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

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.