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.
Combined Data
When combining data from multiple sources, ensure same units, time period and scope.
Strategy
Identify the structure – Is it compound growth? Weighted average? Multi-step?
Use variables – Work symbolically when numbers aren't given. The answer may not depend on actual values.
Check for shortcuts – Sometimes the problem simplifies.
Practice with numerical reasoning questions and the numerical reasoning test.
Frequently Asked Questions
When do I use simple vs compound growth?
Simple: add the same amount each period. Compound: multiply by (1+r) each period. Most business "growth rate" questions mean compound.
How do I calculate weighted average when weights are percentages?
Treat percentages as weights. E.g. A is 60% at 20% margin, B is 40% at 10%. Blended margin = 0.6×20 + 0.4×10 = 16%.
What if the problem has too many unknowns?
Look for relationships. Express one variable in terms of another. Or assume values from a given ratio.