GRE Quant: Quantitative Comparison (QC) Strategy

Quantitative Comparison questions on the GRE present two quantities, Quantity A and Quantity B, and ask you to compare their values using one of four fixed answer choices. The setup feels simple, but the real skill sits in how you reason with limited information. These questions stay unique because you do not compute a single final number as the goal. You evaluate relationships, test hidden cases, and notice when the comparison changes under different valid values. They test quantitative reasoning, algebraic sense, number properties, estimation, and disciplined decision-making under time pressure.

A part of our GRE Prep course, the following video shares a sound and efficient approach for solving Quantitative Comparison questions on the GRE. You learn a simple, organized, and methodical way to work through QC questions, see the layers in each prompt, and navigate the commonly tested traps in this engaging question type. The lesson then demonstrates the approach across multiple GRE-style problems with realistic, trappy answer choices that reflect frequently tested traps, so you learn how to apply the approach correctly and handle those traps first-hand. Take your time with this important lesson and carry the methodology and learnings into your GRE practice drills, GRE sectional mocks, and GRE full mocks.

 

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Overview of Quantitative Comparison Questions on GRE

Quantitative Comparison Overview

Quantitative Comparison (QC) is a specific question format rather than a unique mathematical subject. It presents a different way of framing problems and seeking answers compared to standard multiple-choice questions.

Importance and Frequency

On the GRE, approximately 33% of the Quantitative Reasoning section consists of QC questions.

Core Strategy

The primary key to mastering these problems is to consider all possibilities and maintain a critical mindset.

• Consistency is Essential: A relationship between the two quantities must hold true in every possible scenario for an answer choice to be correct.
• The Four Standard Answer Options:
  • (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.

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Strategy for Solving Quantitative Comparison Questions on GRE

To master Quantitative Comparison (QC) problems, you must adopt a mindset of “proving the problem wrong” before settling on a definitive relationship. Here is the academic breakdown of the methodology:

Core Principles

• Exhaust All Possibilities: Never assume variables are restricted to positive integers. You must account for all number types, including negatives, fractions, decimals, zero, and extremely large or small values.
• Requirement of Consistency: For an answer choice to be correct (specifically A, B, or C), the relationship between the two quantities must hold true in every single possible case.

The Strategic Workflow

• Target Choice D First: The most effective way to approach these problems is to attempt to prove that the relationship is not consistent. This we call “aiming for Choice D.”
• Search for Contradictions: Your goal is to find one scenario where Quantity 1 is greater, and another scenario where Quantity 2 is greater (or they are equal).
• Identify Unique Answers: If you have tested a wide range of diverse numbers and find it impossible to create a contradiction, you can conclude that there is a unique, fixed relationship. Only then should you select Choice A, B, or C.

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GRE-style Practice Question 1

Correct Answer: D

The relationship cannot be determined from the information given.

 

For a detailed explanation of this question, please refer to the video presented earlier on this page.

 

Following is a step-wise written explanation:

For GRE quantitative comparison questions, our approach is to aim for answer choice D by testing for contradictory outcomes. If no contradictions appear, the relationship is unique and the correct answer falls under A, B, or C.

 

Question

ABC is a right triangle with AB = 12 and BC = 5.

Quantity A                   Quantity B

AC                                   13

1. Quantity A is greater.
2. Quantity B is greater.
3. The two quantities are equal.
4. The relationship cannot be determined from the information given.

 

Explanation

Case 1: Side AC is the Hypotenuse

If AB and BC are the legs, we use the Pythagorean theorem to find the longest side.

(12)² + (5)² = (AC)²

144 + 25 = 169

The square root of 169 is 13.

In this case, AC is 13.

Result: Quantity A is equal to Quantity B.

Case 2: Side AB is the Hypotenuse

The problem does not state which side is the hypotenuse. If AB is the hypotenuse, it must be the longest side.

(AC)² + (5)² = (12)²

(AC)² + 25 = 144

(AC)² = 119

The square root of 119 is approximately 10.9.

In this case, AC is less than 13.

Result: Quantity B is greater than Quantity A.

Conclusion

We followed the approach to aim for Choice D by finding contradictory answers.

In Case 1, the quantities are equal.

In Case 2, Quantity B is greater.

Because we succeed in getting contradictory answers, the relationship cannot be determined.

 

Final Answer: D

The relationship cannot be determined from the information given.

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GRE-style Practice Question 2

Correct Answer: D

The relationship cannot be determined from the information given.

 

For a detailed explanation of this question, please refer to the video presented earlier on this page.

 

Following is a step-wise written explanation:

For GRE quantitative comparison questions, our approach is to aim for answer choice D by testing for contradictory outcomes. If no contradictions appear, the relationship is unique and the correct answer falls under A, B, or C.

 

Question

m > 0.

Quantity A               Quantity B

      m²                            √m

1. Quantity A is greater.
2. Quantity B is greater.
3. The two quantities are equal.
4. The relationship cannot be determined from the information given.

 

Explanation

Case 1: Let m be a large number

If m is 4, we calculate both quantities.

Quantity A: (4)² = 16

Quantity B: √4 = 2

In this case, 16 is greater than 2.

Result: Quantity A is greater than Quantity B.

Case 2: Let m be a fraction between 0 and 1

If m is 0.25, we calculate both quantities.

Quantity A: (0.25)² = 0.0625

Quantity B: √0.25 = 0.5

In this case, 0.5 is greater than 0.0625.

Result: Quantity B is greater than Quantity A.

Conclusion

We followed the approach to aim for Choice D by finding contradictory answers.

In Case 1, Quantity A is greater.

In Case 2, Quantity B is greater.

Because we succeed in getting contradictory answers, the relationship cannot be determined.

 

Final Answer: D

The relationship cannot be determined from the information given.

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