It is currently 14 Dec 2017, 13:08

# Decision(s) Day!:

CHAT Rooms | Wharton R1 | Stanford R1 | Tuck R1 | Ross R1 | Haas R1 | UCLA R1

### 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?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178

Kudos [?]: 3654 [0], given: 0

Is 5^k less than 1,000? [#permalink]

### Show Tags

26 Dec 2012, 03:41
24
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

66% (01:52) correct 34% (02:05) wrong based on 1198 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 [?]: 3654 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42607

Kudos [?]: 135655 [2], given: 12705

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

### Show Tags

26 Dec 2012, 03:42
2
KUDOS
Expert's post
7
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 [?]: 135655 [2], given: 12705

Intern
Joined: 07 Oct 2012
Posts: 8

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

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

### Show Tags

06 Apr 2013, 22:12
Is 5^k less than 1,000?

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

(2) 5^(k-1) = 5^k - 500

I would to ask why is this wrong
(1) 5^(k+1) > 3000

5^(k+1) > 5^5
Hence, k+1= 5 , k =4

If so, 5^4 is less than 1000. The answer should b sufficient for (1).

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

Intern
Joined: 06 Apr 2013
Posts: 2

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

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

### Show Tags

07 Apr 2013, 08:40
From 1: (5^k)*5 > 3000
(5^k) > 600
Hence, insufficient.

From 2: Solving the equation k = 4

Hence, B
_________________

Please hit the +1 Kudos button if you found my post informative.

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

Math Expert
Joined: 02 Sep 2009
Posts: 42607

Kudos [?]: 135655 [0], given: 12705

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

### Show Tags

07 Apr 2013, 22:03
LMKong wrote:
Is 5^k less than 1,000?

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

(2) 5^(k-1) = 5^k - 500

I would to ask why is this wrong
(1) 5^(k+1) > 3000

5^(k+1) > 5^5
Hence, k+1= 5 , k =4

If so, 5^4 is less than 1000. The answer should b sufficient for (1).

First of all 5^5=3,125>3,000, thus 5^(k+1) > 3000 does NOT necessarily mean that 5^(k+1) > 5^5.

Next, even if we had 5^(k+1) > 5^5 it still does not mean that k+1=5. It means that k+1>5 --> k>4.

Hope it's clear.
_________________

Kudos [?]: 135655 [0], given: 12705

Intern
Joined: 02 Jul 2013
Posts: 26

Kudos [?]: 7 [0], given: 91

Concentration: Technology, Other
GMAT Date: 01-17-2014
GPA: 3.84
Re: Is 5^k less than 1,000? [#permalink]

### Show Tags

21 Nov 2013, 08:15
Bunuel,
How did you factor out this
5^k-5^{k-1}=500 --> factor out 5^{k-1}: 5^{k-1}(5-1)=500

is that possible?

Kudos [?]: 7 [0], given: 91

Manager
Joined: 09 Apr 2013
Posts: 148

Kudos [?]: 125 [3], given: 24

Location: India
WE: Supply Chain Management (Consulting)
Re: Is 5^k less than 1,000? [#permalink]

### Show Tags

21 Nov 2013, 10:05
3
KUDOS
Statement(1) : 5^(k+1) > 3000
The above inequality can be reduced to 5^k > 600. From this, we clearly know few possible values for k i.e., 4,5,6,..
Substituting these values in the inequality given in the question gives away both yes and no answers.
k = 4, 5^(4-1) < 1000
k = 5, 5^(5-1) < 1000
k = 6, 5^(6-1) > 1000
Hence statement(1) is not sufficient.

Statement(2): 5^(k-1) = 5^k - 500
Reducing the above inequality, 4/5 * 5^k = 500
So 5^k = 625 = 5^4. Clearly k = 4 and the original inequality is satisfied: 5^4 < 1000.
Hence statement(2) is sufficient.

_________________

+1 KUDOS is the best way to say thanks

"Pay attention to every detail"

Kudos [?]: 125 [3], given: 24

Retired Moderator
Joined: 29 Oct 2013
Posts: 285

Kudos [?]: 505 [8], given: 197

Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Re: Is 5^k less than 1,000? [#permalink]

### Show Tags

23 May 2014, 13:08
8
KUDOS
1
This post was
BOOKMARKED
The biggest take-away here should be that we don't need to solve the St-2. The moment you start solving St2, you have fallen for GMAT's classic time waster trap. See below.

Statement1: As 5^(k+1) > 3,000 --> k>4 and hence insufficient
Statement2: We dont need to solve the equation. Since this is an EQUATION (and not an inequality) with one variable, we will get the exact value of k and we will be able to answer the question one way or the other. SUFFICIENT.
_________________

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Kudos [?]: 505 [8], given: 197

Intern
Joined: 20 Dec 2013
Posts: 40

Kudos [?]: 5 [0], given: 2

GMAT 1: 620 Q48 V27
GPA: 3.9
Re: Is 5^k less than 1,000? [#permalink]

### Show Tags

11 Dec 2014, 05:24
Can some one explain how opt B is the ans.

And choice is B

Pls see attachment
Attachments

Exponents.PNG [ 6.02 KiB | Viewed 6383 times ]

Kudos [?]: 5 [0], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 42607

Kudos [?]: 135655 [0], given: 12705

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

### Show Tags

11 Dec 2014, 05:33
gameboy11887 wrote:
Can some one explain how opt B is the ans.

And choice is B

Pls see attachment

Merging topics.

