ISEE Quantitative Reasoning: Comparisons and Word Problems
What the section tests
Quantitative Reasoning (Upper and Middle Levels: 37 questions in 35 minutes) is not a computation test. It mixes quantitative comparison items with multi-step word problems and measures number sense, estimation, and reasoning. No calculator is permitted.
Core rules
- In a quantitative comparison you see Column A and Column B and four fixed answers: (A) if Column A is greater, (B) if Column B is greater, (C) if the two are equal, (D) if the relationship cannot be determined from the information given.
- D is a real answer, not a surrender. If a variable could be positive, negative, zero, or a fraction and the comparison changes accordingly, the answer is D. Test those values deliberately.
- Compare, don’t calculate. If both columns share a term, cancel it. If both sides are positive you may square them, but multiplying or dividing by a negative number reverses the comparison.
- Diagrams are not drawn to scale unless the problem says so.
Worked example
Column A: (0.4)² Column B: 0.4 Many candidates assume squaring always makes a number bigger and answer A. Here 0.4 lies between 0 and 1, so squaring shrinks it: (0.4)² = 0.16, and 0.16 < 0.4. The answer is B. The rule worth memorizing: for any number strictly between 0 and 1, the square is smaller than the number; for any number greater than 1, the square is larger.
Traps that cost marks
- Assuming variables stand for positive integers; fractions and negatives break most such assumptions.
- Choosing D whenever the algebra looks hard, or refusing D when a value is genuinely unconstrained.
- Doing full long division when rounding would settle the comparison.
- Answering the sub-question you solved rather than the one asked.