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 twowheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a twowheeler 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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