# If Z is placed in the fifth position, then which one of the following is a complete and accurate list of the position...

Zia on September 8, 2020

Setup and explanation

Can someone please explain the setup and question explanation for this game.

Victoria on September 24, 2020

Hi @zia305,

Happy to help!

We know that there are eight files to be arranged in order: H, M, O, P, V, X, T, and Z.

_ _ _ _ _ _ _ _
1 2 3 4 5 6 7 8

There are three categories of files: R, G, and Y.

R = H, M, O
G = P, V, X
Y = T, Z

Now let's go through our conditions.

Rule 1 - H must be placed before O, but not immediately preceding O

H > O

Not |HO|

Rule 2 - X must be placed before V

X > V

Rule 3 - X and V must be separated by the same number of files as separate H and O

Rule 4 - Z must immediately precede M

|ZM|

Rule 5 - the first file cannot be R

Therefore, the first file cannot be H, M, or O.

Now that we've gone through the rules, let's address the question stem. The question stem imposes an additional condition: Z is placed fifth. Rule 4 means that M must be placed sixth.

The question stem asks us which answer choice outlines the complete list of possible positions in which H could be placed.

_ _ _ _ Z M _ _
1 2 3 4 5 6 7 8

We can immediately eliminate answer choices (A) and (B) because H is a R file. Therefore, H cannot be placed first.

We can also eliminate answer choice (E) as Rule 1 tells us that H must be placed before O, but not immediately before O. If H was placed seventh, the only possible position for O would be eighth, but this would violate Rule 1.

We can also eliminate answer choice (D) because we know from Rule 4 and the additional condition imposed by the question stem that M must be placed sixth.

This means that answer choice (C) should be our correct answer but let's double check.

Option 1: H is placed second

_ H _ _ Z M _ _
1 2 3 4 5 6 7 8

We know that H and O must have the same number of files separating them as X and V. Let's put O fourth and V third. This would mean that X would be first and each pair would have one file separating them.

X H V O Z M P/T T/P
1 2 3 4 5 6 7 8

Option 2: H is placed third

_ _ H _ Z M _ _
1 2 3 4 5 6 7 8

Again, we know that H and O must have the same number of files separating them as X and V. This setup is a bit more restricted. Let's put O in seventh and V in eighth. This would mean X would be fourth and each pair would have three files separating them.

P/T T/P H X Z M O V
1 2 3 4 5 6 7 8

Option 3: H is placed fourth

_ _ _ H Z M _ _
1 2 3 4 5 6 7 8

Again, we are more restricted here. We can only put O in eighth and V in seventh. This would mean X would be third and each pair would have three files separating them.

P/T T/P X H Z M V O
1 2 3 4 5 6 7 8

Notice that each of the above scenarios meets all of our conditions.

1) H (2, 3, 4) is before O (4, 7, 8) and does not immediately precede O.

2) X (1, 4, 3) is before V (3, 8, 7).

3) X and V are separated by the same number of files as separate H and O (1, 3, 3).

4) Z (5) must immediately precede M (6).

5) The first file cannot be a R file. The first file in each of our scenarios above is either G or Y.

Hope this helps! Please let us know if you have any further questions.