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

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.