GRE Quant: Must Be and Can Be Questions

Must-be and can-be quant questions on the GRE ask you to judge what always holds true and what may hold true based on the information provided. The primary emphasis stays on logical certainty, supported by careful calculations wherever needed. You examine conditions closely, track how values behave across valid cases, and decide whether a statement holds in every situation or only in some. This question type builds clarity in logical reasoning, strengthens your command over constraints, and sharpens your ability to separate guaranteed outcomes from possible ones with precision and care.

As part of our GRE preparation course, the following video presents a clear and efficient framework for solving must-be and can-be quant questions. You learn a structured, step-by-step method that helps you read conditions accurately, test cases thoughtfully, and recognize the patterns these questions rely on. The lesson then applies the approach to multiple GRE-style problems with realistic and thoughtfully designed answer choices, helping you see exactly how to apply the method in practice.

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Approach for GRE “Must be…” and “Can be…” Questions

“Must be…” and “Can be…” questions on GRE Quant

When tackling logical reasoning or data sufficiency problems, the strategy changes based on whether the question asks what must be true versus what could be true.

“Must be…” Questions

The goal here is to find a counterexample. You are actively looking for a “No.”

If you can find even one scenario where the statement is false (a “No”), you can immediately eliminate that answer choice.
If you exhaust your options and find that you absolutely cannot get a “No,” then the statement is always true, and you must select that answer choice.

“Can be…” Questions

The goal here is to find a single working example. You are actively looking for a “Yes.”

If you find one scenario where the statement works (a “Yes”), that is sufficient to select the answer choice.
If you try various scenarios and cannot get a “Yes” to occur, the statement is impossible, and you must eliminate that answer choice.

This method creates a decisive flow for your analysis and builds confidence in every decision you make. Duly understand this approach and apply it in your GRE drills, GRE sectional mocks, and GRE full mocks.

Worked Examples

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

Following is a step-wise written explanation:

Both questions start by solving the quadratic equation:

x² – 5x + 6 = 0

Factoring the quadratic: (x – 2)(x – 3) = 0

The possible values for x are 2 and 3.

Question 1: If x² – 5x + 6 = 0, x must be…

The Approach: Try to get a “No” to eliminate choices. If you can’t get a “No,” that’s your answer.

Odd
- Can I get a “No”? Yes. If x = 2, it is not odd. Eliminate.
Even
- Can I get a “No”? Yes. If x = 3, it is not even. Eliminate.
Prime
- Can I get a “No”? Let’s check our values: 2 is prime, and 3 is prime. I cannot find a value for x that results in a “No.”