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TAGS: Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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then the average of x, x^2, x^3, x^4. [#permalink]
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Expert's post 00:00

Question Stats: 73% (01:07) correct 26% (01:14) wrong based on 136 sessions
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

Practice Questions
Question: 9
Page: 157
Difficulty: hard
[Reveal] Spoiler: OA

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Sandy
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Try our free Online GRE Test Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Re: then the average of x, x^2, x^3, x^4. [#permalink]
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Expert's post
Here we have $$1 + x + x^2 + x^3$$ = 60.

Now we multiply both sides with x and divide both sides by 4.

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

Now the LHS corresponds to the average of x, x^2, x^3, x^4. and RHS is 15x.

Hence option B is correct!
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Sandy
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Re: then the average of x, x^2, x^3, x^4. [#permalink]
How would a student know to multiply by 4 ? Is it intuition? Can you explain the logic/ principle? Intern Joined: 12 Jul 2016
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Re: then the average of x, x^2, x^3, x^4. [#permalink]
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sagnik242 wrote:
How would a student know to multiply by 4 ? Is it intuition? Can you explain the logic/ principle?

The question asks for the arithmetic mean, and that entails dividing by 4 (which is the number of x variables they've given you). Honestly, I was confused by this question too. The process by which we get the answer always make me feel dumb, because it's so obvious when you see it. GRE Instructor Joined: 10 Apr 2015
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Re: then the average of x, x^2, x^3, x^4. [#permalink]
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Expert's post
sandy wrote:
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

To find the average of x, x^2, x^3 and x^4, we need to find the SUM of x + x^2 + x^3 + x^4 and divide it by 4.

We're told that 1 + x + x^2 + x^3 = 60, so if we multiply both sides of the equation by x, we get: x(1 + x + x^2 + x^3) = 60x
When we expand the left side, we get: x + x^2 + x^3 + x^4 = 60x

So, the average of x, x^2, x^3 and x^4 = (x + x^2 + x^3 + x^4)/4
= 60x/4
= 15x

[Reveal] Spoiler:
B

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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Manager  Joined: 01 Nov 2018
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Re: then the average of x, x^2, x^3, x^4. [#permalink]
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Expert's post
The first thing I would do is look at the relationship between

x^3+ x^2 + x + 1 and x^4 + x^3 + x^2 + x

if you put them side by side, at least in writing, then you can see that the right expression is simply the left expression times X.

then x^4 + x^3 + x^2 + x= x*(x^3+ x^2 + x + 1) = x*60

(x^4 + x^3 + x^2 + x) = 60x/4= 15x Senior Manager  Joined: 10 Feb 2020
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Re: then the average of x, x^2, x^3, x^4. [#permalink]
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Applying Average Formula:

(x+x^2+x^3+x^4)/4

Taking common:

x(1+x+x^2+x^3)/4
=x(60)/4
=15x
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Ever Tried? Ever Failed? No Matter. Try Again. Fail Again. Fail Better!! Re: then the average of x, x^2, x^3, x^4.   [#permalink] 29 Apr 2020, 13:19
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