# Which one of the following could be true?

Ryan-Mahabir on September 17, 2019

Why is D correct? Why is E incorrect?

Thanks

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SamA on September 20, 2019

Hello @Ryan-Mahabir,

With logic games, I'm not able to see the exact question you are looking at. I can only see question 1 of the game. Can you direct me to the practice test and question number?

Thanks.

Skylar on October 13, 2019

@Ryan-Mahibir Happy to help! Let's take a look.

L, M, N, O, P, S, T

__ __ __ __ __ __ __
1 2 3 4 5 6 7

Rules:

(1) L-N
From this rule, we know that L cannot be in spot 7 and N cannot be in spot 1.
(2) M-T
From this rule, we know that M cannot be in spot 7 and T cannot be in spot 1.
(3) (L/O) _ (O/L)
(4) (M/P) _ (P/O)
(5) P = 1 or 7
Combining rules (4) and (5), we see that there are only two options for the placement of P and M. We can either have P in spot 1 and M in spot 3, or we can have P in spot 7 and M in spot 5.

The question asks what could be true, so let's look at each answer choice.

(A) says M is in spot 4. We know this is impossible, as our analysis of rules (4) and (5) show that M can only go in either spot 3 or spot 5.

(B) says N is in spot 1. We know this is impossible from our analysis of rule (1), because L needs to come in a spot before N.

(C) says O is in spot 5. Let's think about this. According to rule 3, L needs to be one spot away from O. So if O is in spot 5, L either needs to be in spot 7 or in spot 3. We know that L cannot be in spot 7 because rule (1) states that N must be in a spot later than L. Therefore, we would have to put L in spot 3. However, if we do this there's nowhere to put M, as our analysis of rules (4) and (5) show that M can only go in spots 3 or 5, and both of these spots are taken in our setup by L and O. Therefore, it is impossible to put O fifth.

(D) says S is in spot 7. Let's try this. If S is in spot 7, then we know that P needs to be in spot 1 according to rule (5). According to rule (4), this also means that M needs to be in spot 3. We can fill in spots 2 and 4 with L/O in order to fulfill rule (3). Lastly, we can put N and T in the remaining spots.

This gives us: P-L-M-O-N-T-S. Note that this is not the only possible setup with S in spot 7, but it is enough to prove this condition could be true, which is what the question is asking. This setup follows all of the rules of the game and puts S in spot 7, so (D) is correct.

(E) says T is in spot 2. From rule (1), we know that M precedes T, so we would need to put M in spot 1. However, from our analysis of rules (4) and (5), we know that M can only go in spots 3 or 5, so this is impossible.

Does this make sense? Please let us know if you have any additional questions!