CCAT question types · Logic · Syllogisms and if-then
Syllogism questions on the Criteria Cognitive Aptitude Test (CCAT), the hiring test, give you two statements and a conclusion, and ask whether the conclusion is True, False, or Uncertain. The logic is simple. The traps are not. Here is what each answer means, a drawing method that settles all/some/no questions, and the one rule that settles if-then questions.
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You get two statements you must accept as true, then a conclusion. Your job is to say whether the conclusion is True, False, or Uncertain based only on those two statements. Not on what is likely. Not on what you know about the world.
They come in two shapes. Group statements use all, some, and no: "Some readers are editors. All editors are researchers. Conclusion: some readers are researchers." If-then statements give a rule and a fact: "If a package is express, it gets a tracking code. This package has a tracking code. Conclusion: it is express."
Both reward the same habit: read only what is written, then test it.
The useful way to think about it: True and False are both certainties. Uncertain means the two statements do not settle the question either way. That is a real answer, not a shrug.
Draw each group as a circle. "All A are B" puts circle A entirely inside circle B. "No A are B" keeps them apart. "Some A are B" means the circles overlap and at least one member sits in the overlap.
Then draw two pictures, not one. In the first, try to make the conclusion true while obeying both statements. In the second, try to make it false while obeying both statements.
With practice you do this in your head. These six patterns cover most of what you will see:
| Statements | Conclusion | Answer |
|---|---|---|
| All A are B. All B are C. | All A are C. | True |
| Some A are B. All B are C. | Some A are C. | True |
| Some A are B. No B are C. | Some A are not C. | True |
| Some A are B. No B are C. | All A are C. | False |
| All A are B. All C are B. | All A are C. | Uncertain |
| Some A are B. Some B are C. | Some A are C. | Uncertain |
The last two are where people lose points. Two groups that both sit inside a third need not touch each other. Two "some" statements can be about different members of the middle group, so nothing links the outer groups.
An if-then rule says: whenever the first part (the condition) holds, the second part (the result) holds. "If a badge is active, the door unlocks." It says nothing about what happens when the badge is not active.
Four facts can follow a rule like "If A, then B". Only two of them prove anything.
| You are told | Conclusion | Answer | Why |
|---|---|---|---|
| A is true | B is true | True | The rule fires. |
| B is false | A is false | True | The contrapositive: no result means no condition. |
| B is true | A is true | Uncertain | B might happen for other reasons. |
| A is false | B is false | Uncertain | The rule is silent when A fails. |
The second row is the one to drill. "If A, then B" always means "if not B, then not A". If the door did not unlock, the badge was not active. And if the conclusion states the opposite of something you can prove ("the badge is active"), the answer is False.
Two wordings to translate before you start. "A only if B" means "if A, then B". "A unless B" means "if not B, then A".
Many test takers treat Uncertain as the answer you pick when you are unsure. That is backwards. Uncertain is a precise claim: the statements allow it both ways.
In our bank, Uncertain is the correct answer on 137 of the 314 deductive and if-then questions, more than True (108) or False (69). That is our bank's distribution, not a rule about the real test. The point is that you should expect to answer Uncertain often, and only after you have found both pictures.
A quick check: if you can describe one situation where the conclusion holds and one where it fails, and both obey the statements, the answer is Uncertain. If you can only find one, keep looking for the other for a few seconds, then commit.
These come from our bank, at medium and hard difficulty: four group statements and four if-then rules, with two True, two False and four Uncertain answers. Pick an answer, then open the explanation.
Assume the first two statements are true. Some singers are editors. No editors are volunteers. Conclusion: Some singers are not volunteers. Is the conclusion True, False, or Uncertain?
Answer: A, True
The known overlap with the second group supplies at least one first-group member who cannot be in the third. No extra facts about these groups may be assumed.
The singers who edit are guaranteed non-volunteers, so the some-not claim holds.
Why it's here. Some plus no always gives a some-not.
Assume the first two statements are true. No editors are cyclists. Some musicians are editors. Conclusion: All musicians are cyclists. Is the conclusion True, False, or Uncertain?
Answer: B, False
At least one member of the third group is in the first group and therefore cannot be in the second. That disproves the all-statement. No extra facts about these groups may be assumed.
One musician who is an editor is enough to break an all-statement about cyclists.
