Hi All,
You have to be VERY careful with this question. It's actually built more to test your attention-to-detail than your "math skills"....
We're asked to find the RANGE of the roots of the following equation: |x^2 - 2| = x ?
Before you jump in and start doing calculations, there are a couple of points to note:
1) Absolute value calculations can NEVER equal a negative number. Here, we have an EQUATION set equal to X. As such, X CANNOT be NEGATIVE.
2) The answer choices are small integers, so the roots of the above equation are likely also integers that are relatively close to one another.
3) Since the question mentions ROOTS, there should be at least 2 solutions.
A bit of basic "brute force" is all that's really needed to find the roots of the equation....
Could X = 0?
|0-2| is NOT 0, so X cannot be 0
Could X = 1?
|1-2| does = 1, so X = 1 is a root
Could X = 2?
|4-2| does = 2, so X = 2 is a root
Could X = 3?
|9-2| is NOT 3, so X cannot be 3
As X gets bigger, the absolute value calculation gets even larger (and farther 'away') from X.
Thus, the only roots are 1 and 2. The range is 2-1 = 1
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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