Question - Hard

[jnellaz]

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]

[jnellaz]

I am sure there are many ways to solve this. I was interested in your approaches to this! Thanks in advance

[logitech]

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

[jnellaz]

apologies

[logitech]

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

[uttara]

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...

[jnellaz]

Thanks Logitech but I already read that solution. I was looking to see if there was an alternative way to approach this. Best~

[jnellaz]

And by the way. My apologies for my mistake. I realized that the exponents did not copy correctly.

[sudhir3127]

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...

[jaybrium]

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.

[jaybrium]

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.

[logitech]

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.

[Scott@TargetTestPrep]

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