Venn Diagrams — PYPs

A -> III. Nurses and patients are two distinct groups, and both sit inside the larger category 'hospital' - two separate circles enclosed by one big circle.

B -> IV. All rhombuses are quadrilaterals and all quadrilaterals are polygons, so the three are fully nested - three concentric circles.

C -> I. The engine and the wheel are two separate parts of a car, while the piston is a sub-part of the engine - a circle within a circle, plus one standing apart.

D -> II. Colour, cloth and merchant are unrelated as categories: cloth can have a colour and a merchant sells cloth, but none is a subset of another - three separate circles.

That gives A-III, B-IV, C-I, D-II, which is Option 3.

The four conditions pin the region down exactly: businessman means inside the circle; not a dancer means outside the square; not a musician means outside the triangle; not an Indian means outside the rectangle. So we need a region that lies in the circle and in nothing else.

Scanning the figure, 10 is the only number sitting inside the circle alone - it falls outside the triangle's right edge, and well clear of both the square and the rectangle.

The distractors all fail on the musician condition or the businessman one: 1 and 8 lie inside the triangle only, so both are musicians and neither is a businessman, and 11 lies inside the rectangle only, making it an Indian and not a businessman.

Hence the answer is 10, Option 4.