Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

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

The game scenario produces the following initial setup:

PT42-Dec2003_LGE-G1_srd1.png

Thus, a 9-into-5 scenario exists where 5 scientists must be selected, and 4 scientists are unselected.

The first rule establishes that at least one of each type of scientist is selected:

PT42-Dec2003_LGE-G1_srd2.png

The second rule states that if more than one botanist is selected, then at most one zoologist is selected. Operationally, this means that if two or three botanists are selected, then one zoologist is selected. Via the contrapositive, if two or three zoologists are selected, then one botanist is selected. These relationships can be diagrammed as follows:

PT42-Dec2003_LGE-G1_srd3.png

Depending on the number of biologists or zoologists, then, one could also determine the exact number of chemists.

The third and fourth rules both create negative grouping relationships:

PT42-Dec2003_LGE-G1_srd4.png

The fourth rule limits the total number of chemists that can be selected to two (one of which would have to be L).

The last rule indicates that if M is selected, then P and R must be selected:

PT42-Dec2003_LGE-G1_srd5.png

In this rule, if M (a chemist) is selected, then two zoologists are selected (P, R). When this rule is combined with the second rule, we can deduce that when M is selected, exactly one botanist is selected:

PT42-Dec2003_LGE-G1_srd6.png

Note that G, H, L, and Q do not appear in any rules and are randoms.

With three groups of scientists filling five spaces, and two rules involving numbers, several Numerical Distributions are possible:

PT42-Dec2003_LGE-G1_srd7.png

A 1-3-1 distribution is impossible due to the fourth rule.

The distributions as given play a minimal role in the game (this is more of a rules-oriented game).

[A.Taarabt7]

Hello I am almost done with the powerscore bibles and am continuing my prep for the LSAT. I have come across a few games in older pt's(2004-2005) where the contrapositive answer is different than how a contra positive is labeled in the powerscore bibles.

For example in Game 1 on test 42 section 1 one of the conditions is : if more than one botanist is selected, then at most one zoologist is selected.

I labeled this rule as 2 or 3 botanist ---> 1 zoologist selected

Then I labeled the contrapositive as:if 1 zoologist is not selected ---> then 2 or 3 botanist can not be selected.

In the answer guide they had the contrapositive as 2 or 3 zoologist selected then only 1 botanist is selected. This goes against how the powerscore bible explained contrapositives and now really has me confused on how to draw that contrapositive because if I knew that specific fact than I would had 100% of the questions right for that game, and would help me immensely in the future.

[Dave Killoran]

Hey A.Taarab,

Thanks for the question. In this instance, please take a look at this again because it is actually consistent with what I talk about in the books. In the example you cited, you said that the contrapositive of the sufficient condition is: "if 1 zoologist is not selected." Think about that for a moment--what does it really mean? In this game, if 1 zoologist is not selected, then it means that either 2 or 3 zoologist are selected. Hence, when I say that "2 or 3 zoologist selected," you are looking at a statement that is perfectly identical in meaning, but I stated it in its most useful terms from a game standpoint. The same is true for the contrapositive of the necessary condition.

This type of "equivalence" in conditions is something that you see throughout the LSAT Bibles--I always turn statements into their most useful equivalents whenever possible (as should you). See page 368 (among others) for a perfect example of this happening in a game.

Please take a look at those again and see if it doesn't make sense. If it doesn't, I'd be happy to provide more examples!

Thanks!

[A.Taarabt7]

Hi Dave,

Thanks makes sense. I guess what I was missing was that gap or jump in logic from one zoologist not being selected means 2 or 3 are selected, and at most 1 botanist being selected. I failed to realize that the answer guides answer was equivalent to what I had. When I usually take the contrapositive I see it in plain straight forward form saying that the original statement works backwards, and not seeing the new inference.

[Dave Killoran]

No problem! This is actually a really good moment then, because we covered some ground that wasn't wholly clear to you yet, but that you will definitely be able to use in the future

[CCLSAT1995]

Hello,
I am having trouble setting up this game, making nferences etc.
Could someone please explain how to set this game up and make the inferences?
Thanks

[Francis O'Rourke]

This is a Defined, Overloaded, In & out grouping game.

We have to select 5 out of 9 scientists, so we need 5 scientists in the "IN" group and 4 scientists in the "OUT" group.

What makes this game a bit harder is that the 9 scientists are split into three groups of three scientists, which yields the following set of variables:

Botanists: FGH
Chemists: KLM
Zoologists: PQR


Here's one way to set up the Diagram:

Bot: ____ ____
Che: ____ ____
Zoo: ____ ____
.....IN OUT

The first rule tells us that we must have at least one of each type of scientist on the team, so there are two options for the possibile numbers of each scientist types. Either 3 of one kind and 1 each of the other two, or 2 of two kinds and 1 of the third kind: i.e 3,1,1, or 2,2,1

The second rule states that if we have two or more Botanists, there is only one Zoologist selected. This one is hard to diagram, but what it really tells us is that when you see two Botanists, you cannot have two Zoologists and vice-versa. you could diagram it this way:
2Bot 2Zoo

Thus, if the arrangement of types of variables is 2,2,1 then we have to select 2 Chemists

The third and fourth rules tell us the following
F K
M K

And the final rules tells us
M P
M R


There are not many inferences that you can get from these rules, but I saw one thing that happens when M is selected. Putting the rules together, we can see that if M is selected then we must also select P and R and K must not be selected:
M P & R, K

Which looks like this on the diagram:
Bot: .....___ ____
Che: M K
Zoo: PR ____
.....IN OUT

Since there are two Zoologists whenever M is selected, we can only have 1 Botanist, so we can also infer that when M is selected only one Botanist will be selected, and either Q or L will be selected to make 5 total scientists for the panel.

There's not much on this game to do before you get to the questions, but let me know if you have any other questions so far!

[jbrown1104]

Hi PS!

Could you please explain how you set up the game. Not quite understanding the in/out portion since we are must have 5 in and 4 out.

Thanks!
~JB

[Adam Tyson]

We chose to set up the IN group using three sub-groups based on the types of scientists, because we need at least one of each sub-category. That's why you see three slots for IN and three for OUT, to represent the three types. There can be multiple scientists from one type in each group, though, and we handled that with the numeric distrubtions.

Another approach is to make 5 slots in the IN group and 4 in the OUT group, and then label some of the IN slots as being for each type of scientist, something like this:

B __
C __
Z __
? __
? __

__
IN

Your OUT group could be just four empty, unlabeled slots, or you could label some of them if you make inferences about which ones must be out. For example, if you know for sure that at least one Chemist is always out, you could label one of the slots in the OUT group with a C.

I hope that clarifies it for you! If not, show us how you would propose to do it, or where this approach is going badly for you, and we will happily compare notes.

[T.B.Justin]

Edit: change underfunded to overloaded, thanks Adam!

I identified this game as Grouping: Unbalanced-overloaded, unfixed-numerical distribution

I worked out 4 templates each in the 3-1-1 distribution and 2-2-1 distribution- did anyone identify more?

I also found that in the 2-2-1 distributions:

When G or H is the only botanist selected and M (chemist) is selected, Q cannot be selected.