Number and Quantity
What you must understand
This domain tests fluency with real and complex numbers, ratios and proportional reasoning, percentages, units, and the rules of exponents and radicals. You should be able to move confidently between fractions, decimals, and percents; simplify radical and rational expressions; apply scientific notation; and reason about magnitude and precision. Vector quantities and complex numbers appear at this level too, so know how to add, subtract, multiply, and interpret them geometrically.
Traps that appear in questions
- Percent change direction. A 20% increase followed by a 20% decrease does not return to the original value. Multiply by 1.20 then 0.80 to get 0.96, a 4% net loss.
- Unit mismatch. Questions deliberately mix minutes and hours or grams and kilograms. Convert before computing.
- Absolute vs relative change. "Increased by 5" differs from "increased by 5%."
- Sign errors with exponents. Remember that a negative exponent means reciprocal, not a negative result.
- Rationalizing denominators when the answer choices are in simplified radical form.
Worked example
A jacket costs $80. Its price rises 25%, then falls 20%. Final price? Multiply: 80 × 1.25 = 100; 100 × 0.80 = 80. The price returns to $80 because the multipliers 1.25 × 0.80 = 1.00. Rule of thumb: chain percent changes by multiplying factors, never by adding percents.
Precision and estimation
Pay attention to significant figures and reasonable-magnitude checks. If a computed answer implies a person running 500 miles per hour, the arithmetic or unit conversion is wrong.