ISEE Quantitative Reasoning Strategies
Master the unique quantitative comparison and word problem formats on the ISEE with systematic approaches and proven techniques.
ISEE Quantitative Reasoning Strategies
The ISEE Quantitative Reasoning section is unique among standardized tests. Unlike traditional math sections, it emphasizes logical thinking, number sense, and problem-solving strategies over memorized formulas. With 37 questions in 35 minutes, time management and smart strategies are just as important as math skills.
Section Overview
| Aspect | Details |
|---|---|
| Questions | 37 questions total |
| Time | 35 minutes (~56 seconds per question) |
| Format | Word problems (~20) + Quantitative Comparisons (~17) |
| Calculator | NOT allowed |
| Guessing Penalty | NONE (always guess!) |
The Two Question Types
Type 1: Word Problems (Standard Multiple Choice)
These look like traditional math questions with 4 answer choices (A, B, C, D).
Example:
If 3x + 5 = 20, what is the value of x?
A) 3
B) 5
C) 7
D) 15
Solution:
3x + 5 = 20
3x = 15
x = 5
Answer: B
Type 2: Quantitative Comparisons (The ISEE Special)
This unique format presents two quantities (Column A and Column B) and asks you to compare them.
Standard Answer Choices (ALWAYS the same):
- A) The quantity in Column A is greater
- B) The quantity in Column B is greater
- C) The two quantities are equal
- D) The relationship cannot be determined from the information given
Example 1:
| Column A 5 + 7 × 2 |
Column B (5 + 7) × 2 |
Solution:
Column A: 5 + 14 = 19 (remember order of operations!)
Column B: 12 × 2 = 24
Answer: B (Column B is greater)
Quantitative Comparison Strategies
Strategy 1: Don't Calculate—Compare!
The goal is NOT to find exact values. You only need to determine which is GREATER.
Example:
| Column A 0.125 × 16 |
Column B 0.25 × 8 |
❌ Slow Method:
Calculate both: 0.125 × 16 = 2, and 0.25 × 8 = 2
✅ Fast Method:
Notice: 0.125 = 1/8, so 0.125 × 16 = 16/8 = 2
Notice: 0.25 = 1/4, so 0.25 × 8 = 8/4 = 2
OR even faster: both equal 2 (you can see 16/8 = 8/4 without calculating)
Answer: C (Equal)
Strategy 2: Plug In Numbers for Variables
When you see variables, test specific values to compare.
Example:
n is a positive integer
| Column A n² |
Column B 2n |
Test values:
- If n = 1: Column A = 1, Column B = 2 → B is greater
- If n = 2: Column A = 4, Column B = 4 → Equal
- If n = 3: Column A = 9, Column B = 6 → A is greater
Since the relationship changes depending on n...
Answer: D (Cannot be determined)
Pro Tip:
If you find even ONE case where A > B and ONE case where B > A, the answer is ALWAYS D. Stop testing more numbers!
Strategy 3: Simplify Both Sides Equally
You can add, subtract, multiply, or divide both columns by the same number (just like solving equations).
Example:
| Column A 5x + 10 |
Column B 5x + 7 |
Solution:
Subtract 5x from both sides:
Column A: 10
Column B: 7
Answer: A (10 > 7, so Column A is always greater)
Strategy 4: Watch Out for "Cannot Be Determined" (Choice D)
Choose D when:
- The relationship depends on unknown variables
- You can create scenarios where A > B AND scenarios where B > A
- Not enough information is given
Common Mistake:
Students often forget about Choice D! About 20-25% of quantitative comparison questions have D as the correct answer. Don't assume there's always a definitive relationship.
Content Areas Tested
| Topic | Approx. % | Key Concepts |
|---|---|---|
| Number Operations | ~30% | Fractions, decimals, percentages, ratios, proportions |
| Algebra & Patterns | ~25% | Solving equations, inequalities, patterns, functions |
| Geometry | ~20% | Area, perimeter, angles, volume, coordinate plane |
| Word Problems | ~15% | Age problems, rate/time/distance, work problems |
| Data & Probability | ~10% | Mean/median/mode, charts/graphs, basic probability |
High-Yield Problem Types
Problem Type 1: Fraction & Decimal Conversions
Example:
| Column A 3/8 |
Column B 0.4 |
Quick Method:
Convert 3/8 to decimal: 3 ÷ 8 = 0.375
Compare: 0.375 vs. 0.4
Answer: B (0.4 > 0.375)
OR convert both to fractions:
0.4 = 4/10 = 2/5
Compare 3/8 vs. 2/5: Cross multiply: 3×5 = 15, 2×8 = 16
Since 16 > 15, then 2/5 > 3/8
Problem Type 2: Percent Increase/Decrease
Example:
| Column A 50 increased by 20% |
Column B 60 decreased by 10% |
Solution:
Column A: 50 × 1.20 = 60
Column B: 60 × 0.90 = 54
Answer: A
Problem Type 3: Geometric Comparisons
Example:
Square ABCD has side length 4. Rectangle EFGH has length 8 and width 2.
| Column A Perimeter of square ABCD |
Column B Perimeter of rectangle EFGH |
Solution:
Column A: 4 × 4 = 16
Column B: 2(8 + 2) = 2(10) = 20
Answer: B
Time Management Strategies
The 3-Pass System
Pass 1 (12 minutes): Easy questions
- Do all questions you can solve in under 30 seconds
- Quantitative comparisons are often faster—do these first
- Goal: Complete 15-20 questions
Pass 2 (15 minutes): Medium questions
- Tackle word problems that require more thought
- Use estimation and elimination strategies
- Goal: Complete 12-15 more questions
Pass 3 (8 minutes): Hard questions + guess remaining
- Give difficult questions your best effort
- With 2 minutes left, guess on ALL remaining questions
- Remember: NO GUESSING PENALTY!
Common Traps to Avoid
Trap #1: Forgetting Order of Operations
Wrong: 5 + 3 × 2 = 16 (if you add first)
Right: 5 + 3 × 2 = 5 + 6 = 11 (multiply first!)
Trap #2: Assuming Figures Are Drawn to Scale
ISEE explicitly states figures are NOT necessarily drawn to scale. Don't eyeball—calculate!
Trap #3: Only Testing Positive Integers for Variables
Also try: 0, negative numbers, fractions. These often reveal answer D (cannot determine).
Trap #4: Over-Calculating Quantitative Comparisons
Remember: You DON'T need exact values, just which is BIGGER. Look for shortcuts!
Practice Problem Set
Problem 1:
| Column A 7/12 |
Column B 5/9 |
Answer: A (7/12 ≈ 0.583, 5/9 ≈ 0.556)
Problem 2:
x > 0
| Column A x² |
Column B x³ |
Answer: D (If 0 < x < 1, then x² > x³. If x > 1, then x³ > x². Cannot determine.)
Problem 3:
What is 15% of 80?
A) 10
B) 12
C) 15
D) 18
Answer: B (0.15 × 80 = 12)
Success Story:
"Quantitative comparisons scared me at first. But once I learned to COMPARE instead of CALCULATE, everything clicked. I saved so much time by simplifying both sides or testing just one value to prove answer D. My quantitative reasoning score jumped from 60th percentile to 92nd percentile in two months!"
— Ryan M., Admitted to Lawrenceville School
Remember: ISEE Quantitative Reasoning rewards strategic thinking over brute-force calculation. Master the quantitative comparison format, develop number sense, and always remember—there's no penalty for guessing, so NEVER leave a question blank!
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