If x is a positive integer and z is a non-negative integer : GMAT Problem Solving (PS)
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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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01 Mar 2012, 23:18
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Difficulty:

55% (hard)

Question Stats:

61% (02:18) correct 39% (01:37) wrong based on 232 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

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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02 Mar 2012, 02:05
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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?

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.
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Kudos [?]: 95 [0], given: 41

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

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

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25 Jun 2013, 04:55
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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

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

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

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02 Nov 2015, 01:24
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

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

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14 Mar 2016, 01:00
Here as even number cannot divide an odd number so => z must be zero
hence value=-1
so B is correct
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Re: If x is a positive integer and z is a non-negative integer [#permalink]

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14 Mar 2016, 02:30
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] 14 Mar 2016, 02:30
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