Hi All,
While this Roman Numeral question looks a bit complicated, it just involves comparing fractions, so we can use basic Arithmetic rules to answer it (and you can solve it Algebraically or by TESTing VALUES.)
To start, you should notice that C/D and D/C appear in the two equations – meaning that we can create one gigantic comparison that uses all of the variables. That would be…
X/Y = C/D = A/B
Since each of the fractions is equal to the two other fractions, we can use cross-multiplication to show that several relationships exist among the variables:
(D)(X) = (C)(Y)
(B)(X) = (A)(Y)
(B)(C) = (A)(D)
These three deductions are important – and we can use them against the three Roman Numerals to quickly prove which are true and which are not…
I. Y/X = B/A
When we cross-multiply this equation, we get… (B)(X) = (A)(Y). This is one of the relationships that we already proved is TRUE (above).
II. X/A = Y/B
When we cross-multiply this equation, we get… (B)(X) = (A)(Y). This is the SAME relationship that we already proved is Roman Numeral 1 – so we know it’s TRUE.
III. Y/A = X/B
When we cross-multiply this equation, we get… (A)(X) = (B)(Y). Based on the original equations, we have no proof that this relationship is actually true (If all of the variables were set to equal 1, then it would be true; if the 6 variables were not the same value though, then the it would be false).
Final Answer: C
GMAT Assassins aren’t born, they’re made,
Rich
