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Sets problem

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by metallicafan » Tue May 01, 2012 4:27 pm
Each of the terms in sets R, S, and T are positive integers. If 9 of the integers in R are also in S, 12 of the integers that are in S are also T, and 4 of the integers that are in R are also in T, how many unique positive integers are contained in the three sets?

(1) 1 of the integers is in R, S, and T.
(2) R has 20 terms, S has 24 terms, and T has 30 terms.
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Source: — Data Sufficiency |

by aneesh.kg » Wed May 02, 2012 11:39 am
Total = R + S + T - [R&S + S&T + T&R] + R&S&T

Given:
R&S = 9
S&T = 12
T&R = 4

the 'Total' is being asked.

Statement(1):
Total = R + S + T - [9 + 12 +4] + 1
INSUFFICIENT.

Statement(2):
Total = 20 + 24 +30 - [R&S + S&T + T&R] + R&S&T
INSUFFICIENT.

Upon combining,

Total = 20 + 24 +30 - [9 + 12 +4] + 1

SUFFICIENT.

(C) is the answer.
Aneesh Bangia
GMAT Math Coach
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