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# If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 +

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Math Expert
Joined: 02 Sep 2009
Posts: 51185
If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 +  [#permalink]

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22 Nov 2016, 04:54
4
14
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:06) correct 33% (02:40) wrong based on 300 sessions

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If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 + x^3 + x^4 is equal to which of the following?

A. 3
B. 3x
C. 7x
D. 9
E. 9x

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Joined: 02 Sep 2009
Posts: 51185
Re: If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 +  [#permalink]

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22 Nov 2016, 04:54
Bunuel wrote:
If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 + x^3 + x^4 is equal to which of the following?

A. 3
B. 3x
C. 7x
D. 9
E. 9x

Similar question to practice: if-1-x-4-x-3-x-2-x-80-then-the-average-arithmetic-mean-of-198107.html
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Re: If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 +  [#permalink]

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22 Nov 2016, 05:32
1
Bunuel wrote:
If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 + x^3 + x^4 is equal to which of the following?

A. 3
B. 3x
C. 7x
D. 9
E. 9x

IMO C

x+x^2+x^3= 27
multiply by x on both sides
x^2+x^3+x^4= 27x
(x+27x)/4 = 7x
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Re: If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 +  [#permalink]

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22 Nov 2016, 05:53
1
x + x^2 + x^3+1 = 28
X( x + x^2 + x^3+1) = 28x
(x + x^2 + x^3+x^4)4 = 28x/4=7x
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Re: If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 +  [#permalink]

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19 Jun 2017, 02:05
I did it this way:
x + x^2 + x^3 + x^4 = x + (x + x^2 + x^3) * x = x + 27x = 28x
the arithm mean is 28x/4, ie 7x.

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Re: If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 +  [#permalink]

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20 Jun 2017, 17:48
1
1
Bunuel wrote:
If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 + x^3 + x^4 is equal to which of the following?

A. 3
B. 3x
C. 7x
D. 9
E. 9x

We need to determine the value of (x + x^2 + x^3 + x^4)/4.

We can manipulate x + x^2 + x^3 = 27 by multiplying the entire equation by x and we have:

x^2 + x^3 + x^4 = 27x

Now we have:

(x + x^2 + x^3 + x^4)/4 = (x + 27x)/4 = 28x/4 = 7x

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Re: If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 +  [#permalink]

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11 Jul 2017, 10:08
2
Look at the question, answer is hidden.
x + x^2 + x^3 + x^4
= x(1+x+x^2+x^3)
= x(1+27) [it is given that x+x^2+x^3 = 27]
=28x
Sum is 28x of 4 numbers. So average is 28x/4 = 7x.
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Re: If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 +  [#permalink]

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11 Jul 2017, 10:18
x + $$x^{2}$$ + $$x^{3}$$ = 27

Average of = x , $$x^{2}$$ , $$x^{3}$$ ,$$x^{3}$$ , $$x^{4}$$

==>(x + $$x^{2}$$ + $$x^{3}$$ +$$x^{3}$$ + $$x^{4}$$ ) /4

==> (x + x(x + $$x^{2}$$ + $$x^{3}$$ )) / 4

==> $$\frac{x + 27x}{4}$$

==> $$\frac{28x}{4}$$ = 7x
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Re: If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 +  [#permalink]

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22 Aug 2018, 05:35
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Re: If x + x^2 + x^3 = 27, then the average (arithmetic mean) of x + x^2 + &nbs [#permalink] 22 Aug 2018, 05:35
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