Basic Ability Test Basic Ability Logical Deduction and Syllogisms 4 — Questions and Answers
Question 1: All A are B. All B are C. Which statement must be true?
- All C are A
- All A are C (Correct answer)
- No A are C
- Some B are not C
Correct answer: All A are C
The chain A→B→C means every A is also a C by transitivity.
Question 2: No X are Y. Some Z are Y. Which conclusion follows?
- Some Z are X
- No Z are X
- Some Z are not X (Correct answer)
- All Y are Z
Correct answer: Some Z are not X
The Z that are Y cannot be X (since no X are Y), so at least some Z are not X.
Question 3: If a number is divisible by 6, it is divisible by 3. 18 is divisible by 6. What follows?
- 18 is divisible by 3 (Correct answer)
- 18 is not divisible by 3
- All numbers divisible by 3 are divisible by 6
- 18 is divisible by 9
Correct answer: 18 is divisible by 3
18 is divisible by 6, so by modus ponens it must also be divisible by 3.
Question 4: Some teachers are coaches. All coaches are certified. What must follow?
- All teachers are certified
- Some teachers are certified (Correct answer)
- No teachers are certified
- All certified people are teachers
Correct answer: Some teachers are certified
The teachers who are coaches must be certified, so at least some teachers are certified.
Question 5: Either option A or option B will solve the problem. Option A does not solve the problem. What follows?
- Option B does not solve the problem
- Option B solves the problem (Correct answer)
- Neither option works
- Option A also works
Correct answer: Option B solves the problem
With A eliminated from a valid 'either/or,' B must be the solution.
Question 6: All P are Q. No Q are R. Which is valid?
- All P are R
- No P are R (Correct answer)
- Some P are R
- All R are P
Correct answer: No P are R
Since all P are Q and no Q are R, it follows that no P are R.
Question 7: John passes every exam he studies for. John did not pass today's exam. What follows?
- John studied for today's exam
- John did not study for today's exam (Correct answer)
- The exam was too hard
- Nothing can be concluded
Correct answer: John did not study for today's exam
By contrapositive, not passing means John did not study for that exam.
Basic Ability Test Basic Ability Logical Deduction and Syllogisms 4
All A are B.
All B are C.
Which statement must be true?