BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

divisor of 3,176,793

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 891
Joined: Sat Aug 16, 2008 4:21 am
Thanked: 27 times
Followed by:1 members
GMAT Score:660(

divisor of 3,176,793

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
Top
Source: — Problem Solving |
Legendary Member
Posts: 1153
Joined: Wed Jun 20, 2007 6:21 am
Thanked: 146 times
Followed by:2 members

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?
No rest for the Wicked....
Top
Legendary Member
Posts: 683
Joined: Tue Jul 22, 2008 1:58 pm
Location: Dubai
Thanked: 73 times
Followed by:2 members

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.
Top
Legendary Member
Posts: 891
Joined: Sat Aug 16, 2008 4:21 am
Thanked: 27 times
Followed by:1 members
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. :D
Top
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
Top
User avatar
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
Admission champion, Hauz khaz
011-27565856
Top
Post new topic Post Reply
• Page 1 of 1