Hi canbtg,
When posting PS questions, you should make sure to post the 5 answer choices. Without having those answers, we can still figure out which Roman Numerals must be true, but we'll have to deal with all of them (and we won't actually know which of the 5 answers is correct).
In this Roman Numeral question, we can simplify the inequality and use some Number Properties to determine what MUST be true.
First, we're told that X is NEGATIVE. This is important to know (and we'll come back to it later)....
Next, we're given 4 < 5 - XY < 5
Subtract 5 from each of the three items....
-1 < -XY < 0
Multiply each item by -1 (and don't forget to 'flip' the inequalities)....
1 > XY > 0
Now, since we we were told that X is NEGATIVE, we have...
1 > (Neg)(Y) > 0
Now we can deal with the three Roman Numerals...
I. Y < 0.
Since (Neg)(Y) > 0, Y MUST be negative. Roman Numeral I is ALWAYS TRUE
II. XY < 1
We've already proven that 1 > XY > 0, so Roman Numeral II is ALWAYS TRUE
III. X/Y > 1
We don't know the relative values of X and Y; we just know that they're both NEGATIVE.
IF....X = -.5, Y = -1, then X/Y = .5/1 = 1/2. Thus, Roman Numeral III is NOT always true.
GMAT assassins aren't born, they're made,
Rich
