Syllogisms Aptitude Questions with Solutions
30 Syllogisms questions with hints, worked solutions and time targets — 5 easy · 16 medium · 9 hard.
- Section: Logical Reasoning
- Questions: 30
- By difficulty: 5 easy · 16 medium · 9 hard
- Cost: Free, unlimited on every plan
Which conclusions follow from the statements, and which only seem to.
Syllogisms: the essentials
Treat each statement as a picture, and judge only what the statements say, never what you know of the world.
Drawing the statements
- All A are B: circle A inside B. No A is B: separate circles. Some A are B: overlapping circles. Some A are not B: part of A outside B.
- A conclusion follows only if it holds in every diagram the statements allow; one counter-drawing rejects it.
Rules that save the drawing
- Conversions: 'Some A are B' gives 'Some B are A'; 'No A is B' gives 'No B is A'; 'All A are B' gives only 'Some B are A'; 'Some A are not B' has no converse.
- All A are B + All B are C → All A are C.
- All A are B + No B is C → No A is C.
- Some A are B + All B are C → Some A are C.
- Some A are B + No B is C → Some A are not C.
- No A is B + Some B are C → Some C are not A.
- Two 'some' statements, or 'All A are B' with 'Some B are C', give nothing definite about A and C.
- A 'some' premise can only produce a 'some' conclusion.
- Either–or: if neither conclusion follows alone but the two form a complementary pair, such as 'Some A are C' and 'No A is C', then either one follows.
Questions
- All cats are animals Easy
Statements: All cats are animals. All animals are living things. Conclusions: I. All cats are living things. II. All living things are cats. - Some pens are books Medium
Statements: Some pens are books. All books are papers. Conclusions: I. Some pens are papers. II. All papers are books. Which conclusion follows? - No student is lazy Hard
Statements: No student is lazy. Some lazy people are rich. Conclusions: I. Some rich people are not students. II. No rich person is a student. - All dogs are animals Medium
Statements: All dogs are animals. All animals are living beings. Conclusions: I. All dogs are living beings. II. Some living beings are dogs. - All roses are flowers Medium
Statements: All roses are flowers. Some flowers fade quickly. Conclusions: I. Some roses fade quickly. II. All flowers are roses. Which conclusion follows? - Some books are pens Medium
Statements: Some books are pens. All pens are pencils. Conclusions: I. Some books are pencils. II. All pencils are pens. Which conclusion follows? - No cat is a dog Hard
Statements: No cat is a dog. All dogs are pets. Conclusions: I. No cat is a pet. II. Some pets are not cats. Which conclusion follows? - All A are B, no B is C Medium
Statements: All students are hardworking. No hardworking person is lazy. Conclusions: I. No student is lazy. II. Some hardworking people are students. - Some doctors are writers Medium
Statements: Some doctors are writers. All writers are educated. Conclusions: I. Some doctors are educated. II. All doctors are educated. - Feathers and swimming Hard
Statements: All birds have feathers. Some creatures with feathers can swim. Conclusions: I. Some birds can swim. II. All creatures with feathers are birds. - All pens are blue Easy
Statements: All pens are blue. All blue things are attractive. Conclusions: I. All pens are attractive. II. Some attractive things are pens. - No teacher is rich Hard
Statements: No teacher is rich. Some rich people are generous. Conclusions: I. Some generous people are not teachers. II. No generous person is a teacher. - All squares are rectangles Easy
Statements: All squares are rectangles. All rectangles are quadrilaterals. Conclusions: I. All squares are quadrilaterals. II. All quadrilaterals are squares. - Some players are not tall Medium
Statements: All tall people are players. Some players are not tall. Conclusions: I. Some players are tall. II. All players are tall. Which conclusion follows? - A chain of three Medium
Statements: All pencils are pens. All pens are markers. All markers are erasers. Conclusions: I. All pencils are erasers. II. All erasers are pencils. - Some fruits are apples Hard
Statements: Some fruits are apples. No apple is sour. Conclusions: I. Some fruits are not sour. II. No fruit is sour. Which conclusion follows? - Managers and employees Medium
Statements: All managers are employees. Some employees are shareholders. Conclusions: I. Some managers are shareholders. II. Some shareholders are employees. - Two unconnected statements Hard
Statements: Some cars are buses. Some buses are trains. Conclusions: I. Some cars are trains. II. No car is a train. Which conclusion follows? - All metals are conductors Easy
Statements: All metals are conductors. Copper is a metal. Conclusions: I. Copper is a conductor. II. All conductors are metals. Which conclusion follows? - Some chairs are tables Medium
Statements: Some chairs are tables. All tables are wooden. Conclusions: I. Some chairs are wooden. II. All wooden things are tables. Which conclusion follows? - No fish is a mammal Medium
Statements: No fish is a mammal. All whales are mammals. Conclusions: I. No whale is a fish. II. Some mammals are whales. Which conclusion follows? - Poets and writers Medium
Statements: All poets are writers. Some writers are journalists. Conclusions: I. Some poets are journalists. II. Some journalists are writers. - Two classes inside a third Hard
Statements: All cats are animals. All dogs are animals. Conclusions: I. Some cats are dogs. II. No cat is a dog. Which conclusion follows? - All pens are red Medium
Statements: All pens are red. No red thing is heavy. Conclusions: I. No pen is heavy. II. Some heavy things are pens. Which conclusion follows? - A chain broken by 'some' Medium
Statements: Some doctors are teachers. Some teachers are singers. Conclusions: I. Some doctors are singers. II. Some singers are teachers. - Engineers and graduates Medium
Statements: All engineers are graduates. Some graduates are unemployed. Conclusions: I. Some engineers are unemployed. II. Some unemployed people are graduates. - Books and magazines Hard
Statements: No book is a magazine. All magazines are printed. Conclusions: I. Some printed things are not books. II. No printed thing is a book. - A three-step chain Medium
Statements: All mangoes are fruits. All fruits are food. All food is perishable. Conclusions: I. All mangoes are perishable. II. - When neither follows Hard
Statements: Some pens are red. Some red things are expensive. Conclusions: I. Some pens are expensive. II. No pen is expensive. Which conclusion follows? - Testing a converse Easy
Statement: All lawyers are graduates. Conclusions: I. Some graduates are lawyers. II. All graduates are lawyers. Which conclusion follows?
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