Quantitative Reasoning and Numerical Problem Solving
What you must understand
Quantitative questions test arithmetic fluency, ratio and proportion, percentages, averages, rates, and basic algebra, usually set in word problems. You must convert text into equations, work with fractions, decimals and percentages interchangeably, handle unit conversions, and interpret simple tables and graphs. Estimation and checking reasonableness matter as much as exact calculation.
Traps to watch
- Percentage change vs percentage points: a rise from 20% to 25% is 5 percentage points but a 25% relative increase.
- Percent of what? Always identify the base; successive percentage changes do not simply add.
- Average vs total: you often need the total (average × count) to solve.
- Rate units: keep time and distance units consistent before dividing.
- Misreading the question: it may ask for the remainder, the difference, or the original value, not the obvious number.
Rule of thumb and worked example
Write the formula first, substitute, then estimate to sanity-check. For percentage change use change ÷ original × 100.
Example: A shirt costs $80 after a 20% discount. What was the original price? A common error is adding 20% of 80 ($16) to get $96. Instead, the discounted price is 80% of the original: original = 80 ÷ 0.8 = $100. Checking: 20% of 100 is 20, and 100 − 20 = 80. ✓
For averages, remember total = average × number of items; this unlocks most "new average" problems.