Multiple-Choice (One or More Answers)

What Is Multiple-Choice (One or More Answers)?

Select every option satisfying the stated conditions. Unless the question specifies how many to choose, the correct set can contain one or several options. Each option must be checked independently.

Detail	Study reference
Exam	GRE General Test
Response	Select all correct options
Timing	Shared Quantitative section timer
Primary skill	Quantifiers and exhaustive checking

How It Is Scored

The complete correct selection is required. An extra incorrect option or a missing correct one makes the response incorrect. Finding one acceptable answer does not finish the task.

Official Video

ETS introduces the skills assessed across the GRE. This is a general exam overview; use the worked examples below for this task.

Explore ETS preparation videos for Verbal Reasoning, Quantitative Reasoning and Analytical Writing.

Technical Foundations

Quantifiers

Could be true asks for at least one valid example. Must be true requires all permitted cases. Cannot be true requires impossibility. Convert the wording into the appropriate proof or counterexample task.

Integer constraints

Divisibility, parity and prime factorization can reduce a long list of cases. If n is a multiple of 6, it is even and divisible by 3; that does not mean it is divisible by 12.

Solution sets

When solving inequalities, preserve restrictions from denominators and radicals. Squaring both sides can introduce extraneous solutions. Test candidate values in the original expression.

Step-by-Step Approach

Step	Action and purpose
1	Underline whether the question asks could, must or cannot.
2	Derive the solution set or a decisive condition.
3	Mark each option as valid or invalid with a reason.
4	Check the complete set, including options you initially skipped.

Worked Examples

These are original teaching examples, not official ETS questions. Suggested practice timings are study targets, not extra test time.

Example 1

Select all integers x such that x² < 10. Options: −4, −3, 0, 3, 4.

Explanation / model: Select −3, 0 and 3. Their squares are 9, 0 and 9. Both −4 and 4 give 16. Taking a square root without considering negative values would omit −3.

Example 2

If n is a positive multiple of 6, which must be integers? A n/2; B n/3; C n/4; D n/6.

Explanation / model: A, B and D. Write n = 6k for positive integer k. Then n/2 = 3k, n/3 = 2k and n/6 = k. For C, n = 6 gives 1.5, so it is not guaranteed.

Common Mistakes to Avoid

Mistake	Why it fails	Correction
Stopping after one match	More options can satisfy the condition.	Evaluate the full list.
Treating could as must	The evidence requirement changes.	Use an example for could and a proof for must.
Checking only positive roots	Negative solutions may also work.	Solve and test the complete set.

Practice Routine

For eight select-all problems, make an option-by-option evidence table. Then change must to could in two prompts and examine how the answer set changes. Record false positives separately from omissions; the two errors usually require different review habits.

Quick Reference

Check	Reminder
Before answering	Underline whether the question asks could, must or cannot.
Before submitting	Check the complete set, including options you initially skipped.
Review focus	Quantifiers and exhaustive checking

Sources and Format Check

Format checked on 22 October 2026 against ETS GRE guidance. Explanations, examples, routines and time allocations within tasks are teaching guidance. Follow the instructions and timer on your test screen.