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

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

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New post Updated on: 02 Mar 2012, 04:22
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Question Stats:

60% (01:52) correct 40% (02:00) wrong based on 247 sessions

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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


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Originally posted by pratikbais on 02 Mar 2012, 00:18.
Last edited by pratikbais on 02 Mar 2012, 04:22, edited 2 times in total.
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Re: Exponential Mess  [#permalink]

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New post 02 Mar 2012, 03:05
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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?


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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.

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

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New post 02 Mar 2012, 03:49
I think the question reads the same what you suggested Bunuel :-D

Yeah there is a typo in the sentence below the answer choices, sorry for that...
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Re: If x is a positive integer and z is a non-negative integer  [#permalink]

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New post 25 Jun 2013, 05:55
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

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

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

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New post 03 Aug 2014, 00:37
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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Re: If x is a positive integer and z is a non-negative integer  [#permalink]

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New post 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.

Therefore z=0, and z^x-x^z = 0^x-x^0 = 0-1 = -1

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

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

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New post 14 Mar 2016, 03:30
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


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

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Re: If x is a positive integer and z is a non-negative integer   [#permalink] 02 Mar 2019, 00:18
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