Setup and Rule Diagrams

[Dave Killoran]

Hi AT,

This is one of those games where the rules can't represented in a nice, easy fashion. Instead, try to mentally focus on the distributions and the supervisory relationships, and remember that F is a technician, and G has to me a manager or president.

Please let me know if that helps. Thanks!

[Paul Marsh]

For this setup, we know that there are only 2 possible numeric distributions in the game: 1 president, 2 managers, and 2 technicians; or 1 president, 1 manager, and 3 technicians. We'll refer to these distributions as 1-2-2 and 1-1-3. We know that in the 1-2-2 distribution, each manager supervises exactly one technician (since each manager has to supervise at least one technician and there are only two technicians to choose from). We also know that F must be a technician, and that G must be a manager or president (if we're in the 1-2-2 setup, G must be the president; if we're in the 1-1-3 setup G can be either the manager or the president).

Those inferences (especially the numeric distribution one) will help us a lot for all questions 1-6. I'll have posted a short explanation of all of those questions individually here: https://forum.powerscore.com/lsat/viewforum.php?f=385

[gabmarr]

How do we conclude each manager can only supervise one employee? The rules mention each manager supervises “at least” one employee, not “exactly one”.

[Paul Marsh]

Hey gabmarr! So I think you're asking about why, in the 1-2-2 distribution, each manager can only supervise one employee. (Because remember that in the 1-1-3 distribution, the manager can certainly supervise more than one employee! For example if G is the sole manager, she of course will supervise 2 technicians per our rules.)

Now, why is it that each manager in the 1-2-2 distribution only supervise one employee? Well, like you said, we know from Rule #3 that each manager has to supervise at least one employee. And we also know from the Setup that in this company, managers are only allowed to supervise technicians. And in this distribution we have 2 managers and only 2 technicians for them to supervise. So if the first manager supervised both technicians, there wouldn't be any technicians left for the second manager to supervise! That would violate Rule #3. Same thing if the second manager supervised both technicians, there wouldn't be anyone left for the first manager to supervise. (It's like this: if you and I both are going to eat at least one apple, and there's only two apples, then that means we both get exactly one apple!) So in this 1-2-2 distribution, each manager supervises exactly one technician.

Hope that helps!

[relona]

I'm not exactly sure how in the 1-1-3 distribution, if G is the president, it would supervise one manager and one technician. Can a president supervise a technician? I thought managers supervised technicians and presidents supervised managers. Can I get some clarification on this?

[Robert Carroll]

relona,

There is no indication in the scenario or rules that the president cannot supervise a technician. As with anything in the games, if the scenario, rules, and inferences haven't disallowed it, anything is possible. So the reason the president could supervise a technician is because nothing disallows it.

Robert Carroll

[pmuffley]

Hello- Hoping to get some clarity here. I sort of get the distributions...we can't have a 1:3:1 because 3 people can't supervise 1 employee, right? However, I felt like the instructions were contradictory on this point because they say:

"Other employees are each supervised by exactly one employee, who is either the president or a manager. "

I took this to mean that each employee is supervised by only one manager or by the only president.

BUT then in the rules it says...

"Each manager supervises at least one employee."

"At least" leaves the possibility for 1 or more.

I know it is not contradictory and I'm just not seeing things clearly, but I was hoping maybe you could explain it a little differently because I am not understanding the previous explanation on this point.

Thank you,

[Rachael Wilkenfeld]

Hi pmuffley,

This game gets confusing because of the unequal relationship between supervisors and supervisees. Supervisors can supervise multiple people, but supervisees can only be supervised by one person. That means that each tech and manager has exactly 1 supervisor, but the president and managers have 1 or more supervisees.

Let's look at how this breaks down in the game itself.

We have two possible distributions. 1-1-3 and 1-2-2.

For the 1-1-3, we have 1 president, 1 manager, and 3 technicians. That means 4 people need supervised (1 manager, and 3 techs) and 2 people can supervise (the manager and the president). We might think that there's a lot of leeway in how many people can be supervised by each supervisor here. 3 by the president and 1 by the manager, 3 by the manager and 1 by the president or 2 by each of the manager and president. But our last rule says that G supervises EXACTLY 2 people. That means the only option for distributions of supervision is the 2 for manager and 2 for president so that G can supervise exactly 2 people.
The 1 president must supervise the manager, because no one else can. They also supervise 1 technician.
The 1 manager must supervise 2 technicians.

For the 1-2-2, we have 1 president, 2 managers and 2 technicians. We still have 4 people that need supervised (2 managers and 2 techs) but now we have 3 people to supervise (1 president and 2 managers). We only have 1 potential breakdown here, 2 people for 1 supervisor, 1 person for each of 2 supervisors (adding up to 4 people supervised and 3 people doing the supervising). Further, we can figure out the positions for each.
1 president (G) supervises 2 managers. We know this because the president is the only one who can supervise managers, so the president must supervise 2 people. G has to be the president here, because G must supervise exactly 2 people. Each of the managers supervises 1 technician.

Those are really the only options. The rule that G must supervise exactly 2 people limits possibilities quite a bit.

Hope that helps!

[ange.li6778]

Hi powerscore, this game tripped me up because I wasn't able to effectively diagram the rules about who can or can't supervise whom. I don't see a full diagram for this game in this thread either, so is there any way to effectively represent the supervision rules visually? or do I just have to fix them in my mind? Thanks in advance!!

[Adam Tyson]

You don't have to do it all in your head, ange.li6778! I'll describe it here, but drawing it in this format would be challenging (at least for me).

First, in the 1-2-2 scenario, I would draw it like a pyramid with P at the top above a layer with two Ms, and each M would be directly above a T. Vertical lines from the P to both Ms and from each M to a T would indicate who supervises whom. In that scenario we would know that G must be P, because G has to supervise two employees and only P does that. F would be a T, and the remaining three variables would be interchangeable among the remaining three spaces.

For the 1-1-3 scenario, I would again draw a P at the top, this time above just one M, which would be above three Ts. This one is a little tougher because we cannot be sure if G is P or M, so we might want to split this into two templates. In one of them, G supervises the sole M, but also supervises one T. F is still a T, but we cannot be sure if P supervises F or not. Meanwhile, the M supervises the other two Ts, and F may or may not be one of them.

In the second template for the 1-3-3 scenario I would draw the same pyramid, but I would put G in the M spot. We still don't know who supervises F, but F is, as always, a T. Maybe just draw an "FT" block to the side in both cases?

Basically, I show the concept of "supervision" by drawing a vertical line from an upper layer position (P or M) down to a lower layer position (M or T).

I hope that translates well for you to a useful diagram!