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In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of P, Q, and R ?

Overlapping rectangle, triangle and ellipse. Region labels: 1 in the rectangle only, 2 in the triangle only, 3 in the ellipse only, 4 in rectangle and ellipse, P in all three, Q in triangle and ellipse, R in rectangle and triangle.

  • A.P = 6; Q = 5; R = 3
  • B.P = 5; Q = 6; R = 3
  • C.P = 3; Q = 6; R = 6
  • D.P = 5; Q = 3; R = 6

Answer: A

The answer is P = 6; Q = 5; R = 3.

The labelled region 4 shows the rule: it lies inside the rectangle (1) and the ellipse (3) only, and 1 + 3 = 4. So each region carries the sum of the numbers of the shapes containing it.

  • P lies in all three shapes: 1 + 2 + 3 = 6.
  • Q lies in the triangle and the ellipse: 2 + 3 = 5.
  • R lies in the rectangle and the triangle: 1 + 2 = 3.

The other options swap these sums, for example giving P the value 5, which would leave out the rectangle.

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