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# Restrictive variables in in-out games

Alum Member
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I’m looking at PT 70’s game 2 right now and I’m trying to understand the intuition behind question 12. “Which one of the following is a pair of employees at least one of whom must be on the team?” Would someone mind explaining to me how they know which members must be in in an conditional chain for an in-out game? Is the logic that it’s the friendly variable that doesn’t kick many other variables out?

Any help would be much appreciated!

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• Alum Member 🍌🍌
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This type of question has repeated several times across in and out game history. My recommendation would be to always start your testing of who must in with the necessary conditions for any elements. The reasoning for this is twofold:
1. The removal of the necessary conditions knocks out the sufficient element, thus limiting our ability to get to the number of those needed to be in: in 70-2 that number would be 4
2.The removal of the necessary conditions for certain elements gets rid of a number of pieces leaving us with slim pickings for what we can create a valid world out of: possibly violating a stated condition.

Question 12: is the second option, we have enough "left over" to make 4 (the necessary amount for the game) but we are left forcing everything we have into the "in" category. There is a violation of the M---->O by doing so.

For more information of this question type please see: PT 11-Game 3 Question 19, PT 20 Game 2 question 12

David

• Alum Member 🍌🍌
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M O P S T W Y Z
These are our game pieces. We test the answer choices in 12, by depriving our game board of both elements.
M O P S T W Y Z

W requires Y, so we must now remove W, because we no longer have Y.
M O P S T W Y Z

S requires T, we must now remove S
M O P S T W Y Z

We are left with filtering everything we have left into the "in" group to meet the requirement of "at least 4" :
M O P Z
MOPZ is not a valid construction: we in violation of the first rule.

Therefore any valid team we construct must contain at least one of these two elements: TY

David

• Alum Member
555 karma

Awesome!!! Thanks so much David. I'm so happy my intuition was almost there. I was noticing that all of the safe choices were where you failed the sufficient or satisfied the necessary, but problems occurred when you triggered the necessary/contrapositive. And thanks for giving another question to look at--super helpful!

Numbers seem to be really important too in questions like these. Asking ourselves what puts us over the edge.