gmatpapa
Set A, B, C have some elements in common. If 16 elements are in both A and B, 17 elements are in both A and C, and 18 elements are in both B and C, how many elements do all three of the sets A, B, and C have in common?
(1) Of the 16 elements that are in both A and B, 9 elements are also in C
(2) A has 25 elements, B has 30 elements, and C has 35 elements.
fozzzy
Hi,
Could you please explain this particular question? Thanks in Advance!
Dear Fozzzy,
I got your p.m. and I am happy to help.
First, the prompt.
16 elements are in both A and B --- this 16 includes elements that are just in A & B as well as elements in A & B & C.
17 elements are in both A and C --- this 17 includes elements that are just in A & C as well as elements in A & B & C.
18 elements are in both B and C --- this 18 includes elements that are just in B & C as well as elements in A & B & C.
To understand this, think about real world categories (these categories will include more elements than 18). Suppose
A = set of males
B = set of people who hold public office in the United States of America
C = set of people who are African-American.
Some people are just in one of these categories. I'm a member of A, but not B or C. My senators Dianne Feinstein & Barbara Boxer are members of B, but not A or C. Oprah Winfrey & Alice Walker are members of C but not A or B. The US Secretary of State, John Kerry, is a member of sets A & B but not C. By contrast, the US President, Barack Obama, is a member of all three sets. If I say: list people who are members of A & B, then it would be perfectly acceptable to list both Kerry and Obama --- all males who hold public office would be listed, irrespective of their race. The set of people in A & B, male office holders, would include some members who were part of C (such as Obama) and some members who were not part of C (such as Kerry).
Now, the statements.
(1) Of the 16 elements that are in both A and B, 9 elements are also in CWell, the members of the intersection set A & B includes some elements that are part of C and some elements that are not part of C. The 9 elements of (A & B) who are also included in C are the the nine elements common to all three sets. The remaining 7 would be those elements that, like John Kerry, are members of A & B but not C. Thus, this statement gives us enough information to answer the question, so it is sufficient.
Did you have a question about the second statement as well?
Mike