Numerical Reasoning Practice Test Walkthrough: Step-by-Step Solutions
Numerical reasoning tests measure how quickly and accurately you can work with numbers, tables, and charts under time pressure. Employers across every industry use these tests to screen candidates before interviews, and scoring well often determines whether your application moves forward.
This walkthrough gives you five fully worked practice questions covering percentages, ratios, and data interpretation from tables. Each solution follows a clear four-step method you can apply to any question you encounter on test day.
What Is a Numerical Reasoning Test?
A numerical reasoning test is a timed assessment that presents you with numerical data, usually in the form of tables, charts, or short passages, and asks you to draw conclusions or perform calculations. Unlike a pure math test, these questions focus on applied reasoning. You need to figure out what the data means, select the right operation, and reach the correct answer within a strict time limit.
Major employers rely on these tests during recruitment. Goldman Sachs uses numerical reasoning assessments as part of its early-stage screening. Deloitte includes them in its online application process. Procter & Gamble (P&G) integrates numerical questions into its broader cognitive assessment suite. Regardless of the specific test publisher, whether it is SHL, Cubiks, Kenexa, or Talent Q, the underlying skills being tested remain the same.
💡Numerical reasoning tests are not about advanced math. They test your ability to interpret data, choose the right formula, and calculate accurately under time pressure.
Why Practice Walkthroughs Matter
Reading through worked solutions is one of the most effective ways to prepare. When you study a walkthrough, you see the reasoning behind each step rather than just the final answer. This helps you recognize question patterns, avoid common mistakes, and build a reliable problem-solving method.
Candidates who practice with step-by-step solutions tend to improve faster than those who simply attempt practice questions and check answers. The key difference is understanding why each step is taken, not just knowing the correct result.
The Four-Step Method for Every Question
Before diving into the practice questions, here is the method you should apply to every numerical reasoning question:
- Identify what is being asked. Read the question carefully. Determine exactly what value or comparison you need to find.
- Locate the relevant data. Find the specific numbers in the table, chart, or passage. Ignore information that is not needed.
- Choose and apply the formula. Select the correct calculation. Plug in the values and work through it step by step.
- Verify your answer. If time allows, check your result with a quick reverse calculation or estimation.
This method works across every question type. Use it consistently to avoid careless errors and stay organized under time pressure.
Common Question Types at a Glance
Numerical reasoning tests draw from a predictable set of question types. The table below summarizes what you will encounter and how to approach each one.
| Question Type | What It Tests | Typical Formula | Example Scenario |
|---|---|---|---|
| Percentage change | Calculating increases or decreases | ((New - Old) / Old) x 100 | Revenue growth between two years |
| Percentage of a total | Finding a proportion | (Part / Whole) x 100 | Market share of one product |
| Ratios | Comparing two quantities | Value A / Value B, then simplify | Staff-to-manager ratio |
| Data interpretation | Reading values from tables or charts | Varies by question | Identifying the highest-performing region |
| Currency conversion | Converting between currencies | Amount x Exchange Rate | Comparing international sales figures |
| Rate and speed | Calculating output or distance | Rate = Output / Time | Production units per hour |
| Weighted averages | Combining groups with different sizes | Sum of (Value x Weight) / Sum of Weights | Average salary across departments |
Knowing which type a question belongs to helps you reach the right formula faster on test day.
💡Most numerical reasoning questions fall into a handful of repeating categories. Learn the formula for each type and you will recognize them instantly during the real test.
Practice Question 1: Percentage Increase
Question: A company's revenue was $120,000 in Year 1 and $150,000 in Year 2. What was the percentage increase in revenue?
A) 20% B) 25% C) 30% D) 33%
Step-by-Step Solution
Step 1: Identify what is being asked. You need the percentage increase from Year 1 to Year 2.
Step 2: Locate the relevant data.
- Year 1 revenue (Old value): $120,000
- Year 2 revenue (New value): $150,000
Step 3: Choose and apply the formula. Percentage change = ((New - Old) / Old) x 100
- Change = $150,000 - $120,000 = $30,000
- Percentage = ($30,000 / $120,000) x 100 = 25%
Step 4: Verify. 25% of $120,000 = $30,000. Adding that to $120,000 gives $150,000. This matches Year 2 revenue.
Answer: B) 25%
A common mistake here is dividing by the new value instead of the old value. Always use the original (old) value as the base when calculating percentage change.
Practice Question 2: Ratio Simplification
Question: A department has 48 employees and 8 managers. What is the employee-to-manager ratio in its simplest form?
A) 8:1 B) 6:1 C) 5:1 D) 4:1
Step-by-Step Solution
Step 1: Identify what is being asked. You need the ratio of employees to managers, simplified to its lowest terms.
Step 2: Locate the relevant data.
