The diagram given below has four different shapes, depicting different farmers of a small village, with different assets. The circle represents the farmers who own land of more than 100 yards, the pentagon represents farmers who own cows, the rhombus represents farmers who own goats, and the triangle represents farmers who own tractors. How many farmers are there who have all four assets?

Correct — A. Write the legend down before counting: circle = land over 100 yards, pentagon = cows, rhombus = goats, triangle = tractors.

Rule: all four assets means inside all four outlines at once.

Tracing the boundaries, the diagram encloses one such region, and the number written in it is 16.

The neighbouring regions each fail one boundary: 13 sits outside the pentagon, 14 outside the rhombus and 12 outside the circle. Each of those counts three assets, not four, so option (a) is the figure asked for.

Why the others are wrong

• (b)
  14 — 14 lies inside the circle, the pentagon and the triangle but outside the rhombus. Those farmers hold land, cows and tractors and no goats — three assets.
• (c)
  30 — 30 lies inside the pentagon alone, below the circle's arc and left of the triangle's vertical edge. It counts farmers who own cows only.
• (d)
  21 — 21 lies inside the pentagon and the triangle and nothing else — cows and tractors, with no large landholding and no goats.

A four-shape Venn question is a reading exercise, not an arithmetic one.

The picture carries no labels. The stem assigns the meanings, so the first move is to write circle, pentagon, rhombus and triangle against their assets on the rough sheet.

Then take the candidate number and ask, one outline at a time, whether it lies inside or outside. Four yes answers is the region wanted. Working from a glance at the crowded centre rather than from the boundaries is what produces the wrong options here.

Key facts

• The legend is given in the stem: circle = land over 100 yards, pentagon = cows, rhombus = goats, triangle = tractors.
• 16 is the number lying inside all four outlines.
• 13 lies inside the circle, the rhombus and the triangle but outside the pentagon, so it is land, goats and tractors.

Common traps

• Adding the numbers in the overlapping regions, when the question asks for one region's figure rather than a total.
• Mixing up the pentagon and the rhombus — the pentagon is the five-sided shape at the bottom, the rhombus the tilted square to the right.
• Choosing the largest number in the crowded middle rather than tracing all four outlines.

No directly related past PYQ was found.