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?

- 0
- 20
- 10
- 18
- 25

#### Explanatory Answer

Video explanation will be added soonNumber 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.

## GMAT Sample Questions | Topicwise GMAT Questions

### Target Q-51 in GMAT Quant. Make it a reality @ INR 3000!

Most __Comprehensive & Affordable GMAT Online Course__ for Quant. 20 topics.

Focused preparation for the hard-to-crack eggs in the GMAT basket!