Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusion(s) logically follow(s) from the statements. Statements: All pastries are chocolates. Some chocolates are cookies. All cookies are cakes. Conclusions: (I) No pastry is a cake. (II) Some cakes are chocolates.
- (a)Both conclusions I and II follow.
- (b)Neither conclusion I nor II follows.
- (c)Only conclusion II follows.
- (d)Only conclusion I follows.
Answer
Why
Correct — C. Take the statements as circles and ask of each conclusion whether it is certain, not whether it is possible.
Rule: some chocolates are cookies, and all cookies are cakes. So the chocolates that happen to be cookies are cakes as well.
That forces some cakes are chocolates, which is conclusion II.
Conclusion I claims no pastry is a cake. Pastries lie inside chocolates, and nothing stops a pastry from being one of the chocolates that is also a cookie, and therefore a cake.
A negative conclusion has to hold in every diagram, and this one breaks in that diagram. Only II survives — option (c).
Why the others are wrong
- (a)Both conclusions I and II follow. — Both would need conclusion I to be certain. No pastry is a cake is only one of the possible diagrams, because a pastry may sit among the chocolates that are cookies, and every cookie is a cake.
- (b)Neither conclusion I nor II follows. — Neither is too harsh. Conclusion II is forced, not optional: the chocolates that are cookies are cakes, so at least some cakes are chocolates.
- (d)Only conclusion I follows. — This keeps the conclusion the diagram can break and drops the one that is guaranteed. Conclusion I is possible, conclusion II is certain — the test is certainty.
Concept
A syllogism asks what must be true, not what could be true. Draw the statements as overlapping circles and try to build a diagram in which the conclusion fails. If you can build one, the conclusion does not follow.
Two rules do most of the work here. All B are C puts every B inside C, so anything already inside B is inside C too.
Some A are B guarantees a real overlap, and that overlap can be pushed through any chain of 'all' statements that follows it.
Negative conclusions are the hard ones, because they need the two classes kept apart in every possible drawing.
The stem's instruction to accept the statements even where they clash with common sense is doing real work here — chocolates, cookies and cakes overlap in life, and you must ignore that and read only the three statements.
Key facts
- A conclusion follows only if it is true in every diagram consistent with the statements.
- 'Some A are B' converts freely: some B are A.
- 'Some A are B' plus 'all B are C' yields 'some A are C'.
- A 'No X is Y' conclusion needs the two classes separated in every possible diagram, not just one.
Study next
Common traps
- Reading 'Some chocolates are cookies' as if it also said 'some chocolates are not cookies'.
- Accepting a negative conclusion because one drawing allows it, instead of testing every drawing.
This paper prints the item in two different wordings: Q.1 opens 'Read the given statements and conclusions carefully', while Q.7 opens 'In this question, three statements are given, followed by two conclusions numbered I and II'.
The first wording also runs at 19 Sep 2024, 9:00, Reasoning Q.19.
Related PYQs
No directly related past PYQ was found.