GMAT Quant Practice | Set Theory Q2

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. A medium difficulty, GMAT 600 level, Set Theory sample question.

Question 2: 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

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Video Explanation

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Explanatory Answer | GMAT Set Theory Practice

Objective: Compute number of candidates who had none of the three.

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

Total number of candidates = 200.

Number of candidates who had at least one of the three = n(A ∪ B ∪ 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 ∪ B ∪ C) = n(A) + n(B) + n(C) - {n(A ∩ B) + n(B ∩ C) + n(C ∩ A)} + n(A ∩ B ∩ C)

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

n(A ∪ B ∪ C) is the number of candidates who had at least one of three.
As 190 candidates who attended the interview had at least one of the three,
(200 - 190 = 10) candidates had none of three.

Choice C is the correct answer.