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 + x² + x³ = 60, then the average (arithmetic mean) of x, x², x³, and x⁴ 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 + x² + x³ = 60, then the average (arithmetic mean) of x, x², x³, and x⁴ 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!

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

Re: Help with the means of exponents

Perfect! Thanks!