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Numerical Reasoning

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Numerical reasoning tests measure your ability to work with numbers in practical contexts. You'll calculate percentages, work with ratios, solve rate problems, and interpret numerical information.

These tests are among the most common in employment screening, used across finance, consulting, technology, and virtually every industry requiring quantitative skills. Our procedurally generated word problems cover percentages, ratios, rates, and multi-step calculations, ensuring you'll never see the same question twice.

All questions are generated locally in your browser. Your progress and answers are stored only on your device — we never collect any personal data.

Key Patterns & Formats

Finding Percentages

Calculate what X% of a given number equals.

X% of Y = Y × (X/100) = Y × 0.0X

Reverse Percentage

Find the original value before a percentage change was applied.

If Final = Original × (1 + X/100), then Original = Final ÷ (1 + X/100)

Percentage Change

Calculate the result after increasing or decreasing a value by a percentage.

Increase: Final = Original × (1 + X/100). Decrease: Final = Original × (1 - X/100)

Simple Ratio

Find unknown values when two quantities are in a given ratio.

If A:B = m:n and A = x, then B = x × (n/m)

Ratio Division

Divide a total amount according to a given ratio.

Total T split in ratio a:b → Part A = T × a/(a+b), Part B = T × b/(a+b)

Work Rate Problems

Calculate time or workers needed when the total work stays constant.

Total Work = Workers × Time. If W1 × T1 = W2 × T2, then T2 = (W1 × T1) / W2

Profit Calculation

Calculate profit, cost price, or selling price from given values.

Profit = Selling Price - Cost Price. Profit % = (Profit / Cost) × 100

Compound Percentage

Calculate the result of applying multiple percentage changes in sequence.

After changes of X% then Y%: Final = Original × (1 + X/100) × (1 + Y/100)

Combined Rates

Calculate how long tasks take when multiple workers or machines work together.

Combined Rate = Rate A + Rate B. Time = Total Work / Combined Rate

Solving Strategies

  • Look for 'what is X% of Y' phrasing
  • Convert the percentage to decimal (divide by 100)
  • Multiply the base number by the decimal
  • You're given the final value after a percentage change
  • You need to find what the value was before the change
  • Keywords: 'original price', 'was before', 'started at'
  • Given a starting value and a percentage change
  • Asked for the new/final value

Common Pitfalls

  • Forgetting to divide the percentage by 100
  • Multiplying by the percentage directly (25 instead of 0.25)
  • Confusing 'of' with 'off' (discount calculations)
  • Subtracting the percentage from the final (e.g., $120 - 20% = $96, wrong!)
  • Using the wrong multiplier (1.20 for increase, 0.80 for 20% decrease)
  • Confusing increase (multiply by >1) with decrease (multiply by <1)

Frequently Asked Questions

You'll encounter percentage calculations, ratio problems, rate/work problems, profit margins, and multi-step word problems. Each question presents a real-world scenario requiring mathematical reasoning.
Nearly all major employers: investment banks, consulting firms (McKinsey, BCG, Bain), Big 4 accounting, tech companies, and graduate programs. SHL, Korn Ferry, and Talent Q tests heavily feature numerical reasoning.
Master mental math shortcuts: 10% = divide by 10, 5% = half of 10%, 25% = divide by 4. For reverse percentages, if X after Y% increase, original = X ÷ (1 + Y/100). Practice estimation to quickly eliminate wrong answers.
Each question is procedurally generated using realistic business scenarios with randomized values. The system creates word problems involving percentages, ratios, rates, and multi-step calculations, then generates plausible distractors based on common calculation errors. This ensures every question has a single correct answer and provides unlimited unique practice.

Sources & References

Finding Percentages

Finding Percentages
X% of Y = Y × (X/100) = Y × 0.0X
What is 25% of 80? → 80 × 0.25 = 20
What is 15% of 200? → 200 × 0.15 = 30
What is 40% of 150? → 150 × 0.40 = 60
What is 15% of 80?
  1. 1
    Convert percentage to decimal: 15/100 = 0.1515% = 0.15
  2. 2
    Multiply the base number by the decimal: 80 x 0.1580 x 0.15
  3. 3
    Calculate: 80 x 0.15 = 12= 12
Refs:Khan Academy - Intro to percentages

Reverse Percentage

Reverse Percentage
If Final = Original × (1 + X/100), then Original = Final ÷ (1 + X/100)
After a 20% increase, a price is $120. Original = $120 ÷ 1.20 = $100
After a 25% discount, a price is $60. Original = $60 ÷ 0.75 = $80
After a 10% raise, salary is $55,000. Original = $55,000 ÷ 1.10 = $50,000
After a 25% increase, a price is $150. What was the original price?
  1. 1
    Identify the multiplier for a 25% increase: 1 + 25/100 = 1.251 + 0.25 = 1.25
  2. 2
    Set up the equation: Original x 1.25 = $150Original x 1.25 = $150
  3. 3
    Divide the final value by the multiplier: $150 / 1.25$150 / 1.25
  4. 4
    Calculate: $150 / 1.25 = $120= $120
Refs:Math is Fun - Percentage Change

Percentage Change

Percentage Change
Increase: Final = Original × (1 + X/100). Decrease: Final = Original × (1 - X/100)
100 increased by 20% = 100 × 1.20 = 120
80 decreased by 25% = 80 × 0.75 = 60
150 increased by 10% = 150 × 1.10 = 165
A shirt costs $60. It goes on sale for 30% off. What is the sale price?
  1. 1
    Identify this as a percentage decrease: 30% off30% decrease
  2. 2
    Calculate the multiplier for a 30% decrease: 1 - 30/100 = 0.701 - 0.30 = 0.70
  3. 3
    Multiply the original price by the multiplier: $60 x 0.70$60 x 0.70
  4. 4
    Calculate: $60 x 0.70 = $42= $42
Refs:Khan Academy - Percent word problems

