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# Is 5^k less than 1,000? (1) 5^(k-1) > 3,000 (2) 5^(k-1) =

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SVP
Joined: 01 May 2006
Posts: 1794

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04 May 2007, 13:54
Like others, I think that the answer is (D)

5^(k-1) > 3,000
<=> 5*5^(k-1) > 5*3*1000
<=> 5^k > 15 * 1000 > 1000

Cicerone, we do not care about k an integer or not. Actually, the function f(x) = a^x is definied for all x (removing a=0 to avoid a long dicussion done a while ago with Ps_dahaya ). A great exemple of it is a = e. f(x) = e^x.

So a question remains : where does this question come from?

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Senior Manager
Joined: 03 May 2007
Posts: 270

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04 May 2007, 16:15
Is 5^k less than 1,000?

(1) 5^(k-1) > 3,000

(2) 5^(k-1) = 5^k - 500

to satisfy 5^k<1000 k has to be equal to 4
(2) is sufficient because 5^3=125 and 5^4=625-500-125

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Senior Manager
Joined: 24 Nov 2006
Posts: 349

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11 May 2007, 15:11
VJ: isn´t 1/5^0.0001 = .99983? Lim(k->1) 5^(k-1) = 1, when k approaches 1 from "the left" or "the right". I´d say the answer is D.

vijay2001 wrote:
OK- may be this example helps

Let say k=0.999 so k-1= -0.0001 => 1/5^0.0001, which will be a very big number possibilly greater than 3000. Which satisfies the condition (5^(k-1))>3000 but will not satisfy that that 5^k >1000

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Director
Joined: 09 Aug 2006
Posts: 521

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12 May 2007, 09:29
If I would go for D.

5^k > 15000 would hold true for all k irrespective of the value of k.

-Thanks.

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12 May 2007, 09:29

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