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

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Kudos [?]: 138 [2] , given: 210

If n is a positive integer, is the value of b - a at least [#permalink]  27 Dec 2010, 19:32
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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
[Reveal] Spoiler: OA
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Kudos [?]: 53432 [0], given: 8160

Re: Inequalities + Exponents: OG DS #153 [#permalink]  28 Dec 2010, 00:32
Expert's post
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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 $$3^n$$ – $$2^n$$?

(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.

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Exponential Equation [#permalink]  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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Kudos [?]: 53432 [1] , given: 8160

Re: Exponential Equation [#permalink]  29 Dec 2010, 09:00
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Merging similar topics.

As you can see this question was posted not only in 2006 but also just yesterday.
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Re: If n is a positive integer, is the value of b - a at least [#permalink]  28 Jul 2015, 22:06
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If n is a positive integer, is the value of b - a at least   [#permalink] 28 Jul 2015, 22:06
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