A sample of 100 people was surveyed

GMAT Set TheoryA sample of 100 people was surveyed for the use of computers, cell phones and credit cards. 31 people had credit cards, 61 had computers and 28 had cell phones. If 11 people had none of the three and 32 people had more than one, how many had all the three?

A) 1
B) 2
C) 3
D) 4
E) 5

Solution: This is a question based on Set Theory.

Total = 100
None = 11
Net Total = 100 - 11

P(A) = Credit Cards = 31
P(B) = Computers = 61
P(C) = Cell Phones = 28

Using the formula, P(S) = P(A) + P(B) + P(C) - P(A?B) – P(B?C) – P(C?A) + P(A?B?C)

P (A?B) + P(B?C) + P(C?A) = 32 (More than One)

Plugging in values, we get,

100 – 11 = 31 + 61 + 28 – (P (A?B) + P(B?C) + P(C?A)) + P(A?B?C)
89 = 120 – (32 + P(A?B?C))
P(A?B?C) = 1

Correct Answer: A

About the Author

Gyan OneGyanOne is an educational services firm focused on premium GMAT coaching, application advisory (with a focus on ISB applications), and interview preparation for B-school admissions. GyanOne operates in the New Delhi region of India and has top global B-school alumni with a minimum score of 770 on the GMAT, as instructors. All GyanOne counsellors are professionally trained top B-school alumni with an experience of 100+ MBA applications behind them.

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