#19 - Local

[Jon Denning]

Complete Question Explanation

The correct answer choice is (B).

Answer choice (A):

Answer choice (B): This is the correct answer choice.

Answer choice (C):

Answer choice (D):

Answer choice (E):

This explanation is still in progress. Please post any questions below!

C4E2EE1F-3BFF-4ED0-9159-010A005FF113 12.png

[mallie]

Hi,
I'm hoping someone can shed some light on this question.
I had the same initial setup for this question, but what threw me off was that if R is in both 5 and 10 then we know L has to go with it (contrapositive of the final rule that states L10 R10, if R is in either 5 or in both, L needs to be in 5). So the problem I ran into is that if we place R in both, and we know that L can't be in 5 we're violating a couple of rules: the obvious rule introduced in the question, but also the inference that if L is not in 5, that means it is the perfect spot for H. This felt like a trick question!

Thanks in advance for the guidance.

[Jeremy Press]

Hi Mallie!

The problem you're running into is in your interpretation of the contrapositive of the last rule in the game, that "If L offers 10-year bonds, then R must offer 10-year bonds."

The correct understanding of the contrapositive of that rule is: "If R does NOT offer 10-year bonds, then L does NOT offer 10-year bonds."

To get where you're taking the contrapositive, the original rule would've had to say "If L offers 10-year bonds, then R must offer 10-year bonds and must NOT offer 5-year bonds."

Since the original rule did not say that, it's perfectly possible that when L offers 10-year bonds, R offers both 10-year AND 5-year bonds. That's because with R offering both types of bonds, the necessary condition of the rule is satisfied (R is, in fact, offering 10-year bonds).

Very tricky rule, where you have to be very careful with the contrapositive. The only contrapositive thing we know is, if there's a situation where I can tell R is NOT offering the 10-year, then L is definitely NOT offering the 10-year bonds either.

I hope this helps!

Jeremy

[itsmathuri]

Hey there,

I'm having trouble figuring out why G and S can't just be the two that offer both bonds. Why must R offer both?
Thanks in advance!

[Robert Carroll]

mathuri,

The diagram convention in the Setup thread for this game shows what we mean by our diagram: viewtopic.php?p=47466#p47466

Two spaces are "5" because they are for the two corporations that offer ONLY 5-year bonds. Two spaces are "10" for the two corporations that offer ONLY 10-year bonds. The final two spaces are for the two corporations that offer both.

So, looking at the local condition of Question #19, if L and V aren't 5, they can't be in the "5" spaces or the "B" spaces, so they are BOTH in the "10" spaces. The "10" spaces are then full. The third rule makes R offer 10, since L does, but we have no room in the "10" spaces, so for R to offer 10, R must offer both.

Robert Carroll

[slynnnnn]

Hi PowerScore Team,

I'm having exactly the same confusion as post #2 in the thread. After reading the question, I had the setup as

5: H, __
10: L, V (neither L nor V offers 5-year bonds)
Both: __, __

The explanation given in post #3 says the contrapositive of the third rule should be

If R does NOT offer 10-year bonds, then L does NOT offer 10-year bonds.

However, because both slots in 10-year bonds are taken, meaning R does not offer 10-year bonds. Then according to the contrapositive, we get -- L does not offer 10-year bonds, which is opposite from what I have for setup.

UNLESS, when it says "neither L nor V offers 5-year bonds", it refers to that V can offer either 10-year OR both. Yet, isn't offering both bonds including offering a 5-year bond as well?

Could you please help me to explain that?

Thanks,
Lynn

[Adam Tyson]

Offering both would mean offering 5-year AND 10-year bonds, Lynn, so if V does not offer 5-year bonds then it must offer 10-year bonds only and cannot offer both. But while R must offer 10-year bonds, R COULD offer both!

Try this alternate setup:

5: H/L _ _ _
10: L/H _ _ _

(A group for 5-year bonds with four slots;
A group for 10-year bonds with four slots;
Two variables will be in both groups, the rest will each be in just one group.
H and L have to split between the groups and neither can double up)

When you do it this way, the results from this question may be a bit clearer for you. I set up this local diagram this way:

5: H _ _ _
10: L V _ _

To complete group 5, I have to add S, G and R, because neither L nor V can be there. Since L is in the 10 group, R must also be there (so R is one of the two that goes twice). Then, to finish the 10 group, either G or S has to repeat, like so:

5: HGRS
10: LVR S/G

"Both" literally means both - a company that offers both types must offer 5-year bonds and also offer 10-year bonds!

[slynnnnn]

Adam,

Thank you so much for your explanation! I totally get it now -- I was so obsessed with the thought of putting R in the 5 year bond slot that I got completely stuck right out of the gate.

Thanks again,
Lynn

[g_lawyered]

Hi P.S.,
I'm very confused because I choose answer choice C. This was my diagram:
4 slots for S (2 will be in both/repeat): S, H,G Either G/R can repeat
4 slots for L (2 will be in both/repeat): L,V, S, R

Because either G or R could repeat I thought answer choice A and B were Could Be True. And since the question is asking for What Must Be True. I thought C was correct. What makes C incorrect and B correct?
I'm confused because in the PS explanations original diagram, there's an inferences that S CANT be in repeated unless V is in 5th (as per rule 2). But yet, in the previous explanation it states S CAN go be repeated

"To complete group 5, I have to add S, G and R, because neither L nor V can be there. Since L is in the 10 group, R must also be there (so R is one of the two that goes twice). Then, to finish the 10 group, either G or S has to repeat, like so:

5: HGRS
10: LVR S/G
"

Why isn't C "Samson Gonzales offers both types of bonds." the correct answer? I think I'm having a hard time understanding the implications of Rule 2 (even after inferring the inferences in previous explanations). Can someone please clarify this for me?

Thank in advance

[Adam Tyson]

I'm not sure what you mean about 4 slots for S and 4 for L, GGIBA003@FIU.EDU. Did you mean 4 for 5-year bonds and 4 for 10-year bonds? That's what I was demonstrating earlier in this thread.

If you do it that way, then under the terms of this local question you have to put V and L both in the 10 group, because they cannot offer 5-year bonds. So far, that gives you this:

5: _ _ _ _
10: V L _ _

Putting L into the group for 10 forces H into the group for 5 per the first rule, and it also forces R into the group for 10 per the last rule, so now you have this much info:

5: H _ _ _
10: V L R _

But you still need three more variables in addition to H to finish the group that offers 5-year bonds, right? Neither V nor L can be there per the local restriction. Therefore, the three others in that 5 group must be R, S, and G. Boom, R must be in both groups! The final variable in the 10-year bond group could be S, but it could also be G, and that is why answer C COULD be true but is not something that MUST be true. Here's the final diagram if we do it with the groups this way:

5: HGRS
10: VLR S/G

S doesn't have to be in both groups, although it could be; the rule about V being in the 5 group simply isn't triggered, so the necessary condition in that rule may or may not occur.