KellyMath Blog

“Must be true” and “could be true” questions on the SSAT Upper Level call for opposite strategies, even though the wording looks similar. A “must be true” answer choice has to work for every valid number. The winning move is to hunt for a counterexample that breaks it. A “could be true” answer choice only needs to work for one valid case. The winning move is to find a single example that fits, then stop.

The short answer: For “must be true” questions, test each answer choice with unusual numbers — 0, 1, negatives, fractions. Try to prove it false. If nothing breaks it, it’s true. For “could be true” questions, one valid example that matches an answer choice is enough. “Cannot be true” and “could NOT be true” flip both strategies. Now you’re hunting for the one answer that breaks, not the one that holds.

What Do These Two Phrasings Actually Mean?

These two phrases show up across very different SSAT Upper Level problems — systems of equations, geometry, number theory, even inequalities. They aren’t confined to one chapter or topic. That’s what makes them tricky. A student can master the phrasing in algebra and still get tripped up when it resurfaces in geometry weeks later.

The distinction comes down to one word. “Must” means always. “Could” means sometimes. A statement that must be true has to hold for every number that satisfies the question’s conditions, with zero exceptions. A statement that could be true only has to hold for at least one such number. Misreading which one a question is asking leads to the wrong search strategy. This happens even when a student’s math skills are solid.

“Must Be True” Questions: Look for a Counterexample

The fastest way to test one of these answer choices is to try to disprove it. Plug in unusual numbers — 0, 1, negatives, fractions — and see if the statement survives. If even one number breaks it, that choice is out, no matter how many other numbers make it hold.

This is also why 0 and 1 are normally numbers to avoid when picking values on the SSAT, except here. That’s the “choosing numbers” strategy from Chapter 1: SSAT Strategy in Kelly Campbell’s book Hacking the SSAT Upper Level Math — one of six core strategies used throughout. Ordinary problems want a “magic number” that clearly separates the right answer from the wrong ones. 0 and 1 tend to make too many choices match. This question type wants the opposite: numbers most likely to reveal an exception.

Worked Sample Problem

Which of the following must be true if two positive numbers, S and T, have a difference of 30, and S is two times T? 

Step 1: Translate the given information into equations.

\( S = 2T \), and \( S – T = 30 \)

Step 2: Solve the system.

Substituting \( 2T \) for S: \( 2T – T = 30 \), so \( T = 30 \) and \( S = 60 \).

Step 3: Check each answer choice against \( S = 60 \) and \( T = 30 \).

The answer is (D). Only one equation holds up once the values are found. Kelly Campbell walks through more of these in Chapter 16: Systems of Equations, part of her book Hacking the SSAT Upper Level Math. That chapter also covers the SSAT’s “Quirky Systems.”

“Could Be True” Questions: Just Find One Example That Works

This question type is a much lighter lift. Instead of testing every possibility, a student only needs one valid scenario. That scenario just has to fit both the question’s conditions and one of the answer choices.

An isosceles triangle has an angle measuring 68°. What could be the measure of another angle in the triangle? 

Step 1: Recognize that “could be” signals more than one possible triangle.

An isosceles triangle has two equal angles. The 68° angle could be either one of the equal pair or the different one. Two different triangles are possible here.

Step 2: Solve both versions.

If 68° is one of the two equal angles, the third angle is \( 180 – 68 – 68 = 44° \). If 68° is the different angle, the other two angles split the remaining \( 180 – 68 = 112° \) evenly, giving \( 56° \) each.

Step 3: Check both results against the answer choices.

44° is choice (A). 56° isn’t listed anywhere.

The answer is (A). There was no need to prove 44° works in every isosceles triangle with a 68° angle. It just needed to be one valid possibility that matched a choice.

The Flip Side: “Cannot” and “Could NOT”

“Cannot be true” and “could NOT be true” are the mirror image of the two strategies above. “Cannot be true” uses the same number-testing approach. The goal shifts to finding the answer that breaks, instead of the ones that hold. “Could NOT be true” is the mirror of “could be true.” The goal is finding the one answer with no valid scenario behind it.

Inequality questions add one more wrinkle. When a “could be” question involves a single inequality with answer choices listed in order, there’s a shortcut. It eliminates the three middle choices without any algebra. See when to guess on the SSAT for the full walkthrough.

Common Mistakes to Avoid

Treating “must be true” like a regular solve. It requires testing every answer choice against unusual numbers. That’s different from calculating a single “magic number” the way most SSAT problems work. Skipping the counterexample search is the single most common error here.

Stopping after finding one number that works. For “must be true” questions, one working number proves nothing. A choice is only correct if no number can break it.

Overworking a “could be true” question. Once one valid example matches a choice, the question is solved. There’s no need to check every scenario the way “must be true” requires.

Missing the word “NOT.” A single word changes the entire strategy. Reading quickly under time pressure makes this an easy trap. It’s worth circling “NOT” or “cannot” the moment it appears.

Where Does This Fit in Your SSAT Prep?

“Choosing numbers” is one of the six core SSAT strategies in Kelly Campbell’s book. For more on using strategy under time pressure, see SSAT Math Time Management.

For full SSAT Upper Level Math prep, the Complete Course walks through all 18 chapters – 545 pages covering nothing but SSAT Upper Level Math, written the way a tutor actually explains it, built from real experience working with 50+ SSAT students. If you’d like personalized help along with it, explore the book + tutoring packages. 

If you’re not sure where to start, Kelly offers a free SSAT Upper Level Math diagnostic on her homepage. Take the diagnostic and you’ll know within an hour exactly which topics need the most attention. 

Frequently Asked Questions: “Must Be True” vs. “Could Be True” on the SSAT

What’s the difference between “must be true” and “could be true” questions on the SSAT?

An answer choice that must be true has to hold for every number that satisfies the question’s conditions. The strategy is to test unusual numbers and try to disprove each choice. An answer choice that could be true only needs to work for one valid case. The strategy is to find a single example that fits and matches a choice.

Why do these questions use different numbers than other SSAT problems?

Most SSAT number-choosing questions avoid 0 and 1, since those numbers tend to make too many answer choices look correct. This question type flips that rule. Zero, one, negative numbers, and fractions are exactly the numbers most likely to reveal an exception. They break a false choice fastest.

How do you solve a “could be true” question quickly?

Find one valid example that satisfies the question’s given conditions, then check whether it matches any of the answer choices. There’s no need to test multiple scenarios once a match is found — one working example is enough.

What does “could NOT be true” mean on the SSAT?

It’s the mirror image of “could be true.” Instead of finding a possible answer choice, the goal is finding the one choice with no valid scenario behind it. Missing the word “NOT” is one of the most common reading mistakes on this question type, so it’s worth circling it the moment it appears.