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 Dave Killoran
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#87694
Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=1469)

The correct answer choice is (D)

With any Maximum question, the correct answer reveals an absolute in the game, and consequently all Maximum (or Minimum) questions are classified as Must Be True questions.

The answer to question #18 established that a viable group of at least three courses can be composed of H, P, and T. And, because L is a random and has no restrictions, L can be added to this group without causing an issue. Thus, the correct answer has to be at least four as we know that H, L, P, and T is a viable group. Therefore, answer choice (E) can be eliminated.

Answer choice (A) can also be eliminated rather quickly because a group of seven requires all variables to be present, and each of the rules establishes that when just one of the seven courses is taken, two others cannot be taken.

The same logic applies to answer choice (B). A viable group of six courses removes just one course from consideration. But, because the three rules establish that each of H, M, and W (and, via the contrapositive, P and S) eliminates two other courses, if just one of this group is removed then other courses must be included that knock out two courses. Thus, a viable group of six cannot be created, and answer choice (B) is eliminated as well.

Some students continue the analysis pattern used on answer choices (A) and (B) to correctly conclude that a viable group of five also cannot be created (even with a group of five, there will still be too many variables remaining that eliminate other variables). However, if you are uncertain as to whether a group of five is the maximum, one strategy at this point would be to move on to the remaining questions to see if another question either confirmed that five is a viable group, or provided you with sufficient information to conclude that four was the maximum. This approach is often helpful on difficult questions where seeing additional hypotheticals would shed more light on the question at hand.

Regardless of the approach you choose, groups of five, six, and seven variables are impossible due to the numerous negative grouping rules present in this game. As shown above, a group of four is possible, and thus answer choice (D) is correct.

Note that the question establishes that there are always three or four courses taken by the student, creating a two fixed numerical distributions of courses taken and not taken:

G4-Q19.png

This information can be added to the main diagram.
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 cd1010
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#106414
What's the fastest way to prove that 5 isn't possible? None of the hypotheticals in the answer choices had 5, but then that doesn't necessarily prove that 5 can't be true. I picked 4 just bc it felt right given the other answers, but when I selected it, I wasn't 100% sure. Thanks!
 Adam Tyson
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#106420
Here's how I would think about it, cd1010:

Three different variables (H, M, and W) each knock out two others, so if any of those are in the group, 6 or 7 would be impossible. If none of them are in the group, that leaves only the other 4, which would be fine since none of them are sufficient to knock anything else out. That leaves me the possibility of 5 to consider. So my thought process went like this:

To get 5, I have to include one of the three that knocks stuff out.

If I have H, then M and S are out, but I still have to deal with W and P, which don't get along, so I can't get 5 if H is in.

If I have M, that knocks out P and T, but it also knocks out H (contrapositive of the first rule), so with M I can't have 5.

If I have W, P and S are out, but I still have to deal with other problem pairs like H and M, so I can't get 5 with W.

Oh well, I can't get 5!

It's all about thinking through how the rules interact. Apply one rule and then see what the other rules require in that situation.

One other note on this game: I usually do it with Templates. It's a little more work up front, but then I can answer this question in about 3 seconds. Worth it!

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