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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 27 Dec 2010, 19:32
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72% (02:57) correct 28% (01:20) wrong based on 53 sessions
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
[Reveal] Spoiler: OA
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Re: Inequalities + Exponents: OG DS #153 [#permalink] New post 28 Dec 2010, 00:32
Expert's post
tonebeeze wrote:
Here is a tricky DS problem that I came across today:

If n is a positive integer, is the value of b – a at least
twice the value of 3^n2^n?

(1) a = 2^{n+1} and b = 3^{n + 1}
(2) n = 3


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) --> 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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Exponential Equation [#permalink] New post 29 Dec 2010, 08:55
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


Hi, this was posted in 2006 but it doesn't give a good explanation on how to arrive at the answer. Could someone please explain. Thanks
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Re: Exponential Equation [#permalink] New post 29 Dec 2010, 09:00
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Re: Exponential Equation   [#permalink] 29 Dec 2010, 09:00
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