Chapter 10: Cannot Be True

The job: Read It. Accept the stimulus as true and find the one answer that is impossible.
Frequency: roughly one or fewer per section. Difficulty: medium.

What this question type asks

Cannot Be True is the mirror image of Must Be True (see Chapter 8, Must Be True / Inference). On a Must Be True question, you accept the stimulus as true and hunt for the answer that has to follow from it. Here you accept the stimulus as true and hunt for the answer that cannot follow from it: the one choice that conflicts with the stimulus or with something the stimulus forces to be the case. That conflicting answer is impossible, and impossible is what you want.

This is a Read It job, so the same two rules from Chapter 8 apply. You take every statement in the stimulus as given, even if the reasoning is shaky, and you bring no outside information. The difference is the target. On Must Be True you are looking for what is locked in. On Cannot Be True you are looking for what is locked out.

The flip changes which answers win and which lose, and you have to internalize the change or you will fight yourself the whole question. The standard on Must Be True is certainty: the right answer must be true, and anything that merely could be true is wrong. On Cannot Be True the standard is impossibility, and the relationship between “could” and “right” inverts. An answer that merely could be true is now wrong, because you were asked for what cannot be. So is an answer that must be true, for the same reason: must-be-true and cannot-be-true sit at opposite ends. The only winner is the answer that is flat-out incompatible with the stimulus.

How to recognize it

Look for a stem that asks for the impossible or the false:

“Which one of the following CANNOT be true?”
“Which one of the following must be false?”
“If the statements above are true, which one of the following cannot be true on the basis of them?”
“Each of the following could be true EXCEPT.” (This is the most common form. The four “could be true” answers are the losers; the one that cannot be true is the credited answer.)

Two look-alikes to keep straight. A plain Must Be True stem (“which must be true,” “which can be properly inferred”) is the opposite task, and a Cannot Be True stem flips your target, so read the stem to the end before you commit. And watch the EXCEPT form closely: “could be true EXCEPT” is hunting for the one impossible answer, which is exactly a Cannot Be True question wearing an EXCEPT costume.

The method (step by step)

Read the stem and lock in the target. You want the answer that is impossible given the stimulus. Say it to yourself in those words before the first choice, because the EXCEPT phrasing is built to flip you back into hunting for what is true.
Accept every statement in the stimulus as true. Do not evaluate the argument. There may not even be an argument; Cannot Be True stimuli are often fact sets. Your job is to take the facts as given and work out their consequences.
Map the logical consequences. The impossible answer rarely contradicts a sentence word for word. More often it contradicts something the stimulus forces. If the stimulus gives you conditional statements, diagram them and take contrapositives (see Chapter 3, Conditional Logic). If it gives you quantifiers, note their limits (see Chapter 4, Quantifiers and Numbers). The contradiction usually lives one step downstream of the text, not on its surface.
Test each answer against the stimulus and its consequences. For each choice ask a single question: can this coexist with everything the stimulus tells me? If it can, the answer could be true, so kill it. If it cannot coexist with the stimulus no matter what, you have found the impossible answer.
For conditional statements, remember the one and only impossible scenario. For a rule A → B, the sole combination that cannot happen is A occurring without B, that is, A and ¬B. That is the violation. Every other combination is allowed: A and B, ¬A and B, and ¬A and ¬B are all perfectly possible under A → B. This is the heart of most hard Cannot Be True questions, so the next section drills it.

The conditional violation, and the bait

Take the rule A → B. It promises one thing only: whenever A happens, B happens too. So the only way to break it is to find A without B. Everything else is fine.

That gives the test makers a beautiful trap. The tempting wrong answer is the one where the necessary condition occurs without the sufficient, the ¬A and B case or sometimes B and ¬A dressed up in scenario language. It feels like a violation because the two conditions are “mismatched,” but it breaks no rule at all. A → B says nothing about what happens when B shows up on its own. B is allowed to occur for any reason, with or without A. So B and ¬A could be true, which makes it a loser on a Cannot Be True question.

