Mastering GRE Quantitative Comparison: Strategies for Quick Solutions

Understanding the Format

Each QC question presents two quantities, Quantity A and Quantity B, along with a statement or diagram providing information. Your task is to select one of four standard answer choices:

• A) Quantity A is greater.
• B) Quantity B is greater.
• C) The two quantities are equal.
• D) The relationship cannot be determined from the information given.

Choice D is what differentiates QC from most other math problems. It means that even with all provided information, the relationship between the two quantities can vary depending on the values you consider. This possibility makes it essential to test multiple scenarios rather than assuming the first case you find is universal.

These questions sit at the intersection of algebra and geometry mastery and the trap-avoidance skills covered in the GRE Quant traps guide. Both are worth reviewing alongside QC strategy.

Core Strategies for Quick Solutions

The key to mastering QC is thinking flexibly and avoiding the trap of solving for exact values unless absolutely necessary.

1. Simplify Before You Calculate

If you can perform the same mathematical operation on both quantities without changing their relationship, do it. This can make complex expressions much more manageable.

Rules for simplification:

• Add or subtract the same value from both quantities.
• Multiply or divide both quantities by the same positive value.
• Be cautious when multiplying or dividing by a variable of unknown sign, as this can reverse the inequality.

Example:

Given y ≠ 0:

• Quantity A: (3y + 6) / y
• Quantity B: 3 + (6/y)

Rewrite Quantity A as 3y/y + 6/y = 3 + 6/y. Now both quantities are identical.

Answer: C) The two quantities are equal.

2. Plug in Numbers (Especially for Variables)

When quantities involve variables, testing different types of numbers can quickly reveal the relationship or show that it varies.

Types of numbers to test:

• Positive integers (1, 2, 3)
• Negative integers (-1, -2, -3)
• Zero (0)
• Fractions (1/2, -1/2)
• Large numbers (100, 1000)

If you find A > B with one set and B > A with another, the answer is almost certainly D.

Example:

Given x is an integer.

• Quantity A: x²
• Quantity B: x

Test x = 2: A (4) > B (2). Test x = 0: A (0) = B (0). Test x = -2: A (4) > B (-2). Test x = 1: A (1) = B (1).

Since A > B and A = B both occur, the relationship is not fixed.

Answer: D) The relationship cannot be determined from the information given.

3. Estimate When Exact Calculation Is Unnecessary

Sometimes, precise calculations are not required. A quick estimate reveals which quantity is larger, saving time for harder problems.

Example:

• Quantity A: √80
• Quantity B: 9

Since 9² = 81 and 80 is just below 81, √80 is just below 9.

Answer: B) Quantity B is greater.

4. Analyze Constraints Carefully

Always pay close attention to conditions given in the problem such as x > 0, y is an integer, or triangle inequalities. These constraints often narrow the range of values a variable can take, sometimes making the comparison immediately clear.

Example:

Given x < 0:

• Quantity A: x³
• Quantity B: x²

A negative number cubed is negative. A negative number squared is positive. A negative number is always less than a positive number.

Answer: B) Quantity B is greater.

5. Know When "Cannot Be Determined" Is the Answer

D is not a guess or a fallback. It's the correct answer when:

• The problem gives insufficient information.
• Variables have no sufficient constraints, so plugging in different types of numbers changes the relationship.
• You find one case where A > B and another where B > A or A = B.

Don't shy away from choosing D when your analysis shows genuine variability.

6. Avoid Unnecessary Calculations

Your only job in a QC question is to compare, not to solve. Look for opportunities to compare fractions by cross-multiplication, or compare expressions without fully simplifying them if you can deduce relative sizes by other means.

Example:

• Quantity A: 1/7 + 1/8
• Quantity B: 1/3

Estimate: 1/7 ≈ 0.14 and 1/8 ≈ 0.125. Sum ≈ 0.265. And 1/3 ≈ 0.333. Estimating suggests B is greater. For confirmation: 1/7 + 1/8 = 15/56. Cross-multiply with 1/3: 15 × 3 = 45 vs. 56 × 1 = 56. Since 45 < 56, 15/56 < 1/3.

Answer: B) Quantity B is greater.

Common Pitfalls to Avoid

• Assuming variables are positive integers. Always consider negative numbers, zero, and fractions unless explicitly stated otherwise.
• Dividing by a variable of unknown sign. This can reverse the inequality or cause a division-by-zero error.
• Over-relying on one strategy. Different problems suit different approaches. Be flexible.
• Testing only one scenario. Always test at least two different types of numbers when variables are involved.

Practice and Application

The best way to master QC is through consistent, varied practice. The more you expose yourself to different problem types and apply these strategies, the more intuitive they become. The GRE Quantitative Reasoning prep app offers a focused QC practice bank with worked solutions, which is particularly useful for building the pattern recognition that makes these questions fast to solve.

By applying simplification, number-plugging, estimation, constraint analysis, and recognizing when D is appropriate, you can work through QC questions with speed and accuracy.