# GMAT Prep From Platinum GMAT

### GMAT Prep Materials

### Announcement

What do you think of the new design? Send us your comments at feedback@lighthouseprep.us. Also, are there any PHP experts out there who could help fix the bug on the Practice Test page? Your help would be much appreciated!

### About Us

Platinum GMAT Prep provides the best GMAT preparation materials available anywhere, enabling individuals to master the GMAT and gain admission to any MBA program. We also provide hundreds of pages of free GMAT prep content, including practice questions, study guides, and test overviews.

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}?Correct Answer:

**B**An odd number is never divisible by an even number. What value of z could make the expression (2,066)

^{z}equal to an odd number that is a factor of any number?- An odd integer (e.g., 3,176,793) is not divisible by an even integer. For example, 3 is not divisible by 2 nor is 15 divisible by 2.

(3,176,793/even integer) --> non integer - The only way (2,066)
^{z}can possibly be a divisor of 3,176,793 is if (2,066)^{z}is an odd number. However, if z is any positive integer, (2,066)^{z}will be an even number. (More specifically, it will have a units digit of 6). As a result, (2,066)^{z}will not be a factor of 3,176,793 if z is a positive integer. - Since the question explicitly says that (2,066)
^{z}is a factor of 3,176,793, you know that, somehow, (2,066)^{z}must be an odd number. - Remember that any number raised to the power of 0 will be 1.

(any real number)^{0}= 1 - The key to this problem is realizing that if z = 0, which is allowed because the question stem said z "is a non-negative number," (2,066)
^{z}will equal 1. Since the only way z can be a factor 3,176,793 is if z = 0, you know that z = 0.

(3,176,793/(2,066)^{0}) is the only way 2,066^{z}is a factor of 3,176,793 - You can now rewrite the question as follows:

0^{(any positive integer)}– (any positive integer)^{0}

z^{x}– x^{z}= 0^{x}– x^{0}= 0^{(pos int)}– (pos int)^{0} - Since 0 raised to any positive integer equals 0 and any positive integer raised to 0 is 1, the question boils down to: 0 – 1 = -1.

0^{(pos int)}– (pos int)^{0}= 0 – 1 = -1