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Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]
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24 Feb 2012, 00:42
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Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 (2) 5^(k1) = (5^k)  500 OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/is5kless ... l#p1209238
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Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]
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24 Feb 2012, 00:54
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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^(k1) = (5^k)  500 > we can solve for k and get the single numerical value of it, hence this statement is sufficient. Just to illustrate: \(5^k5^{k1}=500\) > factor out \(5^{k1}\): \(5^{k1}(51)=500\) > \(5^{k1}=125\) > \(k1=3\) > \(k=4\). Sufficient. Answer: B. Hope it's clear.
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Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]
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25 Jun 2013, 04:46



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Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]
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11 Dec 2013, 22:24
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^(k1) = (5^k)  500 > we can solve for k and get the single numerical value of it, hence this statement is sufficient. Just to illustrate: \(5^k5^{k1}=500\) > factor out \(5^{k1}\): \(5^{k1}(51)=500\) > \(5^{k1}=125\) > \(k1=3\) > \(k=4\). Sufficient.
Answer: B.
Hope it's clear. Hey Bunuel, could you explain why you can factor out 5^k1 from 5^k? I don't understand why that is possible.



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Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]
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12 Dec 2013, 03:20
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^(k1) = (5^k)  500 > we can solve for k and get the single numerical value of it, hence this statement is sufficient. Just to illustrate: \(5^k5^{k1}=500\) > factor out \(5^{k1}\): \(5^{k1}(51)=500\) > \(5^{k1}=125\) > \(k1=3\) > \(k=4\). Sufficient.
Answer: B.
Hope it's clear. Hey Bunuel, could you explain why you can factor out 5^k1 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) \(a^n*a^m=a^{n+m}\) \(5^{k1}(51)=5^{k1}*55^{k1}=5^k5^{k1}\) Hope this helps.
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]
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12 Dec 2013, 04:25
Ok now I get it, thank you very much!



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Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]
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12 Nov 2014, 01:37
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.



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Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]
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13 Jan 2018, 12:28




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