Eleven members of Club A are also members of Club B, and five members

VERITAS PREP OFFICIAL SOLUTION

Correct Answer: B

Explanation:

(1) It is possible that the 11 members of Club A who belong to Club B include the 5 members who also belong to Club C. It is also possible that no one who belongs to Club A also belongs to Club C. Accordingly, statement 1 is insufficient.

(2) This statement answers the question directly, indicating that two people are members of both Club A and Club C. Accordingly, this statement is sufficient. Since statement (2) alone is sufficient to answer the question, the correct answer is B.

Does Statement 2 comprises of both common between A & C and common among A, B, & C. By the term exactly, I understood as if they are just common between A & C and since we do not know those who are common among all three clubs the information is insufficient; and hence Answer is E.

This question asks us if we have enough information to determine how many members of club A are also member of club C- it is important to note that conditional logic doesn't necessarily apply in set theory- in other words, we if know how many members of club C are also members of club A then we know how many members of club A are members of club c. If this were critical reasoning, for example, then the argument if all A are B then all B are A would be fallacious ( All humans are mammals but not all mammals are humans). Though if you look at this scenario on a three circle venn diagram you can see that whatever numbers falls into the intersection of Group A and C ( the circle that intersects those groups) this number applies both ways.

Statement (1) tells us the size of club B which in itself does not allow us to find the number of members in club C. Insufficient

Statement (2) answers the question. Sufficient.

Hi Bunuel

Even i had a similar problem. Can you please explain the flaw in our understanding ?

(2) Exactly two people from Club C are also members of Club A means that the overlap between C and A is 2. Below is one of the possible cases:

Thank you Bunuel for your prompt reply. I understood the case.

From St1, we don't know the number of members of club A in C. It may or may not be an overlapping set.
From St2, Its the other way of projecting the answer. If exactly 2 from Club C are present in Club A, the same is true in vice-versa.

So ans is B.

Exactly, language is imprecise and hence there gotta be an inference to solve the question...
Veritas' inferece is that AuC excludes B, we (cause I made the same inference) is that not necessary does, because the problem doesn't says so...

I've find Veritas practice kinda annoying because of that

We consider the image attached.

\(? = x + y\)

\(\left. \begin{gathered}\\
y + z = 11 \hfill \\\\
y + w = 5 \hfill \\ \\
\end{gathered} \right\}\,\,\,\,\left( * \right)\)

\(\left( 1 \right)\,\,\underline {B = 16} \,\,\,\left\{ \begin{gathered}\\
\,\,{\text{Take}}\,\,\left( {x,\underline {y,z,w,k} } \right) = \,\,\left( {0,\underline {4,6,1,5} } \right)\,\,\,{\text{viable}}\,\,\,\,\, \Rightarrow \,\,\,\,? = 0 + 4 = 4 \hfill \\\\
\,\,{\text{Take}}\,\,\left( {x,\underline {y,z,w,k} } \right) = \,\,\left( {1,\underline {4,6,1,5} } \right)\,\,\,{\text{viable}}\,\,\,\,\, \Rightarrow \,\,\,\,? = 1 + 4 = 5 \hfill \\ \\
\end{gathered} \right.\)

\(\left( 2 \right)\,\,x + y = 2\,\,\,\, \Rightarrow \,\,\,\,? = 2\,\,\,\,\left( {{\text{immediately}}} \right)\,\,\,\,\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

Solution:

Given: Eleven members of Club A are also members of Club B, and five members of Club B are also members of Club C.
To find: How many members of club A are also members of Club C.

Analysis of statement 1: Club B has 16 members.
It is also possible that five members of club B who are also members of Club C may be or may not be members of Club A.
Hence statement 1 is not sufficient. So we can eliminate A or D.

Analysis of statement 2: Exactly two people from Club C are also members of Club A.
This statement directly answers the question, which indicates there are two people who belong to Club C and Club A. Hence statement 2 is sufficient.

Hence the correct answer option is “B”.

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