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 500,000 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:

I would appreciate it if someone could walk me through this problem. Thanks

Is \(5^k\) less than 1000?

1. \(5^k+1 > 3000\) 2. \(5^k-1 = 5^k -500\)

I am assuming the question is:

Is \(5^k\) less than 1000?

1. \(5^{k+1} > 3000\) 2. \(5^{k-1} = 5^k -500\)

\(5^4 = 625\) and \(5^5 = 3125\) (even if you do not know this, it is fine. You don't need to calculate. Just observe that 625*5 will be greater than 3000)

Statement 1: \(5^{k+1} > 3000\) This means k + 1 is greater than 4 so k is greater than 3 (It doesnt mean that k + 1 is at least 5 because the question doesn't say that k is an integer. k + 1 could be 4.999 making k = 3.999) Since k can take values less than 4 and more than 4, 5^k could be less than 1000 or more than 1000. Not sufficient.

Statement 2: \(5^{k-1} = 5^k -500\) Re-arrange: \(500 = 5^k -5^{k-1}\) \(5^3 *4 = 5^{k-1}(5 - 1)\) Hence k - 1 = 3 and k = 4 So \(5^k\) = 625 which is less than 1000. Answer is 'Yes'. Sufficient.

Can you go over how you went from 500 = 5^k -5^{k-1} to 5^3 *4 = 5^{k-1}(5 - 1)?

Thanks so much in advance!

Left hand side: \(500 = 5*100 = 5*25*4 = 5^3*4\) (Since your concern is the power of 5, separate 5s from the rest)

Right hand side: \(5^k -5^{k-1} = 5^{k - 1} ( 5 - 1)\)(Take \(5^{k - 1}\) common. e.g. if you have \(5^4 - 5^3\), you can take \(5^3\) common and you will be left with (5 - 1))
_________________

I would appreciate it if someone could walk me through this problem. Thanks

Is \(5^k\) less than 1000?

1. \(5^k+1 > 3000\) 2. \(5^k-1 = 5^k -500\)

I am assuming the question is:

Is \(5^k\) less than 1000?

1. \(5^{k+1} > 3000\) 2. \(5^{k-1} = 5^k -500\)

\(5^4 = 625\) and \(5^5 = 3125\) (even if you do not know this, it is fine. You don't need to calculate. Just observe that 625*5 will be greater than 3000)

Statement 1: \(5^{k+1} > 3000\) This means k + 1 is greater than 4 so k is greater than 3 (It doesnt mean that k + 1 is at least 5 because the question doesn't say that k is an integer. k + 1 could be 4.999 making k = 3.999) Since k can take values less than 4 and more than 4, 5^k could be less than 1000 or more than 1000. Not sufficient.

Statement 2: \(5^{k-1} = 5^k -500\) Re-arrange: \(500 = 5^k -5^{k-1}\) \(5^3 *4 = 5^{k-1}(5 - 1)\) Hence k - 1 = 3 and k = 4 So \(5^k\) = 625 which is less than 1000. Answer is 'Yes'. Sufficient.

Answer (B)

I can't get why are we talking about decimals in the first statement. I don't know if I'm doing something wrong here...

I did it like this \(5^{k+1} > 3000\) \(k+1 \geq 5\) \(k \geq 4\)

\(k= 4\) then \(5^4 = 625\) \(k=5\) then \(5^5 = 3000\) (approx)

I would appreciate it if someone could walk me through this problem. Thanks

Is \(5^k\) less than 1000?

1. \(5^k+1 > 3000\) 2. \(5^k-1 = 5^k -500\)

I am assuming the question is:

Is \(5^k\) less than 1000?

1. \(5^{k+1} > 3000\) 2. \(5^{k-1} = 5^k -500\)

\(5^4 = 625\) and \(5^5 = 3125\) (even if you do not know this, it is fine. You don't need to calculate. Just observe that 625*5 will be greater than 3000)

Statement 1: \(5^{k+1} > 3000\) This means k + 1 is greater than 4 so k is greater than 3 (It doesnt mean that k + 1 is at least 5 because the question doesn't say that k is an integer. k + 1 could be 4.999 making k = 3.999) Since k can take values less than 4 and more than 4, 5^k could be less than 1000 or more than 1000. Not sufficient.

Statement 2: \(5^{k-1} = 5^k -500\) Re-arrange: \(500 = 5^k -5^{k-1}\) \(5^3 *4 = 5^{k-1}(5 - 1)\) Hence k - 1 = 3 and k = 4 So \(5^k\) = 625 which is less than 1000. Answer is 'Yes'. Sufficient.

Answer (B)

I can't get why are we talking about decimals in the first statement. I don't know if I'm doing something wrong here...

I did it like this \(5^{k+1} > 3000\) \(k+1 \geq 5\) \(k \geq 4\)

\(k= 4\) then \(5^4 = 625\) \(k=5\) then \(5^5 = 3000\) (approx)

\(5^{k+1} > 3000\) --> \(5*5^{k} > 3000\) --> \(5^{k} > 600\). Now, we are NOT told that k is an integer, thus we cannot say that \(k\geq{4}\). For example, \(5^{3.99}\approx{615}\), thus k could be 3.99.

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.

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...