GMAT® Practice : Set Language Theory

Concept: Union of 3 sets. Complement of a set.

The GMAT practice question is a problem solving question from the topic Set Theory. Concept tested: Compute the union of 3 sets and compute its complement.

Question: Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?

  1. 0
  2. 20
  3. 10
  4. 18
  5. 25

Explanatory Answer

Video explanation will be added soon

Number of candidates who had none of the three = Total number of candidates - number of candidates who had at least one of three devices.

Total number of candidates = 200.

Number of candidates who had at least one of the three = n(A \\cup) B \\cup) C)
Where A is the set of those who have a two wheeler, B is the set of those who have a credit card and C is the set of those who have a mobile phone.

n(A \\cup) B \\cup) C) = n(A) + n(B) + n(C) - {n(A \\cap) B) + n(B \\cap) C) + n(C \\cap) A)} + n(A \\cap) B \\cap) C)

Therefore, n(A \\cup) B \\cup) C) = 100 + 70 + 140 - {40 + 30 + 60} + 10
Or n(A \\cup) B \\cup) C) = 190.

As 190 candidates who attended the interview had at least one of the three gadgets, (200 - 190 = 10) candidates had none of three.

Choice C is the correct answer.

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