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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] New post 01 Mar 2012, 23:18
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Question Stats:

56% (02:17) correct 44% (01:18) wrong based on 66 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


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[Reveal] Spoiler: OA

Last edited by pratikbais on 02 Mar 2012, 03:22, edited 2 times in total.
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Re: Exponential Mess [#permalink] New post 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?


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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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Manager
Manager
avatar
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: 1

Kudos [?]: 23 [0], given: 41

Re: If x is a positive integer and z is a non-negative integer [#permalink] New post 02 Mar 2012, 02:49
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] New post 25 Jun 2013, 04:55
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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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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If x is a positive integer and z is a non-negative integer   [#permalink] 25 Jun 2013, 04:55
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