Scheduling Z's session for which one of the following days determines the day for which U's session must be scheduled?

Victoria on July 17, 2020

Hi @Skyler-Simon,

Hopefully I can help to clarify things a bit!

Let's start by going through the stimulus. We know that a gymnastics instructor is planning a weekly schedule (Monday to Friday) for six students. The instructor coaches exactly one student per day. However, as there are six students and five days, then there is one day where the instructor coaches two students separately.

M: _ _
T: _ _
W: _ _
R: _ _
F: _ _

Now let's go through the rules.

Rule 1: H must be coached before Z.
H > Z
This means that Z cannot be first on Monday and H cannot be last on Friday.

Rule 2: I is scheduled on R.

Rule 3: K is scheduled the day immediately before or immediately after the day when O is scheduled.
[KO] or [OK]

Rule 4: Neither M nor W are days where two students are scheduled.

So, what do we know now?

M: _
T: _ _
W: _
R: I _
F: _ _

The only restrictions that we have on our set-up right now are that two students could only be coached on T, R, or F, and that I must be coached on R.

The question stem asks us to select a day on which to schedule Z which would definitively determine which day U must be scheduled on. Remember that to eliminate an answer choice we only need to determine that there are multiple possible days on which U could be scheduled. Therefore, we can work through the options pretty quickly based on the rules.

We know that Z cannot be scheduled on M because H must be scheduled before Z so we can eliminate answer choice (A).

[KO] are our next most restrictive variables as they must be coached on consecutive days. So, let's try different placements for Z, K, and O and see if there are at least two possibilities for U, thereby eliminating that answer choice.

If we schedule Z on T, H would have to be scheduled on M. [KO] could be scheduled TW, WR, or RF, meaning that U could be scheduled on W, R, or F. Therefore, we can eliminate answer choice (B).

If we schedule Z on W, [KO] could be scheduled MT or RF, meaning that there are multiple possible days on which U can be scheduled. Therefore, we can eliminate answer choice (C).

If we schedule Z on F, [KO] could be scheduled MT, TW, WR, or RF. This means that there are multiple possible days on which U can be scheduled and that we can eliminate answer choice (E).

This means the correct answer must be (D) but let's double check.

If we schedule Z on R, this means that R is the day where two students are coached, and every other day will only have one student scheduled.

[KO] can therefore only be scheduled on MT or TW. Regardless of which one we choose, the other remaining spot i.e. M or W must be filled by H as H must be scheduled before Z. Therefore, U can only be scheduled on F.

We cannot schedule U on M because [KO] would have to be scheduled TW, meaning that H would be scheduled after Z, violating Rule 1.

We cannot schedule U on T because [KO] would not be able to be scheduled consecutively, violating Rule 3.

Finally, we cannot schedule U on Wednesday because [KO] would have to be scheduled MT, meaning that H would be scheduled after Z, breaking Rule 1.

M: H/K/O
T: K/O/H
W: O/H/K
R: Z I
F: U

When addressing these types of questions, always look for the placement of the variable which restricts your options the most and work from there. Here, placing Z on R means that all other days can only have one student scheduled, severely restricting our options.

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

fdaniel on July 21, 2020

This makes so much sense! Now I see why we look to Thursday first. Thank you for clearing things up!