Hi mesutthefail,
The GMAT often tests you on rules/patterns that you know, but sometimes in ways that you're not used to thinking about. This prompt is really just about factoring and Classic Quadratics, but it looks a lot more complicated than it actually is.
A big part of properly dealing with a Quant question on the GMAT is in how you organize the information and 'simplify' what you've been given. This prompt starts us off with....
X^6 –12X^4 + 32X^2 = 0
This certainly looks complex, but if you think about how you can simplify it, then you'll recognize that can 'factor out' X^2 from each term. This gives us...
(X^2)(X^4 - 12X^2 + 32) = 0
Now we have something a bit more manageable. While you're probably used to thinking of Quadratics such as X^2 + 6X + 5 as (X+1)(X+5), that same pattern exists here - it's just the exponents are slightly different (even though the math rules are exactly the SAME). We can further rewrite the above equation as...
(X^2)(X^2 -4)(X^2 - 8) = 0
At this point, you don't really need to calculate much, since each 'piece' of the product should remind you of a pattern that you already know.....
X^2 = 0 --> 1 solution
(X^2 - 4) = 0 --> 2 solutions
(X^2 - 8) = 0 --> 2 solutions
Final Answer:
GMAT assassins aren't born, they're made,
Rich
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