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## #5 - Global, Must Be True, Maximum

Administrator
• PowerScore Staff
• Posts: 8310
• Joined: Feb 02, 2011
#27094
Complete Question Explanation

The correct answer choice is (D)

The question asks that you maximize the number of members each committee has in common. There are seven volunteers in total, but we know that no committee can have seven members because from the second rule F and K cannot be on the same committee. Thus, answer choice (E) is immediately eliminated.

If we remove either F or K from a committee and thereby avoid violating the second rule, the two possible groupings of the remaining six volunteers would be:

• G H J K L M (all but F)
or
F G H J L M (all but K)
Could either of these groups of six volunteers exist as the exact membership of both committees? Yes, both could—none of the other rules are negative grouping rules, and two committees of six identical members would fulfill all of the rules requiring membership. Thus, six members in common is possible, and answer choice (D) is correct.
mford
• Posts: 25
• Joined: Aug 27, 2011
#1716
The question I have is in regards to question #5 of game #1 from page 6-2 of the full course books. It asks what the largest number of members the planting and trails committee could have in common could be. Apparently the answer is six. However, given that F and K have to be on different committees (diagrammed as a F/K on the board) wouldn't that take those two variables out of the running? I don't understand how you can get more than 5 variables in common on the committees given the restrictions.
mford
• Posts: 25
• Joined: Aug 27, 2011
#1717
Nevermind, I just realized you can have FF or KK, just not F&K--Right?
Nikki Siclunov
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#1737
The fact that you cannot have F and K on the same committee means you cannot have all seven members on a given committee, and therefore the two committees cannot have 7 members in common. However, as long as either F or K is not on a particular committee, the remaining six variables can be on that committee (and the same can be said about the other committee). As a result, the two can have six members in common: either F is on both committees (without K volunteering on either committee), or - in the alternative - K is on both committees (without F volunteering on either committee).

Remember, you don't have to have F or K on either committee: the only variable that must be included on at least one committee is M.
jyglecias
• Posts: 1
• Joined: Sep 13, 2011
#1849
Hello! I am a bit confused on the answer to this question. The question asks what the largetst number of members that the planting and trails committee could have "in common." In the stimulus we are given that the committees have at least one member in common, and since the only rule restricting this would be that F and K cannot be in the same group, we are left with 6 members in each group jflhgm on one committee and lhgmkj on the other. That gives each group 6 members, however, the question asks about the most members that the two groups can have "in common." Since the committees don't have f in common or k in common, this leaves only 5 members in common in the committees. I even diagrammed it out and drew lines to match each member from one committee to the other and the only members that the two groups have in common are j, l, h, g,m. I would think that the correct answer would therefore be 5. Any help with understanding where I am going wrong would be greatly appreciated! Thank you in advance.
Dave Killoran
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#1850
Hi jyglecias,

You are really close on this one, but it looks like the F/K rule tripped you up. That rule states that they can't be on the same committee together, but you could put one (say F) on each committee and then simply remove K from both committees, giving you six members in common. Let's look at it more closely.

If we remove either F or K from a committee and thereby avoid violating the second rule, the two possible groupings of the remaining six volunteers would be:

G H J K L M (all but F)
or
F G H J L M (all but K)

You got to this point, but it looks like to me that you then made the further assumption that one of the groups was the membership of one committee, and the other group was the membership of the other committee, leaving 5 members in common. But, what if the one of the groups of six existed as the exact membership of both committees? Say G H J K L M is the complete membership of both committees—is that possible? Yes—none of the other rules are negative grouping rules, and two committees of six identical members would fulfill all of the rules requiring membership. Thus, six members in common is possible (under either scenario above, both committees are G H J K L M, or both committees are F G H J L M), and answer choice (D) is correct.

Does that help make this clear? Please let me know.

Thanks!
mariela45
• Posts: 2
• Joined: Aug 08, 2021
#89474
I am confused because of the rule if k then j must be in the committee.
I understand you are replacing F and K but the other rule with k confuses me
Beatrice Brown
• PowerScore Staff
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• Joined: Jun 30, 2021
#89510
Hi Marie! Thanks for your question

The explanation of the correct answer says that there are two possibilities where the two committees can have 6 members in common:
1. Both committees consist of: K, G, H, J, L, M
2. Both committees consist of: F, G, H, J, L, M
Neither of these possibilities violates the rule that if K is on a committee, then J is on that same committee. In the first possibility, K is on both committees, and so is J. In the second possibility, K is not on either committee, but this does not prevent J from being on both committees. The rule about K and J means that if K is on a committee, then J must also be on that committee, or if J is not on a committee, then K cannot be on that committee; however, since K not being on a committee is not in the sufficient condition, K being out does not force anything to be true about J.

The important thing to realize on this question is nothing in the rules prohibits the committees from being identical. Since they can be identical and the only negative grouping rule is that F and K cannot be on the same committee, it is possible for there to be two identical committees of 6 members, making answer choice (D) correct.

I hope this helps, and let me know if you have any further questions!

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