Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 15:58

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 20 Feb 2012
Posts: 41
Followers: 1

Kudos [?]: 348 [3] , given: 6

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

### Show Tags

23 Feb 2012, 23:42
3
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:23) correct 27% (01:51) wrong based on 365 sessions

### HideShow timer Statistics

Is 5^k less than 1,000?

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

(2) 5^(k-1) = (5^k) - 500
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93662 [3] , given: 10583

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

### Show Tags

23 Feb 2012, 23:54
3
KUDOS
Expert's post
3
This post was
BOOKMARKED
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.

Hope it's clear.
_________________
Intern
Joined: 20 Feb 2012
Posts: 41
Followers: 1

Kudos [?]: 348 [0], given: 6

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

### Show Tags

24 Feb 2012, 00:09
thank u
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93662 [0], given: 10583

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

### Show Tags

25 Jun 2013, 03:46
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

_________________
Current Student
Joined: 21 Oct 2013
Posts: 194
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Followers: 1

Kudos [?]: 37 [0], given: 19

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

### Show Tags

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.

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.
Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93662 [0], given: 10583

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

### Show Tags

12 Dec 2013, 02:20
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.

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.
_________________
Current Student
Joined: 21 Oct 2013
Posts: 194
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Followers: 1

Kudos [?]: 37 [0], given: 19

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

### Show Tags

12 Dec 2013, 03:25
Ok now I get it, thank you very much!
Intern
Joined: 23 Aug 2014
Posts: 42
GMAT Date: 11-29-2014
Followers: 0

Kudos [?]: 9 [0], given: 28

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

### Show Tags

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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13549
Followers: 578

Kudos [?]: 163 [0], given: 0

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

### Show Tags

28 Jan 2016, 05:17
Hello from the GMAT Club BumpBot!

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000   [#permalink] 28 Jan 2016, 05:17
Similar topics Replies Last post
Similar
Topics:
If b > 1, is integer b less than 11? 3 06 Dec 2016, 06:29
40 Is 5^k less than 1,000? 13 26 Dec 2012, 03:41
Is less than 5000? (1)4^x+1 > 16000 (2)4^x+1 = 4^x + 1 30 Jun 2011, 18:16
3 Is 5^k less than 1,000? 9 07 Dec 2010, 17:19
9 Is 5^k less than 1,000? 12 22 Jun 2008, 23:20
Display posts from previous: Sort by