Quantitative Reasoning: Comparisons and Word Problems
What the section tests
The ISEE Upper Level Quantitative Reasoning section has 37 questions in 35 minutes. It emphasizes mathematical reasoning rather than heavy computation. Expect quantitative comparison items and word problems drawn from arithmetic, algebra, geometry, and data analysis. Calculators are not permitted.
Core rules
- Quantitative comparison asks you to compare Quantity A and Quantity B. The choices are fixed: A is greater, B is greater, the two are equal, or the relationship cannot be determined.
- Do only enough computation to establish the comparison. Simplify both quantities, use properties, or test numbers.
- When testing numbers, include zero, fractions between 0 and 1, and negatives if the variable is not restricted.
- For word problems, identify the unknown, translate one relationship at a time, and track units.
- For geometry, use formulas confidently and do not assume a figure is to scale unless stated.
Worked example
x is a negative integer. Quantity A = x squared. Quantity B = x cubed. Because x is negative, x squared is positive and x cubed is negative. A positive number is greater than a negative number, so Quantity A is greater. Answer: A. Testing x = -2 gives A = 4 and B = -8, which confirms the comparison.
Traps that cost marks
Testing only positive integers can make a variable relationship look fixed when it is not. In percent problems, distinguish percent of from percent greater than. In quantitative comparison, do not pick equal just because both quantities simplify to expressions with the same variable. Also check units and avoid rounding too early.