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Average = (x + x^2 + x^3 + x^4)/4 = x (1 + x+ x^2 + x^3 )/4 = x(1+27)/4 = 28x/4 = 7xM7MBA 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
[spoiler]OA=C[/spoiler]
Source: Veritas Prep
GMATinsight wrote:We can PLUG IN THE ANSWERS, which represent the average of x + x² + x³ + x�.M7MBA 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
Test B:
(x + x² + x³ + x�)/4 = 3x
Multiplying both sides by 4, we get:
x + x² + x³ + x� = 12x
Dividing both sides by x, we get:
1 + x + x² + x³ = 12
Substituting x+x²+x³=27 into 1+x+x²+x³ = 12, we get:
1 + 27 = 12
28 = 12
The right side needs to be greater.
Test C:
(x + x² + x³ + x�)/4 = 7x
Multiplying both sides by 4, we get:
x + x² + x³ + x� = 28x
Dividing both sides by x, we get:
1 + x + x² + x³ = 28
Substituting x+x²+x³=27 into 1+x+x²+x³ = 28, we get:
1 + 27 = 28
28 = 28
Success!
The correct answer is C.
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