CCAT Logical Reasoning 2 — Questions and Answers
Question 1: All doctors are professionals. Some professionals are athletes. Which conclusion MUST be true?
- All doctors are athletes
- Some doctors are athletes
- No doctors are athletes
- None of the above must be true (Correct answer)
Correct answer: None of the above must be true
The 'some professionals' who are athletes may or may not include any doctors. No specific conclusion about doctors and athletes must be true.
From 'All doctors are professionals' and 'Some professionals are athletes,' we cannot conclude anything definite about doctors and athletes. The 'some professionals' who are athletes might or might not be doctors. None of the specific conclusions must be true.
Question 2: If it rains, the picnic is cancelled. The picnic was NOT cancelled. What can you conclude?
- It rained
- It did not rain (Correct answer)
- It might have rained
- The picnic was rescheduled
Correct answer: It did not rain
Modus tollens: If P then Q; not-Q; therefore not-P. If rain implies cancelled, and not-cancelled, then it did not rain.
The statement 'If it rains, picnic cancelled' has a contrapositive: 'If picnic not cancelled, it did not rain.' Since the picnic was not cancelled, we can definitively conclude it did not rain.
Question 3: No mammals are cold-blooded. All snakes are cold-blooded. Which statement must be true?
- All snakes are mammals
- No snakes are mammals (Correct answer)
- Some snakes are mammals
- Some mammals are snakes
Correct answer: No snakes are mammals
No mammals are cold-blooded, and all snakes are cold-blooded, so snakes and mammals share no members.
Mammals and cold-blooded animals are disjoint sets. Snakes are entirely within the cold-blooded set. Since mammals have no members in the cold-blooded set, snakes and mammals share no members. No snakes are mammals.
Question 4: In a race: Alex finished before Beth. Beth finished before Carlos. Dana finished after Carlos. Who finished last?
- Alex
- Beth
- Carlos
- Dana (Correct answer)
Correct answer: Dana
Order: Alex, Beth, Carlos, Dana. Dana finished after Carlos, making Dana last.
From the clues: Alex < Beth < Carlos < Dana. The full order is Alex, Beth, Carlos, Dana. Dana finished last.
Question 5: Every Friday, Sam goes to the gym. Sam did not go to the gym today. What can be concluded?
- It is Friday
- It is not Friday (Correct answer)
- Sam is sick
- Sam went somewhere else
Correct answer: It is not Friday
Contrapositive: if Sam did not go to the gym, it cannot be Friday.
'Every Friday implies gym visit' means 'no gym visit implies not Friday' (contrapositive). Since Sam did not go, today cannot be Friday.
Question 6: Three mislabeled boxes contain apples, oranges, and a mix. The 'Mixed' box is opened and reveals only apples. What does the 'Oranges' box contain?
- Apples
- Oranges
- Mixed (Correct answer)
- Cannot be determined
Correct answer: Mixed
All labels are wrong. 'Mixed' has apples. 'Oranges' cannot have oranges (wrong label) so it has mixed. 'Apples' has oranges.
All labels are wrong. 'Mixed' box has apples. Remaining contents (oranges and mixed) must go into 'Oranges' and 'Apples' boxes. 'Oranges' label cannot hold oranges (all labels wrong), so it holds mixed. 'Apples' label holds oranges.
CCAT Logical Reasoning 2
All doctors are professionals.
Some professionals are athletes.
Which conclusion MUST be true?