Hi All,
In Roman Numeral questions, the arrangement of the answer choices often provides a clue as to how you could deal with the prompt in the most efficient way possible (and avoid some of the work). From these answer choices, we know that only 1 or 2 of the 3 Roman Numerals MUST be true, so we can deal with the Roman Numerals 'out of order' if it will save us some effort.
We're given a range of possible values (-1 < x < 1) and that X CANNOT be 0. We can prove/disprove the various Roman Numerals by TESTing VALUES and looking for patterns.
I. I. |x| > \(x^{2}\)
|x| will be positive for any value of X that we can choose. Since we'll be SQUARING a fraction (regardless of whether it's a positive fraction or a negative fraction), the result WILL be smaller than the |x|.
eg.
IF....
X = 1/2
\((1/2)^{2}\) = 1/4
IF...
X = -1/3
\((-1/3)^{2}\) = 1/9
Thus, Roman Numeral 1 is ALWAYS TRUE.
II. x – \(x^{2}\) > \(x^{3}\)
This Roman Numeral is probably the 'scariest looking', but it can also be dealt with by TESTing VALUES.
While....
(1/2) - \((1/2)^{2}\) > \((1/2)^{3}\)
1/2 - 1/4 > 1/8
1/4 > 1/8
Is TRUE
(-1/2) - \((-1/2)^{2}\) > \((-1/2)^{3}\)
-1/2 - 1/4 > -1/8
-3/4 > -1/8
is NOT TRUE
Thus, Roman Numeral 2 is NOT always true.
III. |1 – x| = |x – 1|
This Roman Numeral is actually a math 'truism'; it's always true for any rational value of X. You can use as many different values as you like, the resulting calculations are ALWAYS equal.
Thus, Roman Numeral 3 is ALWAYS TRUE.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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