Quantitative Reasoning: Comparisons and Word Problems
What Quantitative Reasoning tests
The ISEE Middle Level Quantitative Reasoning section has 37 questions in 35 minutes. It tests mathematical thinking through word problems and quantitative comparisons. Calculators are not permitted, so estimation and number properties matter more than long computation.
Quantitative comparisons
Each question gives Column A and Column B with four choices: A if Column A is greater, B if Column B is greater, C if they are equal, D if the relationship cannot be determined. Simplify both columns using the same operation when the quantities are positive. Test special values-0, 1, a fraction between 0 and 1, and a negative number-before choosing D. If one set of values gives A > B and another gives A < B, the answer is D.
Word problems
Translate the sentence into an equation or a list of steps. Identify exactly what is asked, because the last number calculated is not always the answer. Backsolving from answer choices can turn a confusing algebra problem into arithmetic.
Worked example
Given x > 0, compare Column A: x² and Column B: x. Try x = 1/2: x² = 1/4, which is less than 1/2, so Column B is greater. Try x = 2: x² = 4, which is greater than 2, so Column A is greater. Both values satisfy x > 0, and the comparison changes, so the answer is D.
Traps
- Assuming a variable is an integer or positive when the problem does not say so.
- Multiplying or dividing an inequality by a negative without flipping the sign.
- Choosing D simply because the problem looks hard; D requires evidence that more than one relationship is possible.
- Computing exact values when comparing simplified expressions is faster.