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.

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: Exponential Mess [#permalink]
02 Mar 2012, 02:05

Expert's post

3

This post was BOOKMARKED

pratikbais wrote:

If x is a positive integer and z is a non-negative integer such that (2,066)z is a divisor of, 176,793, what is the value of zx - xz?

A) -81 B) -1 C) 0 D) 1 E) It Cannot Be Determined

An odd number is never divisible by an even number. What value of z could make the expression (2,066)z equal to an odd number that is a factor of any number?

pratikbais please format the questions properly. Thank you. The question should read:

If x is a positive integer and z is a non-negative integer such that 2,066^z is a divisor of 3,176,793, what is the value of z^x - x^z? A. -81 B. -1 C. 0 D. 1 E. It Cannot Be Determined

3,176,793 is an odd number. The only way it to be a multiple of 2,066^z (even number in integer power) is when z=0, in this case 2,066^z=2,066^0=1 and 1 is a factor of every integer. Hence z=0 --> z^x-x^z=0^x-x^0=0-1=-1.

Answer: B.

Must know for the GMAT: a^0=1, for a\neq{0} - any nonzero number to the power of 0 is 1. Important note: the case of 0^0 is not tested on the GMAT.

Re: If x is a positive integer and z is a non-negative integer [#permalink]
02 Aug 2014, 04:33

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. _________________

Also, 2066^z = a number that ends with digit 6. If you multiply 6 *6*6*..... , it always end with 6 at the end. So 3176793 cannot be divided by 2066, then z= 0 -> B is the answer _________________

......................................................................... +1 Kudos please, if you like my post

gmatclubot

Re: If x is a positive integer and z is a non-negative integer
[#permalink]
02 Aug 2014, 23:37