Approach to solve the question:

• Draw a Venn diagram with sets M (Marketing), F (Finance), H (HR).

• Assign variables to each region: only M, only F, only H, exactly two overlaps, and all three.

• Use the given condition that “only” values form an AP and similarly “exactly two” values form an AP.

• Apply the relations:

  • only F = ½ only H

  • all three = (1/20) × only F

• Use fixed values:

  • |H| = 120

  • |M∩F| = 15

  • |F∩H| = 19

• Break down intersections (e.g., |M∩F| includes both exactly MF and all three).

• Substitute values into equations, reduce unknowns, and solve step by step.

• Finally, add all regions + 4 students outside sets to get the total.