- Employees: 48
- Managers: 8
Step 3: Choose and apply the formula. Ratio = Employees : Managers = 48 : 8
Find the greatest common divisor (GCD) of 48 and 8. The GCD is 8.
- 48 / 8 = 6
- 8 / 8 = 1
Simplified ratio = 6 : 1
Step 4: Verify. 6 x 8 = 48 employees. 1 x 8 = 8 managers. The ratio holds.
Answer: B) 6:1
Ratio questions are straightforward once you find the GCD. On test day, try dividing both numbers by small primes (2, 3, 5) until you cannot simplify further.
Practice Question 3: Data Interpretation from a Table
Question: Use the table below to answer the question.
| Region | Q1 Sales ($) | Q2 Sales ($) | Q3 Sales ($) | Q4 Sales ($) |
|---|---|---|---|---|
| North | 45,000 | 52,000 | 48,000 | 55,000 |
| South | 38,000 | 41,000 | 39,500 | 43,000 |
| East | 50,000 | 47,000 | 53,000 | 51,000 |
| West | 42,000 | 44,000 | 46,500 | 49,000 |
Which region had the highest total annual sales?
A) North B) South C) East D) West
Step-by-Step Solution
Step 1: Identify what is being asked. You need to find which region has the highest total across all four quarters.
Step 2: Locate the relevant data. You need all four quarterly values for each region.
Step 3: Choose and apply the formula. Add the quarterly sales for each region:
- North: $45,000 + $52,000 + $48,000 + $55,000 = $200,000
- South: $38,000 + $41,000 + $39,500 + $43,000 = $161,500
- East: $50,000 + $47,000 + $53,000 + $51,000 = $201,000
- West: $42,000 + $44,000 + $46,500 + $49,000 = $181,500
Step 4: Verify. East ($201,000) is the highest total. Double-check: $50,000 + $47,000 = $97,000. Then $97,000 + $53,000 = $150,000. Then $150,000 + $51,000 = $201,000. Confirmed.
Answer: C) East
Data interpretation questions test your ability to stay organized. When working with tables, write down subtotals to avoid losing track. Under time pressure, you can also estimate. North and East are clearly close, so focus your careful calculation on those two.
💡With table-based questions, eliminate obviously wrong options first. In this example, South is clearly the lowest, so you can skip verifying it and focus your time on the close contenders.
Practice Question 4: Percentage of a Total
Question: A company's total operating costs are $250,000. Marketing accounts for $45,000 of that total. What percentage of operating costs is spent on marketing?
A) 15% B) 18% C) 20% D) 22%
Step-by-Step Solution
Step 1: Identify what is being asked. You need to express marketing costs as a percentage of total operating costs.
Step 2: Locate the relevant data.
- Marketing costs (Part): $45,000
- Total operating costs (Whole): $250,000
Step 3: Choose and apply the formula. Percentage = (Part / Whole) x 100
- Percentage = ($45,000 / $250,000) x 100
- Percentage = 0.18 x 100 = 18%
Step 4: Verify. 18% of $250,000 = $250,000 x 0.18 = $45,000. This matches the marketing figure.
Answer: B) 18%
A useful shortcut for division by 250,000: divide by 25 first, then adjust the decimal. $45,000 / 25 = 1,800. Since you divided by 25 instead of 250,000, you already have your percentage as 18. Mental math tricks like this save valuable seconds on timed tests.
Practice Question 5: Combined Data Interpretation and Percentage Change
Question: Using the table below, calculate the percentage change in total production from Week 1 to Week 2.
| Product | Week 1 Units | Week 2 Units |
|---|---|---|
| Widget A | 1,200 | 1,350 |
| Widget B | 800 | 750 |
| Widget C | 1,000 | 1,100 |
A) 5.0% B) 6.7% C) 8.3% D) 10.0%
Step-by-Step Solution
Step 1: Identify what is being asked. You need the percentage change in total production (all products combined) from Week 1 to Week 2.
Step 2: Locate the relevant data. You need to sum all products for each week.
Step 3: Choose and apply the formula.
First, calculate weekly totals:
- Week 1 total: 1,200 + 800 + 1,000 = 3,000
- Week 2 total: 1,350 + 750 + 1,100 = 3,200
Then apply the percentage change formula:
- Change = 3,200 - 3,000 = 200
- Percentage change = (200 / 3,000) x 100 = 6.67%, which rounds to 6.7%
Step 4: Verify. 6.67% of 3,000 = 200. Adding 200 to 3,000 gives 3,200. Confirmed.
Answer: B) 6.7%
This question combines two skills: data aggregation and percentage change. Many candidates rush to calculate percentage changes for individual products, but the question asks about total production. Always re-read the question before you start calculating.
