Number properties

Question

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

masuhari · Answer

If x > 0 and z > 0
then zx - xz = 0, regardless of whether z is a divisor of that large #...

So my pick - C

HG · Answer

Sorry , I don't have the answer. I got 0 as well. But just wondering isn't the question too easy. That's why I posted.

prasun84 · Answer

IMO E
we are assuming zx/xz to be product of x and z.
what if zx and xz are 2-digit integers formed by x and z ?

take for example 41 and 14....
also. stem says z is a non-negative...it can be 0 as well....

so we may have a case 40-04....But the question says nothing of X..

phdizzle · Answer

I'm going to be even more bold than masuhari and say that as long as x and z are *any real numbers* that answer will be 0. Multiplication is commutative, so \(xz-zx=xz-xz=0\) no matter what x and z are! As far as I'm concerned all the extra information (the sign of x and z, the divisor stuff) is a red herring designed to trick you.

And woohoo for Latex in the forum!

And woohoo for Latex in the forum!

professoroffunk · Answer

I pick c.

To satisfy that (2,066)z is a divisor of 3,176,793, z must be a positive number.
As stated in the question, x is a positive integer as well.
One positive integer multiplies another positive integer, no matter what their sequences are, the results are the same. So zx – xz must be 0.

grumpyoldman · Answer

No, it really is that easy. The question is testing your ability to see what information is really necessary to answer the question. The whole thing about divisors and that seven digit number has nothing to do with it.

Whenever the GMAT intends something like "zx" to mean "a two digit number where the first digit is z and the second is x", they tell you so very explicitly and clearly. When they simply write zx in an algebraic expression, it means z times x.

prasun84 · Answer

thanks for that info..!!
it must C then.

Number properties

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