Help with the means of exponents

I'm studying for the GRE and going through and reviewing. I have a question about the properties of the means of exponents, I hope this is the right place to post this thread. I'm doing a practice test and I came across this question that I can't figure out how they came to the answer:

If 1 + *x* + *x*^{2} + *x*^{3} = 60, then the average (arithmetic mean) of *x*, *x*^{2}, *x*^{3}, and *x*^{4} is equal to which of the following?

a) 12x

b) 15x

c) 20x

d) 30x

e) 60x

The correct answer is b) 15x but I can't figure out how to arrive at that answer.

Any input would be appreciated!

Re: Help with the means of exponents

Quote:

Originally Posted by

**blync** I'm studying for the GRE and going through and reviewing. I have a question about the properties of the means of exponents, I hope this is the right place to post this thread. I'm doing a practice test and I came across this question that I can't figure out how they came to the answer:

If 1 + *x* + *x*^{2} + *x*^{3} = 60, then the average (arithmetic mean) of *x*, *x*^{2}, *x*^{3}, and *x*^{4} is equal to which of the following?

a) 12x

b) 15x

c) 20x

d) 30x

e) 60x

The correct answer is b) 15x but I can't figure out how to arrive at that answer.

Any input would be appreciated!

$\displaystyle AM = \frac{x+x^2+x^3+x^4}{4}=\frac{x(1+x+x^2+x^3)}{4}= \frac {60x}{4}=15x $

Re: Help with the means of exponents