Quantitative Reasoning: Compare First, Calculate Second
What this section tests
Quantitative Reasoning asks you to reason about numbers, not grind through arithmetic. At the Middle and Upper levels it is about 37 questions in 35 minutes with no calculator, so speed comes from choosing the right method. Roughly half the section is quantitative comparisons; the rest is multi-step word problems, number properties, and logic-style questions.
Core rules
- Every quantitative comparison uses the same four choices: Quantity A is greater, Quantity B is greater, the two are equal, or the relationship cannot be determined.
- Compare before you calculate. If both quantities share a term, cancel it; if both are positive, squaring or taking a square root preserves the order - but only under the stated conditions.
- When a variable's value is not fixed, test cases: a positive number, a negative number, a fraction between 0 and 1, and zero. If two cases disagree, the answer is "cannot be determined."
- In word problems, translate one phrase at a time and keep units attached. Backsolving from the answer choices is often faster than algebra.
Worked example
x is a real number and 0 < x < 1. Quantity A is x²; Quantity B is x.
Because x is positive and less than 1, multiplying by x makes a number smaller: x² = x · x < x · 1 = x. Testing x = 0.5 gives 0.25 versus 0.5, so Quantity B is greater for every value in the range.
Traps
- Importing a familiar rule without its conditions: x² > x holds for x > 1 and for x < 0, but not here.
- Treating a percent decrease as reversible by the same percent: a $40 price after 20% off means the original was $50, not $48.
- Reaching for "cannot be determined" when the quantities are always equal, or when a hidden constraint such as "positive integer" fixes the case.