Quantitative Reasoning Basics
Quantitative reasoning is the ability to understand, interpret and work with numerical information. It underpins numerical reasoning tests used in recruitment. Here are the core concepts to master.
Core Skills
Arithmetic – Addition, subtraction, multiplication, division. Work confidently with whole numbers, decimals and fractions. Know order of operations (BODMAS/PEMDAS).
Percentages – X% of Y = (X ÷ 100) × Y. Percentage change = ((New − Old) ÷ Old) × 100. Percentage increase: add to 100% (e.g. +20% = × 1.20).
Ratios and proportions – If A : B = 2 : 3, then A = (2/5) of total, B = (3/5) of total. Cross-multiply to solve: A/B = C/D implies A×D = B×C.
Averages – Mean = Sum ÷ Count. For weighted average: (Value1×Weight1 + Value2×Weight2) ÷ (Weight1 + Weight2).
Rates – Speed = Distance ÷ Time. Work rate = Output ÷ Time. Unit cost = Total cost ÷ Quantity.
Data Interpretation
Reading tables – Check row and column headers. Note units. Identify the cell you need before calculating.
Reading charts – Bar charts: compare heights. Line graphs: trends over time. Pie charts: proportions (slice ÷ whole × 100).
Extracting values – Get the right number from the right place. Don't confuse similar-looking rows or columns.
Problem-Solving Approach
- Understand the question – What is being asked? What is the target?
- Identify the data – What information do you have? Where is it?
- Choose the method – Which formula or operation applies?
- Calculate – Work step by step. Use estimation to check.
- Verify – Does the answer make sense? Is it in the right units?
Common Pitfalls
- Wrong units – Mixing £000 and £m, or per unit vs total. Convert before combining.
- Wrong base – For percentage change, the base is always the original (old) value.
- Rushing – Misreading the question or grabbing the wrong data. Read carefully.
Practice with numerical reasoning questions and the numerical reasoning test.
Frequently Asked Questions
Do I need to memorise formulas?
The core ones (percentage change, averages, ratios) are worth knowing by heart. For others, understand the logic so you can derive them. Practice helps retention.
How do I improve speed?
Practice under timed conditions. Learn shortcuts (e.g. 10% of X = X ÷ 10). Use estimation and elimination when options are far apart. Avoid unnecessary steps.
What if I'm not good at mental math?
Many tests allow a calculator. Use it for complex calculations. Focus on setting up the problem correctly—that's often where errors occur. Practice with the same calculator you'll use in the test.