divisor of 3,176,793

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Mon Dec 22, 2008 8:50 am

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

OA Soon

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Source: Beat The GMAT — Problem Solving | Mon Dec 22, 2008 8:50 am

parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

Re: divisor of 3,176,793

by parallel_chase » Mon Dec 22, 2008 9:34 am

4meonly 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

OA Soon

Only way 2066^z can be the divisor of 3176793, when z = 0

Because they both are not divisible by any integer from 2-7

then 2066^0 = 1, and 1 is the divisor of every number

x could be any integer

z^x - x^z = 0^x - x^0 = 0 - 1 = -1

Hence, B

OA?

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mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

by mals24 » Mon Dec 22, 2008 9:45 am

Yup agree with PC on B

Z is a non negative integer , you can take this as a clue that you have to consider 0 as well.

Plus 2066^n the units digit will always be 6 and there is no integer which when you multiply by 6 you'll get a units digit of 3.

So z is 0.

0-1 = -1.

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Mon Dec 22, 2008 10:00 am

Yes, folks, u r correct.
OA B

The key here is to understand that z=0.

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vin25: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Mon Dec 22, 2008 1:01 pm

Re: divisor of 3,176,793

by vin25 » Mon Dec 22, 2008 1:10 pm

4meonly 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

OA Soon

Since gcd(3,176,793)=1 =>z=0 =>z^x - x^z=-1

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ronniecoleman: Legendary Member; Posts: 546; Joined: Sun Nov 16, 2008 11:00 pm; Location: New Delhi , India; Thanked: 13 times

by ronniecoleman » Tue Dec 23, 2008 3:32 am

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

3176793 is a ODD number
so we don't expect any even no as its factor

2066 is a even number

hence 2066 or its multiple cannot be divisior.

So z = 0

hence IMO B

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011-27565856

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