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If n is a positive integer, is the value of b - a at least

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If n is a positive integer, is the value of b - a at least [#permalink] New post 18 Dec 2012, 09:00
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If n is a positive integer, is the value of b - a at least twice the value of 3^n - 2^n?

(1) a= 2^(n+1) and b= 3^(n+1)
(2) n = 3
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Re: If n is a positive integer, is the value of b - a at least [#permalink] New post 18 Dec 2012, 09:03
If n is a positive integer, is the value of b - a at least twice the value of 3^n - 2^n?

Question: is b-a\geq{2(3^n - 2^n)}?

(1) a= 2^(n+1) and b= 3^(n+1). The question becomes: is 3^{n+1}-2^{n+1}\geq{2*(3^n - 2^n)}? --> is 3*3^{n}-2*2^{n}\geq{2*3^n-2*2^{n}? --> is 3^{n}\geq{0}? 3^n is always more than zero, so this statement is sufficient.

(2) n = 3. Clearly insufficient.

Answer: A.
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Re: If n is a positive integer, is the value of b - a at least   [#permalink] 18 Dec 2012, 09:03
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