Burn the table into memory for a rule A → B:

Scenario	Possible?
`A and B`	Yes
`A and ¬B`	No (this is the impossible one)
`¬A and B`	Yes (the bait)
`¬A and ¬B`	Yes

When a Cannot Be True question is built on a conditional, the credited answer is almost always a disguised A and ¬B, and the trap is a disguised ¬A and B. Find the rule, then check each scenario answer against this table.

Quantifier limits

The same logic runs through quantifiers. If the stimulus says all of group X are Y, then “some X are not Y” cannot be true. If it says no X are Y, then “some X are Y” cannot be true. If it says most X are Y (more than half), then “most X are not Y” cannot be true, because both cannot hold at once. Read the quantity word exactly and ask what it forbids. In everyday terms, if every egg in the carton is brown, then “some egg in the carton is not brown” is flat-out impossible, no peeking required.

Worked example

Stimulus: At the Halvorsen Institute, every researcher who has been awarded a senior fellowship has published at least one book. No researcher who joined the Institute after 2015 has yet been awarded a senior fellowship. Dr. Imai is a researcher at the Institute who has never published a book.

Stem: If the statements above are true, which one of the following CANNOT be true?

(A) Dr. Imai joined the Institute after 2015.
(B) Dr. Imai joined the Institute before 2015 and has not been awarded a senior fellowship.
(C) Dr. Imai has been awarded a senior fellowship.
(D) Some researchers who joined the Institute before 2015 have not been awarded a senior fellowship.
(E) Some researchers who have published a book have not been awarded a senior fellowship.

Lock in the target. I want the one answer that is impossible given the facts. Four answers could be true; one cannot.

Accept the facts and map them. This is a fact set, so I diagram. “Every senior fellow has published a book” is senior fellowship → published. The contrapositive is ¬published → ¬senior fellowship. Then: no post-2015 researcher has a senior fellowship. And the key fact about Dr. Imai: she has never published a book, so ¬published applies to her. Run her through the contrapositive: ¬published → ¬senior fellowship. Dr. Imai cannot have a senior fellowship. Hold that.

Test each answer.

(A) Imai joined after 2015. Nothing stops this. She has no fellowship, and post-2015 researchers have no fellowships, so this is fully consistent. It could be true. Kill.
(B) Imai joined before 2015 and has no senior fellowship. Also fine. We proved she has no fellowship, and nothing says when she joined. Both halves are consistent with the facts. It could be true. Kill.
(C) Imai has been awarded a senior fellowship. This is exactly what the contrapositive forbids. She never published a book, and every senior fellow has published a book, so she cannot be a senior fellow. This cannot be true. Keep, and this is the answer.
(D) Some pre-2015 researchers have no senior fellowship. Easily possible; the rules set no floor on how many fellowships are handed out, so plenty of pre-2015 researchers could lack one. It could be true. Kill.
(E) Some researchers who published a book have no senior fellowship. The rule runs senior fellowship → published, not the reverse. Publishing a book does not earn anyone a fellowship, so published researchers without fellowships are entirely allowed. This is the ¬A and B bait: the necessary condition (published) occurring without the sufficient (senior fellowship). It could be true. Kill.

The answer is (C).

Notice the two traps. Choice (E) is the classic conditional bait, a necessary-without-sufficient scenario that feels like a violation but breaks no rule. Choice (D) is a plain “could be true” answer that is consistent with everything. Only (C) collides head-on with a consequence the stimulus forces.

Trap patterns

Could Be True. The most common trap by far. The answer is fully consistent with the stimulus; it just is not impossible. On a Read It hunt for the impossible, anything that can coexist with the facts is a loser. Tell: you can imagine a world where the stimulus and the answer are both true.
Must Be True. A close second, and the sneakiest, because the answer is airtight, so it feels like the strong, “correct” one. But you were asked for impossible, not certain. An answer the stimulus proves is the opposite of what you want. Tell: you can point to the text that guarantees it.

Necessary-without-sufficient (the conditional bait). A scenario showing the necessary condition occurring without the sufficient (¬A and B). It looks like a rule violation but breaks no rule. Tell: it pairs a fired necessary condition with a missing sufficient one, and A → B says nothing about that case.
Consistent but unsupported. An answer that neither follows from nor conflicts with the stimulus. It introduces a new actor or fact the stimulus never constrains, so it could be true. Tell: the stimulus simply has nothing to say about it.
Reversed conflict. An answer that would be impossible if the conditional ran the other direction. It baits you into using a Mistaken Reversal (see Chapter 3). Tell: it only “cannot be true” if you swap the sufficient and necessary terms.

