Of the 200 candidates who were interviewed for a position at call centre, 100 had a two-wheeler, 70 had a credit card and 140 had a 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, 60 had both a two-wheeler and a mobile phone, and 10 had all three. How many candidates had none of the three?
  • a)
    0
  • b)
    20
  • c)
    10
  • d)
    18
Correct answer is option 'C'. Can you explain this answer?
Related Test: Test: Sets- 3

CA Foundation Question

Dinesh Kukreja
Aug 01, 2018
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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