This is a Grouping Game: Defined-Fixed, Unbalanced: Overloaded, Numerical Distribution.

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In order to track the three treatment subcategories, subscripts are used for each treatment group.

There are only two possible numerical distributions of the three treatment groups to the five prescriptions in this game:

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In addition, there are also a number of powerful inferences that can be drawn from the rules:

Second and Third Rules Combined

The second rule indicates that exactly one dietary regimen is prescribed. The third rule indicates that if F is prescribed, then O—a dietary regimen—must be prescribed. Hence, if F is prescribed, no other dietary regimen besides O can be prescribed, and thus F cannot be prescribed with M or N.

Second and Last Rules Combined

The last rule indicates that if V is prescribed, then both H and M are prescribed. As M is a dietary regimen, if V is prescribed then no other dietary regimen besides M can be prescribed, and thus V cannot be prescribed with N or O.

Second, Third, and Last Rules Combined

From the second rule, only one dietary regimen can be prescribed. The third rule indicates that if F is prescribed, then O—a dietary regimen— is prescribed. The last rule states that if V is prescribed, then H and M—a dietary regimen—is prescribed. Thus, F and V cannot be prescribed together as they both require different dietary regimens.

By applying the five not-block inferences explained above, the following answer choices can be eliminated:

Question #18: Answers (A), (B), and (C) Question #19: Answers (A), (B), and (C) Question #20: Answers (B) and (D) Question #21: Answers (A), (B), (C), and (D) Question #22: Answers (A), (C), and (E)

Many of the remaining answers can be eliminated by a simple application of the rules.

In fact, due to the many rules and restrictions, there are only five solutions to this game:

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A student who identified each of these five possibilities could easily destroy the game. However, because the game can so easily be solved by using the inferences, and identifying the possibilities is somewhat time-consuming, we do not feel it is necessary to identify the possibilities.

Your setup looks good - this is a simple grouping game, with an in-group and an out-group, as you have correctly identified and labeled. All good so far.

Your rules are accurate as well - you have correctly diagrammed each conditional rule, as well as its contrapositive. Good work.

Where you get off track a bit is with your inferences - neither of them is correct.

For the first inference, there is no double arrow; in other words, your inference seems to indicate that if O is prescribed, F must be; that is not the case. We have no rule that tells us that.

The second inference is also incorrect. It is true that, if G is prescribed, either N or U (or both) must not be prescribed; but it could be the case that G is prescribed, and N is prescribed, but U is not prescribed. That would violate your inference without violating any of the rules. Thus, the inference is not an accurate reflection of the rules and is incorrect.

When looking for inferences in this game, I would encourage you to consider the numerical limits on how many treatments from each category of treatment can or must or cannot be prescribed. That is where the inferences are to be found in this game. Beware converting causal arrows to double arrows erroneously; it is an easy mistake to make, I can tell you from experience, but it will totally derail your approach to the game.

I diagrammed the conditional rules as the following: Not O → Not F F → O

W → Not F F → Not W

N and U → G Not G → Not N or Not U

V → H and M Not H or Not M → Not V

For the conjunction of the fifth and sixth rules, it can be taken that there are three possibilities for each, right? Not G → Not N or Not U (or Not N and Not U)

Not H or Not M → Not V Not H or Not M (or Not H and Not M) → Not V

As for inferences, I focused on the implications of the second rule, 'There must be exactly one dietary regimen prescribed.' For example, if O was selected, M and N would be out, meaning that V would be out. And if M was selected, O and N would be out, meaning that F would be out. And if N was selected, M and O would be out, meaning that V and F would be out, and the remaining are G, H, U and W, which would be impossible given the fifth rule. Hence, M or O must always be selected.

LSAT2018 - one error in your diagram is in the rule about N, G, and U. Rather than:

N and U G it should be N and U G

That's because it says that IF N and U are prescribed, G cannot be (I switched the order and added emphasis, but it means the same thing)

That means that if G is prescribed, either N or U must not be.

Fix that rule and revisit your inferences, which mostly look good. For example, V and N will never be together, nor will V and O ever be together. Good inference about N - it can never be prescribed - but it's unclear how you got there given your error in the 5th rule. The way you have it written, a solution of NGHUW looks acceptable, but it should not be.

I happen to like doing this game as a template game, based on which dietary regimen is selected. Give that a try, too, and see if you make any additional inferences. There is another good one lurking out there for you to find!

ava17, you got that rule just right! If G is selected, then N or U must be out, maybe both. There is at least one inference related to that rule, but it comes from a combination of several rules working together. Nothing comes from it immediately, independent of the other rules. But, if you want to dig some, try this:

G and N in, U out

G and U in, N out

G in and N and U both out

I wouldn't do that much on a timed test, but it can be a good exercise in untimed practice. See what you get as a result! Have fun with it!