Q10

[m_elian]

I was wondering why its not D?

I have two possible templates for this question:
7654321
TMSVRPL
TMVSRPL

So S & V could be ranked fifth highest. But according to the answers key the correct choice is C and not D, why?

Thank you

[timmydoeslsat]

I was wondering why its not D?

I have two possible templates for this question:
7654321
TMSVRPL
TMVSRPL

So S & V could be ranked fifth highest. But according to the answers key the correct choice is C and not D, why?

Thank you

The game prompt tells us that the restaurants are ranked from best to worst (highest to lowest)

So this question is asking us what could be the fifth highest ranked if V is higher than R.

According to your diagram, you have S and V showing to rank 3rd or 4th highest.

7-6-5-4-3-2-1
......X

The X is showing what is the third highest, not fifth. Your sequencing is backwards.

7 is not the highest ranking. 1 is the highest ranking. 7 would be the worst (or lowest ranking) that a variable could receive in this game.

I will go through my set up:



The checkmarks above the variables denote that they were discussed in the rules, which all of them were in this case.

The third and fourth rules, the conditional ones, indicate biconditionality.

Essentially, A <--> B

Both variables are necessary for each other and are sufficient for each other.

In this game, we know what happens when M - S and we know what happens when S - M.

At this point, since I have the only two possible ways that S can go, I decide to run the two different ways this game can go with what I know from the first two rules which gave me two different ordering lines.

I knew initially:

R-P-L
T-M-V

None part of those ordering lines interacted with each other until the two S conditional statements were made.

So using those two ordering lines with:

P-S-M
M-S-P

(Those two conditionals essentially made the point that S is in the middle of M and P, whether M or P is before or after S.

I now have this:



Now let us look at #10.

If V-R...

We know that we are talking about our second hypothetical.

So let us recreate that diagram with the V-R condition in there.



The cloud around S is what Noah Teitelbaum would call the "cloud of uncertainty." We can place S anywhere between 3, 4, and 5. We just have to remember that we have to maintain a V-R ordering as well. So we know that who could go fifth is either S or R. S is the only answer choice listed. We know that V cannot go fifth because then R would not be able to be listed.

[ohthatpatrick]

Spectacular response.