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Re: Is 5^k less than 1,000? [#permalink]
23 Feb 2012, 23:54
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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.
Re: Is 5^k less than 1,000? [#permalink]
11 Dec 2013, 21:24
Bunuel wrote:
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.
Hey Bunuel,
could you explain why you can factor out 5^k-1 from 5^k? I don't understand why that is possible.
Re: Is 5^k less than 1,000? [#permalink]
12 Dec 2013, 02:20
Expert's post
unceldolan wrote:
Bunuel wrote:
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.
Hey Bunuel,
could you explain why you can factor out 5^k-1 from 5^k? I don't understand why that is possible.
Operations involving the same bases: Keep the base, add or subtract the exponent (add for multiplication, subtract for division) \(a^n*a^m=a^{n+m}\)
Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]
12 Nov 2014, 00:37
If we know the first few powers of 5 it gets real easy. for example \(5^2=25, 5^3=125, 5^4=25^2=625, 5^5=3125\)
I read somewhere that a gmat taker should ideally know these - decimal value of common fractions- 1/2, 1/3, 1/4, 1/5- in turn we'll know 2/3, 2/5, 3/4, 1/8... - factorials till 6! maybe - perfect squares (say till 25) - first 5 powers of 2,3,4,5
Sorry if this is bad advice. Works for some, not all.
Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]
28 Jan 2016, 05:17
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