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