Why it's here. One counterexample breaks an all-statement.
Assume the first two statements are true. Some runners are bakers. Some bakers are editors. Conclusion: Some runners are editors. Is the conclusion True, False, or Uncertain?
Answer: C, Uncertain
The two some-statements can concern different members of the middle group. An overlap between the outer groups is not guaranteed or ruled out. No extra facts about these groups may be assumed.
Two some-statements never link: the bakers who run may not be the bakers who edit.
Why it's here. Two "some" statements never link the outer groups.
Assume the first two statements are true. All designers are singers. All mentors are singers. Conclusion: All designers are mentors. Is the conclusion True, False, or Uncertain?
Answer: C, Uncertain
Two groups inside the same larger group need not include one another. They might coincide, overlap, or be disjoint. No extra facts about these groups may be assumed.
Sharing a larger group does not put designers inside mentors.
Why it's here. Two groups inside a third need not touch.
In Omar’s system, the following rule always holds: If a member is eligible, then their account is verified. For the item in question, it is NOT the case that their account is verified. Conclusion: it is NOT the case that a member is eligible. Is the conclusion True, False, or Uncertain?
Answer: A, True
If the required consequence is absent, the original condition cannot hold. This is the contrapositive.
If A implies B, not B implies not A. B alone does not prove A.
Why it's here. The contrapositive, stated with negations.
In Eli’s system, the following rule always holds: If a badge is active, then the door can be unlocked. For the item in question, it is NOT the case that the door can be unlocked. Conclusion: a badge is active. Is the conclusion True, False, or Uncertain?
Answer: B, False
If the required consequence is absent, the original condition cannot hold. This is the contrapositive. The conclusion asks the opposite of that deduction.
If A implies B, not B implies not A. B alone does not prove A.
Why it's here. The contrapositive, then a conclusion that claims the opposite.
In Lena’s system, the following rule always holds: If a report is final, then it has a version number. For the item in question, it has a version number. Conclusion: a report is final. Is the conclusion True, False, or Uncertain?
Answer: C, Uncertain
The consequence might occur for other reasons. Reversing an if–then statement is not a valid deduction.
If A implies B, not B implies not A. B alone does not prove A.
Why it's here. Affirming the result: the result can happen without the condition.
In Lena’s system, the following rule always holds: If a shipment is fragile, then it receives a special label. For the item in question, it is NOT the case that a shipment is fragile. Conclusion: it is NOT the case that it receives a special label. Is the conclusion True, False, or Uncertain?
Answer: C, Uncertain
The rule says what happens when the condition holds, not what happens when it does not hold.
If A implies B, not B implies not A. B alone does not prove A.
Why it's here. Denying the condition: the rule is silent when the condition fails.
Syllogisms are logic questions. In our simulator, each 50-question test has 6 logic questions spread across 5 logic families: deductive statements, if-then reasoning, ordering, overlapping groups, and letter sequences. That is our simulator's mix, built to match the format; Criteria does not publish a per-type breakdown. With about 18 seconds per question, a syllogism you can settle in ten seconds banks time for slower questions.
The other logic types are on the CCAT logic questions page. Math has its own subtypes; the number series guide and the word problems guide cover the two that take the most practice.
Use the tables above until you can call each pattern without drawing. Then drill both families together, because the habit is the same. In the app, a focus drill on deductive statements and if-then reasoning times every answer and explains every miss, and the AI coach points out which trap you keep falling for.
Then put them in context with a free CCAT practice test, where a syllogism sits between a word problem and a rotation and you have to switch modes fast. More question types are on the CCAT practice questions hub.
It means the two statements allow the conclusion to be true in some situations and false in others, so you cannot tell from what is given. It is a definite answer, not a guess.
False means the statements rule the conclusion out completely. Uncertain means they neither prove it nor rule it out. If you can picture one valid situation where the conclusion holds, it is not False.
Uncertain. B might be true for some other reason. Only the reverse works: if B is false, then A must be false.
"Some A are B" means at least one A is a B, and possibly all of them. It does not tell you that any A is not a B.
No. Treat the two statements as true even if they sound wrong, and judge the conclusion only from them.
No. They are our own questions, written to match the True, False, or Uncertain format. Clever Cat Prep is not affiliated with Criteria Corp.
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