Simple Ratio

Simple Ratio
If A:B = m:n and A = x, then B = x × (n/m)
If A:B = 2:3 and A = 10, then B = 10 × (3/2) = 15
If X:Y = 3:4 and Y = 20, then X = 20 × (3/4) = 15
If P:Q = 5:2 and P = 35, then Q = 35 × (2/5) = 14
The ratio of boys to girls in a class is 3:5. If there are 12 boys, how many girls are there?
  1. 1
    Identify the ratio parts: boys = 3, girls = 53:5
  2. 2
    Find the multiplier: 12 boys / 3 parts = 412 / 3 = 4
  3. 3
    Apply the multiplier to find girls: 5 parts x 45 x 4
  4. 4
    Calculate: 5 x 4 = 20 girls= 20
Refs:Khan Academy - Ratio and proportion

Ratio Division

Ratio Division
Total T split in ratio a:b → Part A = T × a/(a+b), Part B = T × b/(a+b)
Split $100 in ratio 3:2 → Shares = 5, each share = $20 → Parts are $60 and $40
Divide 45 items in ratio 4:5 → Shares = 9, each = 5 → Parts are 20 and 25
Split 120 in ratio 1:2:3 → Shares = 6, each = 20 → Parts are 20, 40, and 60
Divide $180 between two people in the ratio 2:7.
  1. 1
    Add the ratio parts to find total shares: 2 + 7 = 92 + 7 = 9 shares
  2. 2
    Find the value of one share: $180 / 9 = $20$180 / 9 = $20
  3. 3
    Calculate the first person's share: 2 x $20 = $402 x $20 = $40
  4. 4
    Calculate the second person's share: 7 x $20 = $1407 x $20 = $140
Refs:Math is Fun - Ratios

Work Rate Problems

Work Rate Problems
Total Work = Workers × Time. If W1 × T1 = W2 × T2, then T2 = (W1 × T1) / W2
4 workers in 12 days = 48 worker-days. 6 workers = 48 ÷ 6 = 8 days
3 machines in 10 hours = 30 machine-hours. 5 machines = 30 ÷ 5 = 6 hours
2 people in 15 days = 30 person-days. 5 people = 30 ÷ 5 = 6 days
5 workers can complete a project in 12 days. How many days would it take 10 workers?
  1. 1
    Calculate total work in worker-days: 5 workers x 12 days = 60 worker-days5 x 12 = 60 worker-days
  2. 2
    The total work stays constant at 60 worker-daysTotal work = 60
  3. 3
    Divide total work by new number of workers: 60 / 10 workers60 / 10
  4. 4
    Calculate: 60 / 10 = 6 days= 6 days
Refs:Khan Academy - Rate problems

Profit Calculation

Profit Calculation
Profit = Selling Price - Cost Price. Profit % = (Profit / Cost) × 100
Buy at $80, sell at $100 → Profit = $20, Margin = 20/80 × 100 = 25%
Cost $50, 40% markup → Selling = $50 × 1.40 = $70, Profit = $20
Sold at $90 with $18 profit → Cost = $90 - $18 = $72
A shop buys an item for $60 and sells it for $75. What is the profit margin percentage?
  1. 1
    Calculate the profit: Selling Price - Cost Price = $75 - $60 = $15$75 - $60 = $15
  2. 2
    Divide profit by cost price: $15 / $60$15 / $60
  3. 3
    Convert to percentage: ($15 / $60) x 100x 100
  4. 4
    Calculate: 0.25 x 100 = 25%= 25%
Refs:Investopedia - Profit Margin

Compound Percentage

Compound Percentage
After changes of X% then Y%: Final = Original × (1 + X/100) × (1 + Y/100)
100 increased by 10% then 20%: 100 × 1.10 × 1.20 = 132 (not 130)
200 up 25% then down 20%: 200 × 1.25 × 0.80 = 200 (back to start)
Price up 50% then down 50%: Not zero! 100 × 1.50 × 0.50 = 75
A price of $200 increases by 20%, then decreases by 10%. What is the final price?
  1. 1
    Calculate the multiplier for 20% increase: 1 + 0.20 = 1.201.20
  2. 2
    Calculate the multiplier for 10% decrease: 1 - 0.10 = 0.900.90
  3. 3
    Apply both multipliers in sequence: $200 x 1.20 x 0.90$200 x 1.20 x 0.90
  4. 4
    Calculate step by step: $200 x 1.20 = $240, then $240 x 0.90 = $216= $216
Refs:Khan Academy - Compound interest

Combined Rates

Combined Rates
Combined Rate = Rate A + Rate B. Time = Total Work / Combined Rate
A makes 4/hr, B makes 6/hr → Together 10/hr → 50 units take 5 hours
Pipe A fills in 6 hrs, B in 3 hrs → Rates: 1/6 + 1/3 = 1/2 → Together: 2 hours
Worker A: 8 items/day, B: 12 items/day → 100 items = 100/20 = 5 days together
Pipe A can fill a tank in 4 hours. Pipe B can fill the same tank in 6 hours. How long to fill the tank using both pipes?
  1. 1
    Calculate Pipe A's rate: 1 tank / 4 hours = 1/4 tank per hourRate A = 1/4
  2. 2
    Calculate Pipe B's rate: 1 tank / 6 hours = 1/6 tank per hourRate B = 1/6
  3. 3
    Add the rates: 1/4 + 1/6 = 3/12 + 2/12 = 5/12 tank per hour1/4 + 1/6 = 5/12
  4. 4
    Calculate time: 1 tank / (5/12 per hour) = 12/5 = 2.4 hours= 2.4 hours
Refs:Math is Fun - Rates