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I have a question on Question 2 on Set Theory (main page for this website).

http://www.questionbank.4gmat.com/mba_p ... 2805.shtml

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?

I might be mistaken but I think this question is not correct. These are the problems that I see:

1) It says that of the 200 people interviewed 100 had a two wheeler. 40 had a TW AND a credit card, 60 had a TW AND a mobile, and 10 had a TW AND credit card AND mobile. Adding up all the people that had a TW AND something else comes up to 110. So it looks to me that that there can not be 100 people that had a TW since there are 110 that had a TW AND something else. At very minimum there has to be 110 people that have a TW.

2) Same for CC. 70 people have a CC but there are 80 people that have a CC AND something else. Again there has to be at least 80 people with CC.

Am I missing something?

Jorge

Hi JorgeV,

I think when the question says there were 40 people had TW and a credit card, it does not necessarily imply that these people should not have a mobile. The set of people who have all 3 (10 people) is a subset of this set. So, there are 30 people who have only TW & credit card and 10 people who have all 3.

So, with the following 3 statements
People with TW & credit card: 40
People with Mobile & credit card: 30
People with All 3: 10

The correct inference would be
People with only TW & credit card: 40-10=30
People with mobile and credit card: 30-10=20
People with all three = 10.

Adding these three, we get 60, which is still lower than the number given for people having credit card (70).

Hope this is helpful

Cheers,

Thanks that was a very useful clarification.