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 two-wheeler and credit card, 30 had both credit card and mobile phone and 60 had both two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?

A . 0

B . 10

C . 20

D . 18

Solution Answer: Option B :
B

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 =n(U), where U is the universal set

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 the set of those who have a credit card and C the set of those who have a mobile phone.

We know that 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.
As 190 candidates who attended the interview had at least one of the three gadgets, n(U)−n(A∪B∪C)=200 - 190 = 10 candidates had none of three.

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