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Is 5^k less than 1,000? (1) 5^(k+1) > 3,000

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Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink] New post 24 Feb 2012, 00:42
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Is 5^k less than 1,000?

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

(2) 5^(k-1) = (5^k) - 500
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Re: Is 5^k less than 1,000? [#permalink] New post 24 Feb 2012, 00:54
Is 5^k less than 1,000?

Is 5^k<1,000?

(1) 5^(k+1) > 3,000 --> 5^k>600 --> if k=4 then the answer is YES: since 600<(5^4=625)<1,000 but if k=10, for example, then the answer is NO. Not sufficient.

(2) 5^(k-1) = (5^k) - 500 --> we can solve for k and get the single numerical value of it, hence this statement is sufficient. Just to illustrate: 5^k-5^{k-1}=500 --> factor out 5^{k-1}: 5^{k-1}(5-1)=500 --> 5^{k-1}=125 --> k-1=3 --> k=4. Sufficient.

Answer: B.

Hope it's clear.
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Re: Is 5^k less than 1,000? [#permalink] New post 24 Feb 2012, 01:09
thank u :-D
Re: Is 5^k less than 1,000?   [#permalink] 24 Feb 2012, 01:09
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