_________________

Kudos [?]: 135655 [0], given: 12705

Intern
Joined: 12 Aug 2014
Posts: 18

Kudos [?]: [0], given: 72

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

### Show Tags

16 Jan 2015, 06:48
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.

Hi can we generalize that " Every time when there is an equation with exponential expressions and there is only one single variable exponent(and no other variable in equation), we can always find the value of that exponent." Is there any exception possible?

Kudos [?]: [0], given: 72

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10391

Kudos [?]: 3690 [4], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: Is 5^k less than 1,000? [#permalink]

### Show Tags

16 Jan 2015, 12:08
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
Hi All,

1) At NO POINT does it state that K has to be an integer.
2) It's clearly based on exponents, so some exponent rules/patterns MUST be involved.

We're asked if 5^K is < 1,000. This is a YES/NO question.

Fact 1: 5^(K+1) > 3,000

In this Fact, notice how the exponent (K+1) differs from the exponent in the question (K). There's an exponent rule that accounts for this difference.

As an example, consider...
5^2 = 25
5^3 = 125
Notice how 5^3 is "5 times" greater than 5^2? This difference occurs because the base is 5 and we're increasing the exponent by 1. It can also be used in reverse....

5^3/5^2 = 5^(3-2) = 5^1 = 5

This is a standard rule about "dividing" exponents with the same base --> we SUBTRACT the exponents.

With Fact 1, we're dealing with 5^(K+1) and the question is dealing with 5^K. This means that DIVIDING 5^(K+1) by 5 will give us 5^K:

5^(K+1)/5^1 = 5^(K+1-1) = 5^K.

This is all meant to say that we can DIVIDE both sides of this inequality by 5, which gives us...

5^(K+1) > 3,000
5^K > 600

IF....
5^K = 601 then the answer to the question is YES
5^K = 1,001 then the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: 5^(K-1) = 5^K - 500

This is a 1 variable, 1 equation "system", so we CAN solve it (and there will only be 1 answer). Even if you did not know that, it's still easy enough to get to the solution.... Since most Test Takers are better at basic multiplication than they are at manipulating higher-level exponents, here's how you can "brute force" the solution:

5^1 = 5
5^2 = 25
5^3 = 125
5^4 = 625
5^5 = 3125

Find two consecutive powers of 5 that differ by 500 and you have the solution to the above equation.
5^4 - 5^3 = 625 - 125 = 500
Fact 2 is SUFFICIENT.

[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3690 [4], given: 173

Non-Human User
Joined: 09 Sep 2013
Posts: 14839

Kudos [?]: 287 [0], given: 0

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

### Show Tags

24 Feb 2016, 10:21
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 [?]: 287 [0], given: 0

Retired Moderator
Joined: 12 Aug 2015
Posts: 2208

Kudos [?]: 903 [0], given: 607

GRE 1: 323 Q169 V154
Re: Is 5^k less than 1,000? [#permalink]

### Show Tags

08 Mar 2016, 21:18
Here the question will be fairly easy if we consider it as an inequality expression rather than Exponents as never does it state that K is an integer..
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 903 [0], given: 607

Non-Human User
Joined: 09 Sep 2013
Posts: 14839

Kudos [?]: 287 [0], given: 0

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

### Show Tags

12 Apr 2017, 05:13
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 [?]: 287 [0], given: 0

Manager
Joined: 12 Jun 2016
Posts: 225

Kudos [?]: 46 [1], given: 149

Location: India
WE: Sales (Telecommunications)
Re: Is 5^k less than 1,000? [#permalink]

### Show Tags

20 Aug 2017, 03:24
1
KUDOS
Hello Moderators,

Do you think this OG question needs to be made math friendly? Its a 600-700 Level question and it would Nicer to have the Stem made Math friendly :-)

Is 5^k less than 1,000?

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

(2) 5^(k-1) = 5^k - 500

_________________

My Best is yet to come!

Kudos [?]: 46 [1], given: 149

Math Expert
Joined: 02 Sep 2009
Posts: 42607

Kudos [?]: 135655 [0], given: 12705

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

### Show Tags

21 Aug 2017, 00:53
susheelh wrote:
Hello Moderators,

Do you think this OG question needs to be made math friendly? Its a 600-700 Level question and it would Nicer to have the Stem made Math friendly

Is 5^k less than 1,000?

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

(2) 5^(k-1) = 5^k - 500

_______________
Done. Thank you.
_________________

Kudos [?]: 135655 [0], given: 12705

Re: Is 5^k less than 1,000?   [#permalink] 21 Aug 2017, 00:53
Display posts from previous: Sort by