Numerical Dist. ID/Use — TV Executive example

[kky215]

Hi, I have a question about a logic game that was discussed in Chapter 9.

The game says,
"A TV executive is deciding the scheduling for 5 ads to be aired during one week - Mon through Fri. No ad contain more than 2 days per week. Exactly 1 ad is scheduled to air each day"

However, the book says that this is not a "1-1-1-1-1-1" balanced scenario.
And I just can't see why -- I am banging my head on the table for this.

Doesn't the scenario specifically state that "Exactly 1 ad is scheduled to air each day" ???? If I were to see this statement on the real LSAT (which I will be taking this June) I would have definitely drawn a table with M,T,W,Th,F as the column, and have put 5 dashes under each day of the week to indicate that EXACTLY 1 ad is scheduled to air each day, just as the constraint states.

Am I terribly mistaken?
Can someone please elaborate this?

How is the above game different from other types of games (in terms of wording) that are actually "balanced" with 1-1 scenario?

Please help!

[Dave Killoran]

Hi Kky,

Let's see if we can help you out with this (and end the headbanging ).

First, let's look at what a 1-to-1 game actually is. The idea of a 1-to-1 relationship isn't just that there is a single space for each day, but also that there is a single, separate variable for each of those days. So, with that in mind, let's turn to this particular scenario:

• 1. Do we have a single space per day?
  
  Yes, the first rule establishes that "Exactly one advertisement is scheduled to air each day." Ok, so we have that half of the equation.
  
  2. Do we have a single separate variable for each of those spaces?
  
  No, and this is where the game gets very, very tricky. The second rule in that scenario states that "No advertisement can air more than two days per week." That rule, along with the fact that the scenario does not stipulate that each advertisement must be aired, means that not all five of the advertisements have to be aired (and thus some can be doubled, or never used), and that means that the numbers aren't as simple as 1 into 1.
  
  This is why immediately after that scenario, there is a discussion of the multiple numerical distributions that can exist in that game (2-2-1-0-0, etc). Keep in mind that the 1-1-1-1-1-1 scenario is a numerical distribution, and true 1-to-1 games contain only that distribution.

The game I want you to go look at is the second game from the June 1994 LSAT (PT 11). This game looks like a simple 1-to-1 game, but making that assumption killed tons of people on test day.

Please let me know if this helps. Thanks!

[Guadalupe]

Regarding the sample question scenario: The rules do state: " Exactly one advertisement is scheduled to air each day".

I don't understand how or why they both contain zeros.
Distribution #1 2-2-1-0-0
Distribution #2 2-1-1-1-0

From our text " But, nowhere in the rules does it state that each advertisement must be aired and so some advertisements can air more than once and other advertisements do not have to air at all." (468)

I am confused, maybe because I am framing the distribution linear M T W TH FRI. If rule one is correct don't TH and FR have to include an advertisement? "Exactly one advertisement is scheduled to air each day".

Thanks in advance, I am banging my head over this one. I know I am missing something critical or obvious.

[Dave Killoran]

Hi Guadalupe,

This is a tricky one, and the problem is arising because you are "framing the distribution linear M T W TH FRI." The distribution in the book is built around "days to advertisements" (from the top of page 468). In other words, the number of times each advertisement is aired, not the exact days on which each is aired

So, for example, in the 2-2-1-0-0, it's not that Thursday and Friday have no advertisements (which, as you rightly note, be a violation of the first rule), but rather that of the five advertisements, two of them are advertised twice, one of them is advertised once, and two of them aren't advertised at all. If we were to use the variables from the scenario—A, B, C, D, and E—then something like this would be acceptable:


A B C D E

• B C E C B
  M T W Th F
  
  
  A and D are not advertised at all, so the distribution of number of days advertised (which is 5 total) to advertisements is:
  
  A = 0
  B = 2 (Monday and Friday)
  C = 2 (Tuesday and Thursday)
  D = 0
  E = 1 (Wednesday)
  
  That's a 2-2-1-0-0 when it is all added up.

This post also talks a bit more about this particular scenario, and why this works the way it does: http://forum.powerscore.com/lsat/viewto ... f=7&t=3069

Please let me know if this helps. Thanks!

[Roadto180]

Hello!

The example used on the top of the page 546 specifies in the first rule that “exactly one advertisement is scheduled to air each day,” however two of the three possible distributions listed include at least one day with no advertisements scheduled and at least one day with more than one scheduled, as follows:

2-2-1-0-0
2-1-1-1-0
1-1-1-1-1

How does that not violate the rule cited above?

