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

Question

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

Vinayak Shenoy · Accepted Answer

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

Bunuel · Answer

Similar question to practice: if-1-x-4-x-3-x-2-x-80-then-the-average-arithmetic-mean-of-198107.html

vikithebest1 · Answer

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

guialain · Answer

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.

Answer is C.

JeffTargetTestPrep · Answer

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
 
Answer: C

utkarshthapak · Answer

Look at the question, answer is hidden. 
x + x^2 + x^3 + x^4 
= x(1+x+x^2+x^3)
= x(1+27)  
=28x
Sum is 28x of 4 numbers. So average is 28x/4 = 7x.

Leo8 · Answer

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

Jbbaille · Answer

I don't find the question very well formulated. The average of x + x^2 + x^3 + x^4 is just 28x (because it is only 1 number, the average is itself). The average of x, x^2, x^3 and x^4 is 7x.

fireagablast · Answer

x+x^2+x^3 = 27

(x+x^2+x^3+x^4)/4 = y
x(1+x+x^2+x^3)/4 = y
x28/4 = y
7x=y

DiyaSouravi99 · Answer

The explanation was good here

ludicrous · Answer

The question language is a bit wrong. It should say the arithmetic mean of x, x^2, x^3 and x^4, not the arithmetic mean of x + x^2 + x^3 + x^4. The latter term means just one term, not 4.

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

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

Prep Toolkit

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