Crossover Aptitude Test Logical Reasoning: Syllogisms 4 — Questions and Answers
Question 1: Premise 1: All squares are rectangles. Premise 2: All rectangles are parallelograms. What follows?
- All parallelograms are squares.
- All squares are parallelograms. (Correct answer)
- No squares are parallelograms.
- Some rectangles are not squares.
Correct answer: All squares are parallelograms.
By the transitive property of universal affirmatives, all squares must be parallelograms.
Question 2: No X is Y. All Z are Y. Which is a valid conclusion?
- All Z are X.
- Some Z are X.
- No Z is X. (Correct answer)
- Some X are Z.
Correct answer: No Z is X.
Since Z is entirely within Y and X has no overlap with Y, Z and X cannot overlap at all.
Question 3: Some students pass exams. All who pass exams get certificates. Which is certain?
- All students get certificates.
- Some students get certificates. (Correct answer)
- No students get certificates.
- Only students get certificates.
Correct answer: Some students get certificates.
The students who pass exams must get certificates, so some students definitely get certificates.
Question 4: All birds have wings. Penguins are birds. Penguins cannot fly. What can be concluded?
- All winged animals fly.
- Penguins have wings but cannot fly. (Correct answer)
- Birds that cannot fly are not really birds.
- No birds can fly.
Correct answer: Penguins have wings but cannot fly.
All birds have wings so penguins have wings, and the given fact states penguins cannot fly — both are true simultaneously.
Question 5: Some politicians are honest. All honest people are trustworthy. Which is DEFINITELY true?
- All politicians are trustworthy.
- All trustworthy people are politicians.
- Some politicians are trustworthy. (Correct answer)
- No politicians are trustworthy.
Correct answer: Some politicians are trustworthy.
The honest politicians are also trustworthy, so at least some politicians are trustworthy.
Question 6: No herbivores eat meat. Lions eat meat. Therefore:
- Lions are herbivores.
- Lions are not herbivores. (Correct answer)
- Some herbivores are lions.
- Lions sometimes eat plants.
Correct answer: Lions are not herbivores.
By contrapositive, if an animal eats meat, it is not a herbivore — so lions are not herbivores.
Question 7: All A are B. Some C are not B. Therefore:
- Some C are A.
- All C are A.
- Some C are not A. (Correct answer)
- No C are A.
Correct answer: Some C are not A.
The C that are not B cannot be A (since all A are B), so some C are definitely not A.
Crossover Aptitude Test Logical Reasoning: Syllogisms 4
Premise 1: All squares are rectangles.
Premise 2: All rectangles are parallelograms.
What follows?