Quant Sets

In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having either cable TV or VCR?

  1. 23/30
  2. 2/3
  3. 17/30
  4. 19/30

Answer

Let A be set of people that have Cable TV = 66%

Let B be set of people that have VCR = 20%

Both Cable TV and VCR, A ∩ B  = 10%

People that have either Cable TV or VCR = (A ∪ B) - (A ∩ B)

(A ∩ B) = A + B -  (A ∪ B)

(A ∪ B) = A + B - (A ∩ B)

(A ∪ B) - (A ∩ B) = A + B - 2*(A ∩ B)

= 66% + 20% - 2*10%

= 66%

The correct option is B.