# If Goh Industrials offers only one type of bond and HCN offers only the other type of bond, then which one of the fol...

suzanne on October 16, 2019

Game setup

Can someone please set up this game for us? Thanks.

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Irina on October 16, 2019

@suzanne,

This is a challenging matching game that requires us to determine which of the six corporations - G H L R S V - issue 5-year, 10-year, or both types of bonds. Exactly four corporations offer 5-year bonds, exactly four offer-10 year bonds, and two of them offer both since we only have six corporations. We can infer that exactly two companies offer only five-year bonds, exactly two offer only 10-year bonds, and exactly two offer both.

___ ___ ___ ___ ___ ___
5 5 10 10 B B

I think the tricky part about this game is to understand that a company offering 5 or 10-year bonds does not necessarily preclude it from offering both unless the rules tell us otherwise.

The following rules apply:

(1) H cannot offer any bond that L does.

This rule tells us that if L offers 5 year bond, the H offers 10 and vice versa, and it also allows us to infer that neither H nor L can offer both, otherwise H would have no bond options left to offer. This limits the list of corporations that could potentially offer both to: G R S V

___ ___ ___ ___ ___ ___
5 5 10 10 B B
/G/R/S/V

(2) If V offers 5-year bonds, then S must offer both.

V (5) -> S (5 &10)

We can also infer that if S does not offer both, V must offer 10-year bonds.

S ~(5&10) -> V (10)

(3) If L offers 10-year bonds, then R must do so also. Note that this is an open-ended rule meaning, R could also offer BOTH.

L (10) -> R (10) v R (B)

We can infer that if R offers only 5-year bonds, then L must offer 5-year bonds as well.

R (5) -> L(5)

Taken together we have the following rules:

V(5) -> S(B)
S ~(B) -> V(10)
L(10) -> R(10) v R (B)
R(5) -> L(5)
H=/ L

There are not a lot of initial inferences in this game, meaning we'll likely have to make additional inferences for the questions.

The question asks us if G only offers one type of bond and H offers only the other type of bond, which of the following must be true?

Basically, what the question is saying if G offers 5-year bonds and H offers 10-year bonds or vice versa, which of the following must be true?

Let's consider the scenario where G offers 5-year bonds first:

G L H R/V S R/V
5 5 10 10 B B

We can infer that L offers 5-year bonds per rule (1). We have R S V left and we know that two of these companies must offer both and one company only 10-year bonds since we have no 5-year spots left. We can also infer that S must offer both per rule (2) because if they did not offer both, then V had to offer 10-year bonds and we only have 1 10-year slot left. There are no rules that dictate the exact assignment of S/V/meaning they could fill 10 and B slots in any order.

Now, let's look at the scenario where G offers 10-year bonds.
We can infer that H must offer 5-year bonds, and L must offer 10-year bonds per rule (1).

H V G L S R
5 5 10 10 B B

We are again left with S R V, we know that since L offers 10-year bonds, R must offer both as there are no spots left for only 10-year bonds. V must offer 5-year bonds and S must offer both per rule (2).

Looking back at the answer choices, we see that the only constant in every scenario is that R has to offer either both or 10-year bonds, thus we can conclude that (C) R offers 10-year bonds must be true.

Let me know if you have any further questions.