In the given diagram, the no. of people who could play different types of sports is given. The rectangle represents Cricket players, the triangle represents Football players, the circle represents Hockey players, and the square represents Golf players. Find the number of players who could play exactly two types of sports only.
69
A region counts towards 'exactly two sports' when it lies inside exactly two of the four shapes. Regions inside one shape, or inside three shapes, are left out.
Step 1 — Regions in exactly two shapes: 11 (circle and triangle), 25 (triangle and square), 21 (circle and square), 7 (square and rectangle) and 5 (circle and rectangle).
Step 2 — Regions excluded: 13 lies in the circle, triangle and square, and 8 lies in the circle, square and rectangle (three shapes each); 16, 42, 31 and 10 lie in a single shape.
Step 3 — Total = \(11 + 25 + 21 + 7 + 5 = 69\).
25 is just one of the five two-shape regions, 31 is the golf-only region and 16 is the hockey-only region, so each of these counts the wrong regions.
69 option is correct.
Similar Questions
Select the Venn diagram that best illustrates the relationship between the following classes.
Nurses, Pharmacists, Healthcare Workers
In the given diagram, the square represents Technicians, the triangle represents Botanists, the circle represents Managers, and the pentagon represents Physicists.
A research institute plans to recruit personnel for various positions based on the following criteria.
(i) Managers who are also Botanists but not Technicians
(ii) Technicians who are either Botanists or Physicists but not Managers.
Find the number of people in the Venn diagram who are eligible according to the criteria.
This question contains three categories. These categories may or may not be linked to one another. Each category may fit into one of the diagrams given below in the options. Select the diagram which most aptly represents the relationship among the given categories.
Prime numbers, Even numbers, Perfect squares
This question contains three categories. These categories may or may not be linked to one another. Each category may fit into one of the diagrams given below in the options. Select the diagram which most aptly represents the relationship among the given categories.
Dogs, Pets, RabbitsIn the given diagram, the triangle represents Teachers, the circle represents Engineers, the square represents French speakers, and the rectangle represents Musicians. Find the total number of Teachers who can speak French and are also Engineers, and the number of Musicians who can speak French but are not Engineers
Important Questions from Venn Diagram Problems
In a group of 73 friends, 14 friends go to Gym and Karate classes both, whereas 7 friends neither go to Gym class nor to Karate class. If a total of 36 friends go to Gym class, then how many friends go to only Karate class?
In an examination 20% students failed in Mathematics and 15% failed in English. If 10% failed in both and those who passed in both numbered 300, then the total number of students who appeared in the examination was
In the following diagram, the 'circle' stands for 'soldiers', the 'square' stands for 'Indians', and the 'triangle' stands for 'singers'. The numbers given in the different segments represent persons belonging to that category.
Which category is represented by the number '5'?
- In the following diagram, the circle stands for 'policemen', the square stands for 'sportspersons' and the 'triangle' stands for 'tax-payers' the numbers given in the different segments represent the number of persons in that category.
How many policemen are tax-payers but are NOT sportspersons?
Which of the following Venn diagrams represents the relationship between Lions, Deers and Carnivores?
