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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 23 Feb 2012, 23:42
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Is 5^k less than 1,000?

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

(2) 5^(k-1) = (5^k) - 500
[Reveal] Spoiler: OA
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Re: Is 5^k less than 1,000? [#permalink] New post 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.

Answer: B.

Hope it's clear.
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Re: Is 5^k less than 1,000? [#permalink] New post 24 Feb 2012, 00:09
thank u :-D
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Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink] New post 25 Jun 2013, 03:46
Expert's post
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

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 21 Oct 2013
Posts: 186
Location: Germany
Concentration: Accounting, International Business
GMAT 1: 660 Q45 V36
GPA: 3.91
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Kudos [?]: 14 [0], given: 19

Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink] New post 12 Dec 2013, 03:25
Ok now I get it, thank you very much!
Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000   [#permalink] 12 Dec 2013, 03:25
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