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# If x is a positive integer and z is a non-negative integer

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Manager
Joined: 09 Feb 2012
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Location: India
Concentration: Marketing, Strategy
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Kudos [?]: 42 [1] , given: 41

If x is a positive integer and z is a non-negative integer [#permalink]  01 Mar 2012, 23:18
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Difficulty:

55% (hard)

Question Stats:

62% (02:16) correct 38% (01:12) wrong based on 123 sessions
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

Source: http://www.PlatinumGMAT.com
[Reveal] Spoiler: OA

Last edited by pratikbais on 02 Mar 2012, 03:22, edited 2 times in total.
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Math Expert
Joined: 02 Sep 2009
Posts: 27215
Followers: 4227

Kudos [?]: 41002 [0], given: 5654

Re: Exponential Mess [#permalink]  02 Mar 2012, 02:05
Expert's post
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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?

Source: http://www.PlatinumGMAT.com

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 $$z=0$$ --> $$z^x-x^z=0^x-x^0=0-1=-1$$.

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.

Similar questions to practice:
tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029223
if-n-is-a-non-negative-integer-such-that-12n-is-a-divisor-of-101264.html

Hope it helps.
_________________
Manager
Joined: 09 Feb 2012
Posts: 72
Location: India
Concentration: Marketing, Strategy
GMAT 1: 640 Q48 V31
GPA: 3.45
WE: Marketing (Pharmaceuticals and Biotech)
Followers: 2

Kudos [?]: 42 [0], given: 41

Re: If x is a positive integer and z is a non-negative integer [#permalink]  02 Mar 2012, 02:49
I think the question reads the same what you suggested Bunuel

Yeah there is a typo in the sentence below the answer choices, sorry for that...
Math Expert
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Posts: 27215
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Kudos [?]: 41002 [0], given: 5654

Re: If x is a positive integer and z is a non-negative integer [#permalink]  25 Jun 2013, 04:55
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Exponents: math-number-theory-88376.html

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Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

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Kudos [?]: 52 [0], given: 0

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).

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Kudos [?]: 59 [0], given: 148

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

Source: http://www.PlatinumGMAT.com

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
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+1 Kudos please, if you like my post

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