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Question - Hard

by jnellaz » Wed Nov 05, 2008 1:05 pm
Can someone help with this one?

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 zx - xz?
A) -81
B) -1
C) 0
D) 1
E) It Cannot Be Determined

The answer is B[spoiler]
[/spoiler]
Last edited by jnellaz on Wed Nov 05, 2008 1:37 pm, edited 1 time in total.
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by jnellaz » Wed Nov 05, 2008 1:13 pm
I am sure there are many ways to solve this. I was interested in your approaches to this! Thanks in advance
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Re: Exponent Question - Hard

by logitech » Wed Nov 05, 2008 1:34 pm
jnellaz wrote:Can someone help with this one?

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 zx - xz?
A) -81
B) -1
C) 0
D) 1
E) It Cannot Be Determined

The answer is B[spoiler]
[/spoiler]

what is the value of zx - xz?

Are you sure ?

Because zx = xz

so the result will be either 0 or -2(xz) EVEN NUMBER

Please make sure that question has no typo
LGTCH
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by jnellaz » Wed Nov 05, 2008 2:07 pm
apologies
Last edited by jnellaz on Thu Nov 06, 2008 5:55 am, edited 1 time in total.
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by logitech » Wed Nov 05, 2008 3:59 pm
jnellaz wrote:There isn't a typo. This was copied directly with no errors.
Next time, check it before you copied.

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?

Here is the original problem and the solution:

https://www.platinumgmat.com/about_gmat ... stion_id=2
LGTCH
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by uttara » Wed Nov 05, 2008 7:11 pm
somehow i found this question too hard for me.

Do we get this kind of question in real GMAT? If yes than can anyone share a real GMAT question of this kind...
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by jnellaz » Thu Nov 06, 2008 5:52 am
Thanks Logitech but I already read that solution. I was looking to see if there was an alternative way to approach this. Best~
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by jnellaz » Thu Nov 06, 2008 5:54 am
And by the way. My apologies for my mistake. I realized that the exponents did not copy correctly.
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Re: Question - Hard

by sudhir3127 » Thu Nov 06, 2008 6:05 am
jnellaz wrote:Can someone help with this one?

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 zx - xz?
A) -81
B) -1
C) 0
D) 1
E) It Cannot Be Determined

The answer is B[spoiler]
[/spoiler]
For 2066^z to be a divisor of 3,176,793 the whole expression of
2066^z has to be a odd number ..

if u see it carefully any number ending with 6 when multiplied by any integer will never give u an odd number .. thus
for 2066^z ...to be odd... the only way its possible is when Z =0 .

because any number raised to the power of zero will be 1, which is odd.

thats the whole trick in this problem ..

Z^x- X^z will be
0^x- X^0
which is -1

hope it makes sense .. do let me know if u have any doubts...
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by jaybrium » Thu Nov 06, 2008 9:40 am
Nice work Sudhir- that's how I approached this problem.

Whenever I come across a problem with large numbers that would require significant calculation (aka- time), I use this as a hint that there is a quick shortcut that can be used to solve the problem. I feel that this makes some of the more difficult problems much easier to handle.

When you see something like 3176793/2066^z realize that the GMAT is not tesing your division skills- it's likely testing something much more simple that is hidden in a "complicated" problem.
- Jay
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by jaybrium » Thu Nov 06, 2008 9:43 am
However, even with this said, if you can't determine the question's "trick" or "shortcut," make an educated guess and move on. No point wasting time on a lost cause.
- Jay
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by logitech » Thu Nov 06, 2008 5:47 pm
jaybrium wrote:However, even with this said, if you can't determine the question's "trick" or "shortcut," make an educated guess and move on. No point wasting time on a lost cause.
Perfect points! Very smart thinking!

Thanks man.
LGTCH
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Re: Question - Hard

by Scott@TargetTestPrep » Thu Feb 13, 2020 5:22 am
jnellaz wrote: ↑
Wed Nov 05, 2008 1:05 pm
 Can someone help with this one?

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 zx - xz?
A) -81
B) -1
C) 0
D) 1
E) It Cannot Be Determined

The answer is B[spoiler]
[/spoiler]
Since 2,066 is even and 3,176,793 is odd, we see that the only possible value for z is 0. In other words, 2,066 does not evenly divide 3,176,793, and no multiple of 2,066 will evenly divide 3,176,793, either. Thus, z must equal 0, making 2,066^0 = 1 (and we see that 1 does evenly divide into 3,176,793).

Since z = 0, then z^x = 0^x = 0, and x^z = x^0 = 1. Thus, their difference is 0 - 1 = -1.

Answer: B

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