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:

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]

Show Tags

02 Aug 2014, 05:33

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

Re: If x is a positive integer and z is a non-negative integer [#permalink]

Show Tags

02 Nov 2015, 02:24

The number 3.176.793 is a multiple of 3 becasue 3+1+7+6+7+9+3 = 36, which is a multiple of 3. The number 2.066 is not a multiple of three because 2+0+6+6 = 14, which is not a multiple of 3.

A quick tip: If the question says "non-negative integer", alarms should go off in your head and you should immediately consider the case of 0. It is easier to say positive integers. When the test maker goes for "non negative integer", it usually means that 0 will have some role to play in the solution. Also considering the huge numbers the question deals with, it is a good idea to try 0 and 1 (if needed). The moment you put z = 0, you get the answer as -1. Since it is a PS question, you are done.
_________________

Re: If x is a positive integer and z is a non-negative integer [#permalink]

Show Tags

15 Mar 2017, 19:35

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.
_________________

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...