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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Is 5^k less than 1,000? [#permalink]
23 Feb 2012, 23:54

3

This post received KUDOS

Expert's post

1

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.

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

Re: Is 5^k less than 1,000? [#permalink]
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) \(a^n*a^m=a^{n+m}\)

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

Sorry if this is bad advice. Works for some, not all.

gmatclubot

Re: Is 5^k less than 1,000? (1) 5^(k+1) > 3,000
[#permalink]
12 Nov 2014, 00:37

Interested in applying for an MBA? In the fourth and final part of our live QA series with guest expert Chioma Isiadinso, co-founder of consultancy Expartus and former admissions...