Numerical Reasoning —
Strategy and Key Techniques

Numerical reasoning tests appear in graduate job applications, bank assessments, civil service exams, and university entrance tests. They don't test advanced mathematics — they test your ability to work with numbers accurately and quickly under time pressure. Tour guide covers the techniques that save you time and prevent errors.

Number Sequences — The Pattern-Finding Formula

Always follow three steps for sequence questions:

1. Find the differences between consecutive terms
2. If differences aren't constant, find the differences of the differences
3. Identify the pattern (constant difference = arithmetic; multiplied = geometric; differences increase = quadratic)

Sequence types to recognise instantly:

• Arithmetic: 3, 7, 11, 15 (+4 each time)
• Geometric: 2, 6, 18, 54 (×3 each time)
• Square numbers: 1, 4, 9, 16, 25, 36, 49
• Cube numbers: 1, 8, 27, 64, 125
• Fibonacci: 1, 1, 2, 3, 5, 8, 13, 21 (each term = sum of previous two)
• Increasing differences: 2, 3, 5, 8, 12 (differences: 1, 2, 3, 4)
• Two interleaved sequences: 15, 30, 20, 40, 25, 50 — split into odd positions (15, 20, 25) and even positions (30, 40, 50)

Percentages — The Mental Shortcuts

Stop reaching for a calculator. These shortcuts work faster:

• 10% of any number: Move the decimal point one place left (10% of 240 = 24)
• 5%: Half of 10% (5% of 240 = 12)
• 15%: 10% + 5% (15% of 240 = 24 + 12 = 36)
• 25%: Divide by 4
• 33.33%: Divide by 3
• 20%: Divide by 5 (or double the 10%)
• Percentage increase: (New − Old) ÷ Old × 100
• Finding original before % change: R240 = 80% of original → original = 240 ÷ 0.8 = R300

Data Interpretation — What to Check Before Calculating

Most calculation errors on numerical tests come from misreading the table, not wrong maths. Before calculating:

1. Check the units. Is it thousands? Millions? Per annum? R or $?
2. Read ALL column headers. A common trap is answering the wrong column
3. Identify what type of answer is needed. Percentage? Absolute value? Ratio?
4. Eliminate clearly wrong options first. If the answer should be between 200 and 300, eliminate anything outside that range before calculating

Ratios — The Share Method

When sharing an amount in a ratio: (1) Add all parts. (2) Divide the total by the sum of parts to find one part's value. (3) Multiply each ratio number by one part's value.

Example: Share R450 in ratio 2:3. Parts = 5. Each part = 450÷5 = R90. Shares: R180 and R270.

Common Test Traps — Don't Fall For These

• Successive percentage changes: A 20% increase then 20% decrease does NOT return to the original — it results in a 4% net decrease (multiply: 1.2 × 0.8 = 0.96)
• Percentage points vs percentage change: If a rate goes from 18% to 24%, it increased by 6 percentage points, but by 33% as a percentage change
• Mean vs median: The mean is affected by outliers; the median is not. If data is skewed, they will differ significantly
• Inverse proportion: More workers = fewer days. 5 workers × 10 days = 50 worker-days. 10 workers = 50÷10 = 5 days

The Rule of 72 — Quick Mental Maths

To find how many years it takes an investment to double: divide 72 by the annual growth rate. At 8% annual growth: 72÷8 = 9 years to double. Tour appears regularly in financial reasoning questions.

The four question types you must master

Numerical reasoning tests in South Africa (used by banks, insurance companies, consulting firms, and government) test four main skills: data interpretation (reading tables, charts, and graphs to extract specific values), percentage and ratio calculations (including percentage change, percentage of a whole, and ratio comparisons), currency and unit conversion (particularly relevant for South African financial assessments), and number series completion (identifying the pattern rule and applying it).

Data interpretation: read the labels first

In data interpretation questions, the most common source of error is misreading what the table or chart is actually showing. Before doing any calculation, read the title, the row and column headers, and the units. Candidates who jump straight to the numbers regularly answer the right calculation for the wrong column, or calculate in the wrong units and get an answer that looks plausible but is wrong by a factor of 1,000.

A reliable technique: re-read the question after you have found your candidate answer, and confirm that the answer actually addresses what was asked. Many questions ask for a ratio, not an absolute value. Or they ask for the change, not the final value. Tour single habit of re-reading the question before submitting your answer prevents a significant number of errors.

Calculator strategy

Most South African numerical reasoning tests allow a calculator. Tour changes your strategy: the premium is on speed and accuracy of setup, not mental arithmetic. Invest your time in reading and understanding the question, setting up the correct calculation, and checking your answer makes sense — not in performing arithmetic mentally. If your answer is not a clean number and the question does not involve messy real-world data, reconsider your setup.

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