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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]

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Is 5^k less than 1,000?

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

(2) 5^(k-1) = (5^k) - 500
[Reveal] Spoiler: OA

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Re: Is 5^k less than 1,000? [#permalink]

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New post 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^(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]

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New post 24 Feb 2012, 01:09
thank u :-D

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

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New post 25 Jun 2013, 04:46
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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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? [#permalink]

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New post 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^(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.

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Re: Is 5^k less than 1,000? [#permalink]

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New post 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^(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)
\(a^n*a^m=a^{n+m}\)

\(5^{k-1}(5-1)=5^{k-1}*5-5^{k-1}=5^k-5^{k-1}\)

Theory on Exponents: math-number-theory-88376.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html


Hope this helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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

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New post 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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New post 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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New post 28 Jan 2016, 06:17
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000   [#permalink] 28 Jan 2016, 06:17
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