Question

Workers are grouped by their areas of expertise and are placed on at least one team. 20 are on the marketing team, 30 are on the Sales team, and 40 are on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers are on both the Sales and Vision teams, 9 workers are on both the Marketing and Vision teams, and 4 workers are on all three teams.
How many workers are there in total?

A. 62 B. 78 C. 74 D. 66 E. 72

Answer 1

Answer: C. 74

Step-by-step explanation:

Let M= Number of workers are in marketing team .

S = Number of workers are in Sales team.

V = Number of workers are in Vision team.

As per given , we have

n(M) = 20 , n(S) = 30 , n(V) = 40

n(M∩S) = 5  ,  n(V∩S) = 6  ,  n(M∩V)  = 9

n(M∩S∩V) =4

Using formula of sets , we get

n(M∪S∪V) =n(M)+n(S) +n(V) -n(M∩S) - n(V∩S)-n(M∩V) +n(M∩S∩V)

Substitute the corresponding values , we get

n(M∪S∪V) =20+30+40-5-6-9 +4

=  74

∴ The number of workers are in at least one team = 74

Therefore , the total number of workers =74

Hence, the correct option is : C. 74