It is currently 20 Oct 2017, 15:26

### 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: 42

Kudos [?]: 489 [3], given: 6

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

### Show Tags

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

Difficulty:

35% (medium)

Question Stats:

73% (01:26) correct 27% (01:54) wrong based on 410 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

Kudos [?]: 489 [3], given: 6

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129030 [3], given: 12187

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

### Show Tags

24 Feb 2012, 00:54
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.
_________________

Kudos [?]: 129030 [3], given: 12187

Intern
Joined: 20 Feb 2012
Posts: 42

Kudos [?]: 489 [0], given: 6

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

### Show Tags

24 Feb 2012, 01:09
thank u

Kudos [?]: 489 [0], given: 6

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129030 [0], given: 12187

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

### Show Tags

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

_________________

Kudos [?]: 129030 [0], given: 12187

Current Student
Joined: 21 Oct 2013
Posts: 193

Kudos [?]: 44 [0], given: 19

Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: Is 5^k less than 1,000? [#permalink]

### Show Tags

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.

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.

Kudos [?]: 44 [0], given: 19

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129030 [0], given: 12187

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

### Show Tags

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.

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.
_________________

Kudos [?]: 129030 [0], given: 12187

Current Student
Joined: 21 Oct 2013
Posts: 193

Kudos [?]: 44 [0], given: 19

Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]

### Show Tags

12 Dec 2013, 04:25
Ok now I get it, thank you very much!

Kudos [?]: 44 [0], given: 19

Intern
Joined: 23 Aug 2014
Posts: 42

Kudos [?]: 10 [0], given: 28

GMAT Date: 11-29-2014
Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000 [#permalink]

### Show Tags

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

Kudos [?]: 10 [0], given: 28

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16636

Kudos [?]: 273 [0], given: 0

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

### Show Tags

28 Jan 2016, 06:17
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.
_________________

Kudos [?]: 273 [0], given: 0

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