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]

02 Mar 2012, 00:18

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Question Stats:

45% (02:03) correct

54% (01:33) wrong

based on 0 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, 04:22, edited 2 times in total.

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Re: Exponential Mess [#permalink]

02 Mar 2012, 03:05

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.

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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Manager

Joined: 10 Feb 2012

Posts: 73

Location: India

Concentration: Marketing, Strategy

GMAT 1: 640 Q48 V31

GPA: 3.45

WE: Science (Health Care)

Followers: 1

Kudos [?]: 10 [0], given: 41

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

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...

Re: If x is a positive integer and z is a non-negative integer [#permalink] 02 Mar 2012, 03:49

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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

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