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If x/4 = (5x−2)/(x+8), then x² − 12x + 40 =

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by Brent@GMATPrepNow » Tue Oct 01, 2019 11:33 am
If x/4 = (5x−2)/(x+8), then x² − 12x + 40 =

A) 0
B) 4
C) 8
D) 12
E) 32

Answer: E
Source: www.gmatprepnow.com
Difficulty level: 650-700
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by deloitte247 » Sun Oct 06, 2019 8:12 am
$$\frac{x}{4}=\frac{5x-2}{x+8}$$
x(x+8) = 4 (5x-2)
$$x^2+8x=20x-8$$
$$x^2-12x+8=0\ \ \ ------\left(i\right)$$
Express eqn (i) as the equation in the question;
$$x^2-12x+8=0\ \ \ \left(add\ 40-8\ to\ both\ sides\right)$$
$$x^2-12x+8+\left(40-8\right)=0+(40-8)$$
$$x^2-12x+8+32=32$$
$$x^2-12x+40=32$$
$$Therefore,\ evaluating\ x^2-12x+40\ will\ provide\ 32\ as\ result$$

Correct answer = option E
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