Thank you for clarifying this.

[Dave Killoran]

Hi Road,

Thanks for the question! Take a closer look at what the distribution represents: the number of time each of the 5 advertisements airs. It does NOT represent how many ads appear each day, as that is fixed at 1-1-1-1-1.

If you look at each distribution, you'll note how it states things like, "Two advertisements air twice, one advertisement airs once, and two
advertisements do not air." this means that each number ultimately corresponds to an advertisement (namely A, B, C, D, and E) and those numbers indicate how many times each will air (but they aren't in A, B, C, D, and E order).

Just to be clear, looking at that first distribution for example, the 2-2-1-0-0 means that two of the ads air twice (that's the 2-2 part, which could be any two of A, B, C, D, and E), one ad airs a single time (1), and at that point we have our 5 ads for the week since there will always be 5. There's no room for the other two ads, and thus they don't air (0-0).

Please let me know if that helps. Thanks!

[Tamirra]

I think my question is along the same line as the one given above but I'm confused enough not to realize it. I'm confused that the distributions can contain any 0s as the the rule stated "Exactly one advertisement is schedule to air each day."

UNLESS the Distributions that are set up represent the ads, as in 2(ads)-2(ads)-1(ad)-0(ads)-0(ads), et al.(?)

Would the mistake in this be in setting up the days of the week as the base instead of the ads? How would I set it up otherwise?

Thanks,

Tamirra

[Dave Killoran]

Hi Tamirra,

Thanks for the question! Take a closer look at what the distribution represents: the number of time each of the 5 advertisements airs. It does NOT represent how many ads appear each day, as that is fixed at 1-1-1-1-1.

If you look at each distribution, you'll note how it states things like, "Two advertisements air twice, one advertisement airs once, and two advertisements do not air." This means that each number ultimately corresponds to an advertisement (namely A, B, C, D, and E) and those numbers indicate how many times each will air (but they aren't in A, B, C, D, and E order).

Just to be clear, looking at that first distribution for example, the 2-2-1-0-0 means that two of the ads air twice (that's the 2-2 part, which could be any two of A, B, C, D, and E), one ad airs a single time (1), and at that point we have our 5 ads for the week since there will always be 5. There's no room for the other two ads, and thus they don't air (0-0).

Please let me know if that helps. Thanks!

[Tamirra]

Yes, thanks. That's what I meant (I think) by my "UNLESS."

I have to set it up in a way not to confuse myself. I just need practice I think.

Thanks again. Love PowerScore!

Tamirra

[yusrak]

Hi Powerscore,

In chapter 9, page 550, of the logic games 2019 Powerscore Bible it explains that games that do not establish minimums increase the amount of distributions. Then it goes on to provide an example that I have been stuck on for a few days and need help understanding:

A TV exec schedules 5 ads - A B C D E - to be aired during 1 week on Mon - Fri. Exactly 1 ad is scheduled to air each day and no ad can air more than 2 days per week.

Then the LG bible explains that there are 3 distributions of days to ads:
Distribution #1: 2-2-1-0-0 (2 ads air twice, 1 ad airs once, 2 ads do not air)
Distribution #2: 2-1-1-1-0 (1 airs, 3 ads air once, 1 does not air)
Distribution #3: 1-1-1-1-1 (Each ad airs once per day. Isn't this the minimum requirement? But I thought the entire point of this example was that games that do not establish minimums increase the amount of distributions?)

I understand that the rules do not establish whether or not each ad must be aired and so that leaves open the possibility that some ads can be aired twice whereas other ads do not have to be aired at all. But why are there only 3 distributions? And why are these 3 distributions more important than other distributions? (I would think that the maximum, 2-2-2-2-2, distribution should be considered, no?) More importantly, how are these 3 distributions organized in terms of allocated versus receiving variables? Which set is being allocated in these ratios/distributions and which set is the receiver set? I first thought that the 3 distributions above of days to ads was organized as receiver variables (days) to allocated variables (ads). But that doesn't make sense because each day must have at least 1 ad. Yet the opposite is also not true because the rules do not establish that the days are being distributed across ads...or does it?

Generally speaking, I often understand the receiver set to be the spaces, base, or groups within the game diagram, is that a correct description of the receiver set?

Thank you in advance for the clarification, I look forward to reading your explanation! Sorry for all the questions, but I hope I was able to articulate my confusion clearly.

Yusra