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

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Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 118
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
If n is a positive integer, is the value of b - a at least  [#permalink]

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27 Dec 2010, 20:32
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Difficulty:

35% (medium)

Question Stats:

70% (01:36) correct 30% (01:45) wrong based on 276 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 49303
Re: Inequalities + Exponents: OG DS #153  [#permalink]

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28 Dec 2010, 01:32
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2
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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Re: If n is a positive integer, is the value of b - a at least  [#permalink]

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03 Sep 2018, 01:00
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Re: If n is a positive integer, is the value of b - a at least &nbs [#permalink] 03 Sep 2018, 01:00
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# If n is a positive integer, is the value of b - a at least

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