Hoping you guys can walk me through this one, not much of an explanation in the solution set...
9. If 1 + x + x^2 + x^3 = 60, then the average of x, x^2, x^3, and x^4 is equal to which of the following?
12x, 15x, 20x, 30x, or 60x?
The answer is 15x, but not certain how that was derived. My hunch is (60 + x^4)/5 is the direction I need to go--but that doesn't simplify to 15x...
Thanks, Jake
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- jakehunter46
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- tommywallach
- Manhattan Prep Staff
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Re: OG p. 157, #9
Hey Jake,
Definitely a confusing question! The key with something weird like this is to try and "create" the expression they're asking you about with the one they've told you about. The answer choices give you a hint as well. The answer is always going to have an x in it, so you might as well have EVERYTHING in terms of x.
In other words, multiply both sides of the equation you already know by x:
1 + x + x^2 + x^3 = 60 --> multiply both sides by x -->
x + x^2 + x^3 + x^4 = 60x
Now all you have to do is divide both sides by 4 (to create the average):
(x + x^2 + x^3 + x^4)/4 = 15x
Hope that makes sense!
-t
Definitely a confusing question! The key with something weird like this is to try and "create" the expression they're asking you about with the one they've told you about. The answer choices give you a hint as well. The answer is always going to have an x in it, so you might as well have EVERYTHING in terms of x.
In other words, multiply both sides of the equation you already know by x:
1 + x + x^2 + x^3 = 60 --> multiply both sides by x -->
x + x^2 + x^3 + x^4 = 60x
Now all you have to do is divide both sides by 4 (to create the average):
(x + x^2 + x^3 + x^4)/4 = 15x
Hope that makes sense!
-t
2 posts Page 1 of 1