Quantitative Reasoning Advanced
Advanced quantitative reasoning extends the basics to more complex scenarios. You'll see compound growth, weighted averages, multi-step problems and combined data sources. Here's how to handle them.
Compound Growth
When growth happens over multiple periods, don't add percentages. Compound growth = (1 + r)^n − 1, where r is the rate per period and n is the number of periods.
Example: 10% growth for 3 years. Total growth = (1.10)³ − 1 = 1.331 − 1 = 33.1%, not 30%.
To find value after growth: Final = Initial × (1 + r)^n.
Weighted Averages
When values have different "weights" (e.g. different quantities or importance):
Weighted average = (V1×W1 + V2×W2 + … + Vn×Wn) ÷ (W1 + W2 + … + Wn)
Example: Test 1 (weight 2): 80%. Test 2 (weight 3): 70%. Weighted average = (80×2 + 70×3) ÷ (2+3) = (160+210) ÷ 5 = 74%.
Multi-Step Problems
Break the problem into steps. Example: "If revenue grows 5% and costs fall 3%, what happens to profit margin?"
- New revenue = Old revenue × 1.05
- New costs = Old costs × 0.97
- New profit = New revenue − New costs
- New margin = New profit ÷ New revenue × 100
Work with variables (R, C) if numbers aren't given. Often the answer simplifies (e.g. percentage change doesn't depend on absolute values if proportions are fixed).
Combined Data
When combining data from multiple sources, ensure:
- Same units (convert £000 to £m if needed)
- Same time period
- Same scope (e.g. same product, same region)
Strategy
Identify the structure – Is it compound growth? Weighted average? Multi-step?
Use variables – If the question uses "revenue" and "costs" without numbers, work symbolically. The answer may be a formula or a percentage that doesn't depend on the actual values.
Check for shortcuts – Sometimes the problem simplifies. E.g. "If A doubles and B triples, what happens to A/B?" → New ratio = 2A/3B = (2/3) × (A/B). The ratio changes by factor 2/3.
Practice with numerical reasoning questions and the numerical reasoning test.
Frequently Asked Questions
When do I use simple vs compound growth?
Simple growth: add the same amount each period (linear). Compound growth: multiply by (1+r) each period (exponential). Most "growth rate" questions in business contexts mean compound. If the question says "10% per year for 3 years", it's usually compound.
How do I calculate weighted average when weights are percentages?
Treat percentages as weights. E.g. Product A is 60% of sales at 20% margin, B is 40% at 10% margin. Blended margin = 0.6×20 + 0.4×10 = 12 + 4 = 16%. (Weights sum to 1, so no division needed.)
What if the problem has too many unknowns?
Look for relationships. Sometimes you can express one variable in terms of another. Or the question might give you a ratio that lets you assume values (e.g. "revenue is twice costs" → assume costs = 1, revenue = 2).