GCAT Syllogistic Reasoning 3 — Questions and Answers
Question 1: All squares are rectangles. All rectangles are parallelograms. Some parallelograms are rhombuses. Which is definitely true?
- All squares are rhombuses.
- Some squares are rhombuses.
- All squares are parallelograms. (Correct answer)
- Some rectangles are squares.
Correct answer: All squares are parallelograms.
Squares ⊆ rectangles ⊆ parallelograms, so all squares are parallelograms.
Question 2: No herbivores eat meat. All cows are herbivores. This animal eats meat. What follows?
- This animal is a cow.
- This animal might be a cow.
- This animal is not a cow. (Correct answer)
- Cows sometimes eat meat.
Correct answer: This animal is not a cow.
Since all cows are herbivores and herbivores never eat meat, an animal that eats meat cannot be a cow.
Question 3: Some X are Y. No Y are Z. Which conclusion is valid?
- No X are Z.
- Some X are not Z. (Correct answer)
- All X are Z.
- Some Z are X.
Correct answer: Some X are not Z.
The X that are Y cannot be Z, so at least those X are not Z.
Question 4: All pilots are trained. All trained people are disciplined. Which is a valid conclusion?
- All disciplined people are pilots.
- Some disciplined people are not pilots.
- All pilots are disciplined. (Correct answer)
- No pilots are disciplined.
Correct answer: All pilots are disciplined.
Pilots ⊆ trained ⊆ disciplined, so all pilots must be disciplined.
Question 5: Some cats are black. All black things absorb heat. Which must be true?
- All cats absorb heat.
- Some cats absorb heat. (Correct answer)
- No cats absorb heat.
- All heat absorbers are cats.
Correct answer: Some cats absorb heat.
The cats that are black must absorb heat, guaranteeing at least some cats absorb heat.
Question 6: No artists are accountants. John is an accountant. What must follow?
- John is an artist.
- John might be an artist.
- John is not an artist. (Correct answer)
- John is sometimes an artist.
Correct answer: John is not an artist.
Because no artists are accountants, any accountant (including John) cannot be an artist.
Question 7: All M are N. Some P are not N. Which is valid?
- Some P are M.
- All P are M.
- Some P are not M. (Correct answer)
- No P are M.
Correct answer: Some P are not M.
The P that are not N cannot be M (since all M are N), so some P are definitely not M.
GCAT Syllogistic Reasoning 3
All squares are rectangles.
All rectangles are parallelograms.
Some parallelograms are rhombuses.
Which is definitely true?