# Which one of the following could be the buildings owned by the three companies after only one trade is made?

Bryan on June 3, 2019

I had no idea where to start when attempting this.

Ravi on June 4, 2019

@Bryan,

Happy to help with the setup.

We know there are 3 real estate companies looking to trade buildings
with each other. The buildings are categorized as class 1, 2, or 3
depending on their value.

R S T

We're told that R has G (class 1), Y (class 3), and Z (class 3)

R

G1
Y3
Z3

S has F (class 1), and L (class 2)

S
F1
L2

T has K, M, and O, and they're all class 2

T
K2
M2
O2

Each trade has to be one of 3 kinds:

1) trading buildings of the same class (X for X)

2) trading 1 class 1 building for 2 class 2 buildings (1 - 22)

3) trading 1 class 2 building for 2 class 3 buildings (2 - 33)

R can trade with S and T, and S and T can trade with each other

If R and S trade, they could either trade F for G or L for Y and Z

If R and T trade, they could trade Y and Z for either K, M, or O, or
they could trade G for two of K, M, and O

If S and T trade, they could trade F for two of K, M, or O or trade L
for one of K, M, or O

We can think of the class 3 buildings as being worth 1, class 2
buildings as being worth 2 (since two class 3 buildings equal 1 class
2 building), and class 1 buildings as being worth 4 (since two class 2
buildings equal 1 class 1 building)

From this, we know that R, S, and T each have buildings that are
collectively worth the same amount. Their properties are each worth 6,
so after trades, R, S, and T must each have collective values of 6
since all trades are of equivalent value.

In looking at this question, we see that (C) says, "(C) RealProp: the
Garza Tower and the Lynch Building Southco: the Flores Tower, the
Yates House, and the Zimmer House Trustcorp: the King Building, the
Meyer Building, and the Ortiz Building"

This is totally possible

R

G1
Y3
Z3

S
F1
L2

T
K2
M2
O2

If R and S trade Y and Z for L, then we would have the same buildings
with the various companies that (C) has.

R

G1
L2

S

F1
Y3
Z3

T
K2
M2
O2

Thus, (C) is the correct answer.

Hope this helps. Let us know if you have any more questions!