CCAT Syllogisms and Deductions 5 — Questions and Answers
Question 1: Some politicians are lawyers. All lawyers passed the bar exam. Which of the following is definitely true?
- All politicians passed the bar exam
- Some politicians passed the bar exam (Correct answer)
- No politicians passed the bar exam
- All lawyers are politicians
Correct answer: Some politicians passed the bar exam
The politicians who are also lawyers must have passed the bar exam, so some politicians passed it.
Question 2: If it rains, the ground gets wet. The ground is not wet. What can be concluded?
- It is raining
- It did not rain (Correct answer)
- It might have rained
- The ground is always dry
Correct answer: It did not rain
By contrapositive, if the ground is not wet, then it did not rain.
Question 3: All X are Y. All Y are Z. No Z are W. Therefore:
- Some X are W
- All X are W
- No X are W (Correct answer)
- Some Z are X
Correct answer: No X are W
X → Y → Z, and since no Z are W, no X can be W.
Question 4: Some birds cannot fly. All penguins are birds. Which conclusion is valid?
- All penguins cannot fly
- Penguins might or might not be able to fly (Correct answer)
- All birds cannot fly
- No penguins are birds
Correct answer: Penguins might or might not be able to fly
The premises do not specify whether penguins are among the birds that cannot fly, so we cannot determine their ability.
Question 5: Every employee who works overtime gets a bonus. James got a bonus. What can you conclude?
- James worked overtime
- James may or may not have worked overtime (Correct answer)
- James did not work overtime
- All employees who got a bonus worked overtime
Correct answer: James may or may not have worked overtime
The conditional only guarantees a bonus for overtime workers; bonuses could also be given for other reasons.
Question 6: No introverts enjoy large crowds. Some engineers are introverts. Which statement is certainly true?
- No engineers enjoy large crowds
- All engineers enjoy large crowds
- Some engineers do not enjoy large crowds (Correct answer)
- All introverts are engineers
Correct answer: Some engineers do not enjoy large crowds
The engineer-introverts don't enjoy large crowds, so some engineers (those who are introverts) do not enjoy large crowds.
Question 7: All squares are rectangles. Shape T is not a rectangle. What follows?
- Shape T is a square
- Shape T might be a square
- Shape T is not a square (Correct answer)
- Shape T is a circle
Correct answer: Shape T is not a square
By contrapositive, if something is not a rectangle, it cannot be a square.
CCAT Syllogisms and Deductions 5
Some politicians are lawyers.
All lawyers passed the bar exam.
Which of the following is definitely true?