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Reply Mon 12 Jan, 2009 04:49 pm
I was riffling through my little brother's PSAT materials recently when I came across this interesting question in the math section:
Quote:
12.) If Lucia is not a member of the outdoor club, then from which of the following statements can it be determined whether or not Lucia is in the hiking club?
A) Anyone in the outdoor club is not in the hiking club.
B) No one is in both the outdoor club and the hiking club.
C) Anyone who is not in the outdoor club is not in the hiking club.
D) Everyone who is in the outdoor club is in the hiking club.
E) Some people who are not in the outdoor club are not in the hiking club.
Pick an answer and justify.
 
kennethamy
 
Reply Mon 12 Jan, 2009 05:06 pm
@hammersklavier,
hammersklavier wrote:
I was riffling through my little brother's PSAT materials recently when I came across this interesting question in the math section: Pick an answer and justify.


From none of the statements can it be determined whether or not she is in the hiking club. Just go through each statement. None of them implies whether she is or is not.
 
Didymos Thomas
 
Reply Mon 12 Jan, 2009 06:05 pm
@kennethamy,
hammersklavier wrote:
12.) If Lucia is not a member of the outdoor club, then from which of the following statements can it be determined whether or not Lucia is in the hiking club?
A) Anyone in the outdoor club is not in the hiking club.
B) No one is in both the outdoor club and the hiking club.
C) Anyone who is not in the outdoor club is not in the hiking club.
D) Everyone who is in the outdoor club is in the hiking club.
E) Some people who are not in the outdoor club are not in the hiking club.


Lucia is not a member of the outdoor club. C) Anyone who is not in the outdoor club (Lucia qualifies) is not in the hiking club.

Thus, Lucia is not in the hiking club because she is not in the outdoor club, as anyone not a member of the ODC is not a member of the HC.
 
Zetherin
 
Reply Mon 12 Jan, 2009 07:05 pm
@kennethamy,
Lucia also qualifies for E. She could be one of those people that are not a member of the outdoor club and are a member of the hiking club.

I think C and E could both be justified.
 
VideCorSpoon
 
Reply Mon 12 Jan, 2009 07:26 pm
@Zetherin,
In the case of A, Lucia is not in the outdoor club. But the questions states that anyone who is in the outdoor club is not in the hiking club. So Lucia may be in the hiking club because she is not in the outdoor club. >>NO<<

In the case of B, Lucia could be in the hiking club because she is not in the outdoor club, but there is nothing definite to suggest that she could be in the hiking club from this statement other than the fact that she is not in the outdoor club and that she could possibly be in the hiking club. So she could be in the hiking club because she is not in the outdoor club, but the answer is too vague. >>NO<<

In the case of C, anyone who is not in the outdoor club is not in the hiking club. Lucia is not in the outdoor club, so she could not be in the hiking club. >>MAYBE<<

In the case of D, everyone who is in the outdoor club is in the hiking club. Lucia is not in the outdoor club, so she could not be in the hiking club. >>MAYBE<<

In the case of E, I think this is a fumble answer because the general question calls for an answer which determines whether or not Lucia is in the hiking club. The answer is indeterminate because she may or may not be one of the some who are not in the outdoor club (which she is not) which are not in the hiking club. >>NO<<

So I'm torn between C and D at face value.

The question calls for whether or not Lucia is in the hiking club. So I will have to agree with Didymos and Zetherin in that C is the most likely answer.
 
Pangloss
 
Reply Mon 12 Jan, 2009 08:01 pm
@hammersklavier,
You guys are making this way too complicated. C is the only possible answer here; remember your "venn diagrams" from math class?

D is not possible, because it simply states that everyone in the outdoor club is in the hiking club. It does not say that everyone in the hiking club is in the outdoor club. Those are two different things, and we do not know if the sets are equivalent from that statement alone.

In the case of E, it is quite obvious; she might not be one of the "some people" referred to in the statement, hence that statement does not allow us to determine anything, as the question asked.
 
Zetherin
 
Reply Mon 12 Jan, 2009 08:12 pm
@hammersklavier,
D is not an explanation because: If P then Q does not equal if Q then P. In other words, we can't deduce if she is the hiking club from her not being in the outdoor club, just because all outdoor club members are hiking club members.

Vibe, you're right. E is indeterminate since you don't know which group of the some she is from those that are not in the hiking club.

You guys are correct: Answer C.

And I would have definitely got that wrong on the exam. This is why I fail most standardized testing.
 
Didymos Thomas
 
Reply Tue 13 Jan, 2009 02:23 am
@Zetherin,
I don't like this question for standardized testing. I mean, what's the subject? Logic? I never had a logic class in high school. Sure, I dropped out after Junior year, but I did register for senior classes; logic was certainly not an option.

Good job, though, with the logic, folks.
 
Kolbe
 
Reply Tue 13 Jan, 2009 01:18 pm
@hammersklavier,
Just because you're part of a club doesn't necessarily mean you partake in what the club is for. Take football (english here, no handegg) clubs as an example, there is a board of directors, treasurers, coaches, support staff, salesmen, financiers and general riff-raff working in the merchandise shops. Not one of them actually goes out on Saturday at 2:00 in the afternoon to kick a ball around.
 
LWSleeth
 
Reply Tue 13 Jan, 2009 05:47 pm
@hammersklavier,
hammersklavier;42220 wrote:
I was riffling through my little brother's PSAT materials recently when I came across this interesting question in the math section: Pick an answer and justify.


The only way any ambiguity can come into the answer is if one loses sight of the assignment, which is to determine "whether or not Lucia is in the hiking club" from one of five statements. So, either definitely include or definitely exclude Lucia from the club by one and only one of the listed statements.

None of the statements definitely include her, but A,B,D,E allow for only the possibility of inclusion. One and only one statement definitely includes or excludes her from the club which, as others have said, is C (excluding her).
 
 

 
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