Drill

For each item, accept the stimulus as true and pick the one answer that CANNOT be true. Cover the answers below first and work it yourself.

1. Every product the company labels “organic” is grown without synthetic pesticides. The company’s tomatoes are labeled “organic.”

Which CANNOT be true?
(A) The company’s tomatoes were grown without synthetic pesticides.
(B) The company’s tomatoes were grown with synthetic pesticides.
(C) Some products grown without synthetic pesticides are not labeled “organic.”
(D) The company also sells carrots that are not labeled “organic.”
(E) The company’s tomatoes are more expensive than its non-organic products.

2. No member of the city orchestra is under the age of eighteen. Every member of the orchestra can read sheet music. Tomas is under the age of eighteen.

Which CANNOT be true?
(A) Tomas can read sheet music.
(B) Tomas is a member of the city orchestra.
(C) Some people who can read sheet music are not in the orchestra.
(D) Some members of the orchestra are over the age of fifty.
(E) Tomas wishes to join the orchestra someday.

3. Whenever the reservoir level falls below the drought threshold, the water authority issues a usage restriction. The water authority has not issued a usage restriction this month.

Which CANNOT be true?
(A) The reservoir level is above the drought threshold this month.
(B) The reservoir level fell below the drought threshold this month.
(C) The water authority issued a usage restriction last month.
(D) The reservoir level is exactly at the drought threshold this month.
(E) The water authority plans to issue a restriction next month.

Drill answers

1. Answer: (B). Diagram the rule: organic-labeled → no synthetic pesticides. The tomatoes are organic-labeled, so they were grown without synthetic pesticides. (B) says they were grown with synthetic pesticides, which is A and ¬B, the one impossible scenario. (A) must be true, so it is the wrong target on a Cannot question. (C) is the necessary-without-sufficient bait: the rule does not require that everything pesticide-free be labeled organic, so unlabeled pesticide-free products are allowed. (D) and (E) introduce facts the rule never constrains, so both could be true.

2. Answer: (B). The rules: orchestra member → at least eighteen and orchestra member → can read music. Tomas is under eighteen, so by the contrapositive of the first rule (under eighteen → not a member) he cannot be a member. (B) says he is a member, which contradicts that consequence. (A) could be true, because reading music is open to anyone, member or not; nothing stops Tomas from reading music even though he is not in the orchestra. (C) is the necessary-without-sufficient case and is allowed. (D) is consistent, since the rule sets only a minimum age. (E) introduces an unconstrained fact.

3. Answer: (B). The rule: below threshold → restriction issued. Contrapositive: no restriction → not below threshold. No restriction was issued this month, so the level did not fall below the threshold. (B) says it did fall below, which is A and ¬B, the impossible scenario. (A) could be true, but it is not forced; the contrapositive only tells us the level was not below the threshold, so it could be exactly at or above it. (D) “exactly at the threshold” is consistent, because the rule triggers only when the level falls below the threshold, not when it sits at it. (C) and (E) concern other months the rule does not pin down, so both could be true.

Key takeaways

Cannot Be True is the mirror of Must Be True. Accept the stimulus as true, bring no outside info, and find the one answer that is impossible.
The standards flip. An answer that merely could be true is wrong, and so is an answer that must be true. You want only the answer that conflicts with the stimulus or its forced consequences.
The contradiction usually lives one step downstream. Diagram conditionals and take contrapositives; read quantifiers for exactly what they forbid.
For A → B, the only impossible scenario is A and ¬B. The cases ¬A and B, A and B, and ¬A and ¬B are all possible.
Beware the bait where the necessary occurs without the sufficient (¬A and B). It feels like a violation but breaks no rule, so it could be true and is therefore wrong.
Recognition stems: “CANNOT be true,” “must be false,” and the common “could be true EXCEPT.”

Put it to work: drill Must Be False questions in the practice platform, free during early access, with every answer choice explained.