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June 2007, Game 4, Question 21

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Question 21. Question 21 is another local question, it's gonna give us a new if condition, so it's gonna take a new sketch that we add that condition to. The new condition here is that if all three centers do three things, so fill in three blanks under each center. Now, as we learned in the last question, if Center 1 and 2 were both doing three things, it's going to be the same three things.

Which means that Center 3 is going to have to do the solitary plastic because we can't put it in both 1 and 2 because we only get one of them. If Center 3 is doing plastic, that means that Centers 1 and 2 are both gonna have to do glass because once you do plastic you can't do glass, and anything that's 1 is also a 2. Also, as we learned back in Question 20, since we have two spaces left, and three things to fill them, N, T and W.

And by Rule 1 if we get rid of N, we also have to get rid of W. There's no way to get rid of N because if you did you would be one item short for the two spaces that are left. So in question 20, N went to Centers 1 and 2, now it's gonna have to go to all three centers because all three centers have two spaces left over they need to fill. And just like in question 20 that means that Center 1 and 2, they'll do the same thing either wood or tin.

Center 3 will do whichever one they don't do. With the sketch finished, we go on to the answer choices. With a could be true it's best just to go answer choice by answer choice looking at your sketch. Answer choice A says that only Center 2 does glass and we know from our sketch that Center 1 and 2 were both doing glass.

Answer choice B says that only Center 3 does newsprint, we know from our sketch that all three centers are doing newsprint. So cross that out, answer choice C says that only Center 1 does plastic. We know that Center 3 is the only one doing plastic not Center 1. Answer choice D says that only Center 3 does tin. And that is something that could be true, it could be that Center 3 does tin and Centers 1 and 2 each do wood.

So since we found what could be true, we have our answer, just for learning purposes, answer choice E, why is it not right? Well, answer choice E says only Center 1 recycles wood and we know that whatever 1 is doing 2 is also doing and vice versa. So it can't be that Center 1 is the only one doing wood, if it were doing it, Center 2 would be doing it as well.

That means the answer is D, on to the next question.

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