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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

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