

Practice timed mini sets, memorize common percentage shortcuts, use estimation, reduce unnecessary calculations, and review faster solution methods.

What is a good numerical reasoning test score?

A good score depends on the provider, employer, role, norm group, and hiring benchmark. Do not rely on generic score claims without context.

Are these official numerical reasoning questions?

No. The questions on this page are practice-style examples designed to reflect common numerical reasoning test themes. They are not official questions from SHL, Criteria, PI, Wonderlic, Aon, Saville, Korn Ferry, JobTestPrep, or any employer.

Use these pages to keep studying after this free practice set: