Numerical reasoning: free guide and practice

Numerical reasoning means using figures and evidence to reach a conclusion. Learn a repeatable method, then practise with original workplace questions.

What numerical reasoning questions test

These exercises test whether you can select the right figures, identify the relevant calculation and interpret the result. Arithmetic alone is not enough: a correct calculation using the wrong denominator still gives the wrong answer.

This guide is for graduate applicants and job seekers, including readers in the UK, US, Canada, Australia, New Zealand and Ireland. Each question supplies its own currency, assumptions and figures.

A five-step solving method

  1. Read what is requested before calculating: a total, difference, percentage, rate or ratio.
  2. Identify the necessary figures and ignore unrelated information.
  3. Write the calculation and keep track of units. Convert hours to minutes or dollars to pounds when required.
  4. Estimate the answer so you can spot an incorrect decimal place.
  5. Calculate, compare the options and check that the result answers the question asked.

Useful calculations

Three worked examples

  1. 1. A UK service team handled 1,200 tickets in April and 1,380 in May. What was the percentage increase?
    1. 12%
    2. 15%
    3. 18%
    4. 20%

    Reference: q-566e2fb1-101 · Report this question

    Show answer and solution

    Answer: B. 15%

    (1,380 − 1,200) / 1,200 × 100 = 15%. Use April, the original value, as the denominator.
  2. 2. A Canadian retailer lists a monitor at C$240 before tax. A 15% discount applies before 5% sales tax. What is the final price?
    1. C$204.00
    2. C$214.20
    3. C$216.00
    4. C$228.00

    Reference: q-a197f013-126 · Report this question

    Show answer and solution

    Answer: B. C$214.20

    Discounted price = 240 × 0.85 = C$204. Tax-inclusive price = 204 × 1.05 = C$214.20. The percentages apply sequentially to different bases.
  3. 3. An Australian warehouse dispatches 540 parcels in 6 hours using 3 equally productive packing lines. At the same rate, how many parcels can 4 lines dispatch in 5 hours?
    1. 450
    2. 600
    3. 648
    4. 720

    Reference: q-18a386fb-168 · Report this question

    Show answer and solution

    Answer: B. 600

    Each line processes 540 / (6 × 3) = 30 parcels per hour. Four lines in five hours process 30 × 4 × 5 = 600 parcels.

Common mistakes and how to avoid them

Use the original value for percentage change. Distinguish margin from markup. Apply successive percentage changes using multipliers. When combining teams, use a weighted average rather than averaging their averages. Check whether tax applies before or after a discount in the question's stated rules.

Calculator and timing

Calculator permission and timing vary by assessment. Check your invitation rather than assuming our practice settings match your test. Begin untimed; when your calculations are reliable, try the 18-minute challenge for our 12 questions. Review the reasoning after every mistake.

Free practice with explanations

Try the 12-question numerical reasoning practice set

Build the underlying skills

Scope and sources

Our practice questions are independently written and are not official assessment items. A score here is a study aid, not a validated prediction of hiring outcomes. For provider-specific instructions, use your invitation and the provider's official candidate help. SHL's candidate practice guidance describes its own practice materials; APTITUDE TESTER is not affiliated with SHL or any employer.