Hi All,
This question involves Exponent rules and some Arithmetic. As pacifist85 and Bunuel have approached it, the "steps" are really just about re-organizing the values until you isolate the value of X. I'd likely approach it the same way under normal circumstances.
Here though, the answer choices ARE numbers, so one of them MUST be the value of X. If you're not comfortable with all of the necessary Exponent rules (in the abstract) just yet, then you can still get to the correct answer by TESTing THE ANSWERS.
I'm going to start with the "right side" of the equation, since it's all numbers:
(6^3)(3^7)
6^3 = (2^3)(3^3)
substituting that value in, we have....
(2^3)(3^3)(3^7) =
(8)(3^10)
So the "left side" must equal (8)(3^10)
Since we're dealing with (3^10), chances are that X isn't much bigger than maybe 10 or 11.
Let's TEST X = 11....
Plugging that into the "left-side", we get...
3^13 - 3^11
We can factor out 3^11, which gives us...
3^11(3^2 - 1) =
(3^11)(9-1) =
(3^11)(8)
This is close to what we're looking for, but is a little too BIG (we need (8)(3^10)), so X MUST be smaller. There's only one answer left...
Final Answer:
Here's the proof:
IF...X = 10
3^12 - 3^10 =
3^10(3^2 - 1)
(3^10)(9 - 1)
(3^10)(8)
GMAT assassins aren't born, they're made,
Rich
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