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If x is a positive integer and z is a nonnegative integer
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Updated on: 02 Mar 2012, 04:22
Question Stats:
60% (01:52) correct 40% (02:01) wrong based on 261 sessions
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If x is a positive integer and z is a nonnegative 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
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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
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02 Mar 2012, 03:05
pratikbais wrote: If x is a positive integer and z is a nonnegative 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.compratikbais please format the questions properly. Thank you. The question should read: If x is a positive integer and z is a nonnegative 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 \(z=0\) > \(z^xx^z=0^xx^0=01=1\). 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: toughandtrickyexponentsandrootsquestions12595640.html#p1029223ifnisanonnegativeintegersuchthat12nisadivisorof101264.htmlHope it helps.




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Re: If x is a positive integer and z is a nonnegative integer
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02 Mar 2012, 03:49
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 nonnegative integer
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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



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Re: If x is a positive integer and z is a nonnegative integer
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03 Aug 2014, 00:37
pratikbais wrote: If x is a positive integer and z is a nonnegative 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.comAlso, 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 nonnegative integer
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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^xx^z = 0^xx^0 = 01 = 1
Answer B



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Re: If x is a positive integer and z is a nonnegative integer
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14 Mar 2016, 02:00
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 nonnegative integer
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14 Mar 2016, 03:30
pratikbais wrote: If x is a positive integer and z is a nonnegative 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.comA quick tip: If the question says "nonnegative 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 nonnegative integer
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02 Mar 2019, 00:18
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Re: If x is a positive integer and z is a nonnegative integer
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