💡Multi-step questions are where most mistakes happen. Break them into smaller pieces, and double-check that you are answering what was actually asked, not what you assumed was asked.
Tips for Test Day Performance
Strong preparation goes beyond knowing formulas. Here are practical strategies that help candidates perform at their best during the actual assessment.
Manage your time actively. Most tests give you 60 to 90 seconds per question. If a question is taking too long, mark it and move on. Coming back with fresh eyes often makes a difficult question easier.
Read the question before the data. Know what you are looking for before you scan the table or chart. This prevents you from getting lost in irrelevant numbers.
Use estimation to check answers. If you calculate 18.2% and the options are 15%, 18%, 20%, and 25%, you can be confident in 18% without needing a precise calculation to six decimal places.
Practice with realistic conditions. Set a timer when you work through practice tests. Untimed practice builds understanding, but timed practice builds the speed you need on test day. The numerical reasoning test on Assessment-Training.com simulates real test conditions so you can practice under pressure.
Review every mistake. After each practice session, go back and understand why you got a question wrong. Was it a calculation error, a misread of the data, or a wrong formula choice? Fixing the root cause prevents the same mistake from happening again.
How Employers Use These Tests
Understanding why companies use numerical reasoning tests can help you frame your preparation. These tests are not designed to trick you. They are built to predict how well you will handle number-based tasks in the role.
At Goldman Sachs, numerical reasoning scores factor into early-stage screening for analyst and associate roles. Candidates who fall below the benchmark are eliminated before interviews begin.
Deloitte uses SHL-style numerical tests as part of its online assessment stage. Strong performance here moves you to the next round, while a weak score can end the process regardless of your CV.
Procter & Gamble (P&G) embeds numerical reasoning into its broader Peak Performance Assessment. The questions test how candidates interpret business data, a core skill for brand management and operations roles.
The common thread across all three employers is that numerical reasoning tests serve as an objective, standardized filter. Preparation gives you a direct advantage because these tests measure trainable skills, not fixed intelligence.
Ready to start preparing? Try a set of free practice tests to see where you stand, or explore the All Test Package for full access to practice materials across every test type.
Building a Study Plan That Works
Effective preparation follows a structured approach. Here is a practical study plan you can adapt based on the time you have available.
If you have one week: Focus on learning the core formulas (percentage change, percentage of total, ratios) and work through 2 to 3 full practice tests under timed conditions. Review every incorrect answer.
If you have two to three weeks: Add data interpretation practice with tables and charts. Complete 5 to 8 full practice tests, spacing them out over the period. Track which question types you get wrong most often and do extra drills on those.
If you have a month or more: Build all of the above plus practice with advanced question types like weighted averages and combined multi-step problems. Aim to complete at least 10 full practice tests. Your goal is to make the question formats feel automatic so that on test day, you can focus entirely on the numbers in front of you.
The numerical reasoning test section on Assessment-Training.com provides practice tests with detailed explanations for every answer, making it easy to follow this kind of structured study plan.
💡Consistent, focused practice over time beats last-minute cramming. Even two well-structured practice sessions per week will significantly improve your score.
Frequently Asked Questions
How do I know which formula to use?
Look for keywords in the question. "Percentage change" or "increase" points you to ((New - Old) / Old) x 100. "Percentage of" or "proportion" means (Part / Whole) x 100. "Ratio" tells you to divide two values and simplify. With practice, matching keywords to formulas becomes second nature.
Should I always verify my answer?
When time allows, yes. A quick reverse calculation can catch errors that cost you marks. In timed tests, spend no more than 10 to 15 seconds verifying. If you are running low on time, prioritize moving to the next question rather than double-checking one you feel confident about.
How many questions are on a typical numerical reasoning test?
Most tests have between 15 and 25 questions, and you usually get about 60 to 90 seconds per question. The exact number depends on the test publisher and the employer. SHL tests tend to have around 18 questions in 25 minutes, while Cubiks tests may have fewer questions with more time per item.
Can I use a calculator during the test?
Some employers allow an on-screen calculator, while others do not. SHL tests generally permit one, but Kenexa and some custom assessments do not. Always check the instructions before you begin, and practice both with and without a calculator so you are prepared for either scenario.
What score do I need to pass a numerical reasoning test?
There is no universal pass mark. Employers set their own benchmarks, often around the 50th to 70th percentile. At competitive firms like Goldman Sachs or Deloitte, you may need to score above the 80th percentile to advance. The best approach is to aim for the highest score you can achieve rather than targeting a specific number.
Where can I find more practice walkthroughs?
Assessment-Training.com offers a comprehensive library of numerical reasoning practice tests with step-by-step explanations for every question. You can also access free tests to get started immediately. Work through them systematically and review any questions you get wrong to identify patterns in your mistakes.