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Set Theory - Quant/Math - CAT 2016

Question 4 the day: February 28, 2005

The CAT Practice question for the day is from the topic Set Theory.

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
Correct choice (3). Correct Answer - 10

Solution:

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 = A U B U C, where A is the set of those who have a two wheeler, B the set of those who have a credit card and C the set of those who have a mobile phone.

We know that AUBUC = A + B + C - {A n B + B n C + C n A} + A n B n C
Therefore, AUBUC = 100 + 70 + 140 - {40 + 30 + 60} + 10
Or AUBUC = 190.

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

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