10.3 Multiple-Choice — Select One or More
Key Takeaways
- MC-Multiple presents 3 choices with 1, 2, or 3 correct; there is NO partial credit - all correct selections must be marked and no incorrect ones.
- The single most common error is selecting only one answer when two or three are correct; evaluate each statement independently and select every true one.
- The opposite trap - selecting all 3 - occurs when the question says "which MUST be true"; test counterexamples to eliminate statements that are only sometimes true.
- Distinguish "must be true" (every valid case) from "could be true" (at least one valid case) framing carefully - the wording flips the answer.
- Use mark-and-review: if you cannot fully verify all three statements in 90 seconds, mark the question and return with the review screen.
10.3 Multiple-Choice - Select One or More
Quick Answer: 3 choices, 1-3 correct, NO partial credit. Evaluate each statement independently. "Must be true" = every case; "could be true" = at least one case. Select every true statement and no false one.
Format Basics
Multiple-Choice - Select One or More (MC-Multiple) presents exactly 3 answer choices labeled (A), (B), and (C). Between 1 and 3 of them are correct - the number is not disclosed. You receive credit only if you select EVERY correct choice and NO incorrect choice. There is no partial credit: marking 2 of 3 correct statements earns zero points, as does marking 1 correct plus 1 incorrect.
This format appears roughly 3-5 times per scored Quant section. It is the format most students get wrong, not because the math is harder but because the selection discipline is unfamiliar.
The Two Big Traps
Trap 1: Selecting Only One When Multiple Are Correct
Trained by years of single-answer tests, many students mark the first statement they verify and move on. If two or three statements are actually correct, this earns zero.
Defense: Treat every MC-Multiple question as three separate true/false questions. Verify (A) on its own, then (B) on its own, then (C) on its own. Select each one that holds; do not stop after the first true statement.
Trap 2: Selecting All Three When Only Some Apply
The opposite trap: deciding "all three sound plausible" and selecting all of them. This typically arises on "which MUST be true" questions where a statement is only SOMETIMES true. Marking it earns zero.
Defense: For each statement, try to construct a counterexample. If you can find even one valid case where the statement fails, it does NOT "must be true" - eliminate it.
Independent Evaluation - The Core Strategy
For each statement, run the same verification you would run for a single true/false question:
- Read the statement carefully, noting any quantifier ("must," "could," "always," "never").
- Construct one or two test cases.
- Decide: TRUE (select) or FALSE (do not select).
Do NOT compare statements to each other; each is judged independently against the question stem.
Worked Example 1
Question: If x is an integer greater than 1, which of the following MUST be true? Indicate all that apply.
(A) x has at least one prime factor. (B) x^2 has at least three positive divisors. (C) x + 1 is even.
- (A): Every integer greater than 1 has a prime factor (Fundamental Theorem of Arithmetic). TRUE.
- (B): If x is prime, x^2 has divisors 1, x, x^2 - that is three. If x is composite, x^2 has even more. TRUE.
- (C): Test x = 2: x + 1 = 3, which is odd. So (C) does NOT must-be-true. FALSE.
Answer: (A) and (B) only.
Note how (C) looked reasonable - "an integer plus one flips parity" - but fails for even x. The counterexample x = 2 eliminates it.
"Must Be True" vs "Could Be True" Framing
The quantifier in the question stem flips the entire approach:
| Framing | Meaning | Strategy |
|---|---|---|
| MUST be true | Holds for EVERY valid case | Find a counterexample to eliminate; if you cannot, select it. |
| COULD be true | Holds for AT LEAST ONE valid case | Find one example to select; if no example exists, eliminate. |
| MUST be false | Holds for NO valid case | Find one example to eliminate; if you cannot, select it. |
| CANNOT be true | Same as MUST be false | Same as above. |
Worked Example 2
Question: If 0 < x < 1, which of the following COULD be true? Indicate all that apply.
(A) x^2 > x. (B) x^3 < x^2. (C) 1/x is an integer.
- (A): For 0 < x < 1, squaring makes the value smaller, so x^2 < x. (A) cannot be true. FALSE.
- (B): Take x = 1/2: x^3 = 1/8, x^2 = 1/4, so 1/8 < 1/4. TRUE.
- (C): Take x = 1/2: 1/x = 2, an integer. TRUE.
Answer: (B) and (C) only.
For "could be true," a single valid example suffices. For (A), no example exists in the given range, so it is eliminated.
Mark-and-Review Discipline
MC-Multiple takes longer than MC-Single because you effectively solve three questions. If you cannot verify all three statements within 90 seconds:
- Mark the question using the GRE interface mark button.
- Select the statements you have already verified - do not leave them unmarked if you are confident.
- Move on. Return via the review screen at the end of the section.
The review screen shows all marked questions and lets you jump back. Fresh eyes often resolve a stuck statement in 15 seconds. Leaving a marked question blank at the end of the section is guaranteed zero; an educated guess based on partial evaluation is strictly better.
Common MC-Multiple Traps
- Quantifier drift: reading "could" as "must" or vice versa. Underline the quantifier on first read.
- Symmetric distractors: the GRE often designs statements so two are true and one is false (or vice versa), but not always - do not assume symmetry.
- Hidden constraints: the stem may say "x is a positive integer," which makes "x > 0" trivially true but traps students who test x = -1.
- Statement interdependence: statement (B) may reference statement (A). Read carefully - (B) is true ONLY IF (A) is true, in which case both must be selected together.
- All-or-nothing scoring reminder: marking two of three correct statements earns zero. If you are uncertain about one statement but confident about the others, consider whether the risk of the uncertain one being false outweighs leaving it blank.
Strategic Notes on the Calculator and Estimation
For MC-Multiple, the calculator is rarely the bottleneck - reasoning is. Estimation and counterexample construction are more valuable than exact arithmetic. When a statement involves a numeric comparison (e.g., "x^3 < x^2 for x = 1/10"), mental math is often sufficient: (1/10)^3 = 1/1000 and (1/10)^2 = 1/100, and 1/1000 < 1/100 is obvious without computing.
Final Selection Discipline
Before submitting a marked MC-Multiple question, do a final pass:
- Re-read the question stem quantifier.
- For each selected statement, confirm it satisfies the quantifier.
- For each unselected statement, confirm you have a counterexample (or no example, for "could").
- Count your selections - is 1, 2, or 3 marked? All are valid outcomes; do not force the count to a specific number.
The discipline of treating MC-Multiple as three independent true/false questions, combined with careful quantifier reading, eliminates the two big traps and turns this format from a point sink into a point source.
If x is an integer greater than 1, which of the following MUST be true? Indicate all that apply. (A) x has at least one prime factor. (B) x^2 has at least three positive divisors. (C) x + 1 is even.
If 0 < x < 1, which of the following COULD be true? Indicate all that apply. (A) x^2 > x. (B) x^3 < x^2. (C) 1/x is an integer.
An MC-Multiple question has 3 choices, 2 of which are correct. You select 2 correct choices and 1 incorrect choice. How many points do you earn?
Which strategy best addresses the trap of selecting only one answer when two or three are correct?