# June 2007 - Logic Game 4 Setup

## Video Transcript:

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Alright so the fourth and final game on the June 2007 LSAT states: There are
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exactly three recycling centers in Rivertown centre 1, center 2, and center 3.
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Exactly five kinds of material are recycled at these recycling centers:
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glass, newsprint, plastic, tin, and wood. Each recycling center recycles at least
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two but no more than three of these kind of materials. The following conditions must hold:
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Alright so we have three centers; Centers 1, 2, and 3. And each of these centers
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recycles at least two but no more than 3. So, again we know that at least 2 but keep in
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mind max 3 of these materials and what are these materials?
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Well we have five options. Glass, newspaper, plastic, tin, and wood. Alright, so now let's
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turn our attention to the conditions. The first condition tells us
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any recycling center that recycles wood also recycles newsprint. So our first
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condition any again introduces sufficient. So if you recycle wood then
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you must recycle newsprint contrapositive. If you don't recycle newsprint then you don't
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recycle wood. Our second condition tells us that every kind of material at center
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2 recycles is also recycled at center 1. Again, every introduces sufficient. So if
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you are recycled in center 2 you must be recycled by center 1. Contrapositive
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If you're not recycled center 1 you can't be recycled in center 2. You should notice from that
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rule that there are only three possibilities because again we know that
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center 2 is gonna have either two or three materials and if center
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2 has two materials then center 1 is going to share those exact same materials.
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The other possibility is that center 2 has three materials and again we know since
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its max 3 center 1 is going to share those exact same three materials. But
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don't overlook the possibility that a material recycled by center 1 is not
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recycled by center 2 because being in center 1 is our necessary condition it
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tells us absolutely nothing about whether or not that material is also in
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center 2 so it is possible for Center 1 to have 3 spots and center 2 to have only 2. Ok so
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keep that in mind as we progress through this game. Turning our attention to the final condition.
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attention to the final condition only Only one of the centers recycles plastic and that recycling center does not recycle
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that recycling center does not recycled glass. So our last condition here is that we
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have exactly one plastic and that center that recycles plastic does not recycle
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glass... Contrapositive. If you recycle glass you're not recycling the only plastic. Now
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thats going to allow us to make another deduction here because if plastic were to appear in center 2
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rule two tell us it must also appear in center 1 which violates the third
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condition that there's only one plastic. Therefore plastic cannot be in recycling center 2.
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So, actually our one plastic is either going to show up in 1 or 3. Now that
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we have all of our rules in deductions clearly laid out let's turn our
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attention to question number eighteen.
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