Read the following statement carefully and identify the conclusion that follows. Statement: All circles are shapes. Some shapes are squares. All squares are polygons. Conclusions: I. Some shapes are polygons. II. Some polygons are circles.

Correct — A.
Rule: Some + All = Some. Some A are B and all B are C give some A are C.

I: some shapes are squares, and all squares are polygons, so some shapes are polygons. Follows.

II: circles are tied to shapes alone. The shapes that are squares need not include any circle, so no link reaches from circles to polygons. Does not follow.

Only I → option (a).

Why the others are wrong

• (b)
  Only II follows — Only II accepts a link that is not there. Circles sit inside shapes, but the squares among shapes need not include any circle, so Some polygons are circles fails.
• (c)
  Both I and II follow — Both accepts II, but circles connect to shapes alone. Nothing ties circles to squares, so no circle need be a polygon.
• (d)
  Neither I nor II follows — Neither misses I. Some shapes are squares and all squares are polygons, so those squares are shapes that are polygons: Some + All = Some.

Draw a Venn diagram: circles inside shapes, squares overlapping shapes, and squares inside polygons.

A conclusion follows only if every possible diagram shows it. Some shapes are polygons holds in every diagram, because the squares that are shapes are also polygons. Circles can sit in a part of shapes that touches no square, so Some polygons are circles fails.

Key facts

• Some A are B + All B are C gives Some A are C.
• All A are B + Some B are C gives no definite link between A and C.
• A conclusion follows only if it holds in every possible Venn diagram of the statements.

Common traps

• Chaining circles → shapes → squares, when the shapes that are squares need not be circles
• Rejecting II from real geometry instead of from the statements

No directly related past PYQ was found.