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Help with Radical Simplification

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by Steve90036 » Fri Jul 10, 2009 6:46 pm
Hello, I am working on OG12 #154 (DS). I a using the GMAT Hacks Guide to the official guide, and can not for the life me, figure out how is simplified this equation:

3^n+1 - 2^n+1 = 3^n(3^1)- 2n(2^1) = 2 (1.5(3^n)-2^n)

I understand the the X^z+y=X^z*X^y

What I DO NOT understand is how he broke out a 2 and 1.5. Can someone please help me understand this.

Thanks,

-Steve
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by ssmiles08 » Fri Jul 10, 2009 7:10 pm
I don't know what exactly you did there as I don't have GMAT hacks

but the question is asking if at least b - a = 2*(3^n - 2^n)

1) tells you a = 2^(n+1) and b = 3^(n+1)

from here you can substitute and see if: 3^(n+1) - 2^(n+1) = 2*(3^n - 2^n)?

2*(3^n - 2^n) = 2*3^n - 2^(n+1) when expanded.

as you can see then, 2*3^n - 2^(n+1) is NOT equal to 3^(n+1) - 2^(n+1), and is definitely less than the value of 3^(n+1) - 2^(n+1).

since we know that they are NOT equal and 2*3^n - 2^(n+1) < 3^(n+1) - 2^(n+1) , we can determine that this statement is sufficient.

2) gives you n= 3. Insufficient b/c doesn't tell us anything about a and b.

(A)
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