Direction : In each of the questions below are given some statements followed…
2020
Direction : In each of the questions below are given some statements followed by two
conclusions. You have to take the given statements to be true even if they seem to be at variance
with commonly known facts. Read all the conclusions and then decide which of the given
conclusions logically follows from the given statements disregarding commonly known facts.
Statements: Some circles are not triangle. Only a few squares are triangle. No rhombus is squares.
Conclusions: I. All rhombus being triangle is a possibility.
II. Some squares can never be circles.
Answer: A. If only conclusion I follows. — Concept: A ‘possibility’ conclusion (phrased as ‘...is a possibility’ or the negative form ‘X can never be Y’) is tested by trying to build one valid Venn…
- A.
If only conclusion I follows.
- B.
If only conclusion II follows.
- C.
If either conclusion I or II follows.
- D.
If neither conclusion I nor II follows.
- E.
If both conclusions I and II follow.
Attempted by 42 students.
Show answer & explanation
Correct answer: A
Concept: A ‘possibility’ conclusion (phrased as ‘...is a possibility’ or the negative form ‘X can never be Y’) is tested by trying to build one valid Venn diagram consistent with every statement: if such a diagram exists, the possibility conclusion follows; if every valid diagram forces the opposite, it does not. A statement of the form ‘Only a few A are B’ is a definite partial-overlap statement — it fixes that some A are B and some A are not B (and, by conversion, that some B are A) — but, unlike the plain statement ‘Only A is B’ (which converts to ‘All B are A’), it leaves anything beyond that undetermined.
Application: Applying this to each statement and conclusion in turn:
‘Some circles are not triangle’ fixes only a partial exclusion between circles and triangles; it says nothing about squares.
‘Only a few squares are triangle’ fixes that some squares are triangles and some squares are not — it does NOT collapse to ‘all triangles are squares’; the portion of the triangle set that is not shared with squares remains open.
‘No rhombus is squares’ fixes that the rhombus set and the square set never overlap, but it places no restriction on how rhombus relates to triangle or circle.
Conclusion I (‘All rhombus being triangle is a possibility’): since rhombus is free to sit anywhere outside the square set, it can be drawn entirely inside the triangle-but-not-square region identified above — a diagram that satisfies all three statements without contradiction. So conclusion I is a valid possibility.
Conclusion II (‘Some squares can never be circles’): no statement links squares to circles at all, so a diagram where part of the square set also overlaps the circle set is equally consistent with every statement. Because that overlap remains possible, the stronger claim that squares ‘can never’ be circles is not established.
Cross-check: the natural objection is to read ‘Only a few squares are triangle’ as the plain ‘Only’ statement, which would convert to ‘All triangles are squares’ and — combined with ‘no rhombus is squares’ — would force rhombus and triangle to be completely disjoint, killing conclusion I. But the statement explicitly says ‘only a FEW’, which caps the overlap without inverting the universal the way plain ‘Only’ does; the diagram built above satisfies all three original statements exactly as given, without contradiction.
So only conclusion I follows — the answer is ‘If only conclusion I follows.’