In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rect...

Question

In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectangle. Out of the total number of people, the percentage of administrators shall be in the range of _______

(The triangle has vertices showing numbers; the circle and rectangle overlap with the triangle. From the figure: triangle region = 50, circle region = 40, rectangle region overlapping areas. The figure shows: 25 inside triangle only, 10 inside circle only, 15 inside rectangle only, 5 in triangle+circle, 8 in circle+rectangle, 12 in triangle+rectangle, 2 in all three. Total = 77.)

A. 0 to 15
B. 16 to 30
C. 31 to 45
D. 46 to 60

Accepted Answer

The percentage of administrators is in the range 31 to 45. Answer: C. Three overlapping shapes represent three groups: triangle = teachers, circle = researchers, rectangle = administrators. People can belong to multiple groups if they are in overlapping regions. We need to count all people in the rectangle (including overlaps) as a percentage of the grand total.