If $\left(6+\frac{2}{x}\right)\left(x-4\right)=0,$ and

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sun May 05, 2019 11:14 am

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If $\left(6+\frac{2}{x}\right)\left(x-4\right)=0,$ and $x$ does not equal $4$, then $x =$

(A) -6
(B) -4
(C) -1/3
(D) 1/3
(E) 3

[spoiler]OA=C[/spoiler]

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Sun May 05, 2019 11:14 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Sun May 05, 2019 1:46 pm

Hi Gmat_mission.

Here, using the zero product rule we have that $$\left(6+\frac{2}{x}\right)\left(x-4\right)=0\ \ \ \ \Rightarrow\ \ 6+\frac{2}{x}=0\ \ \ \ \ \ or\ \ \ \ \ \ \ x-4=0$$ $$\Rightarrow\ \ \frac{2}{x}=-6\ \ \ \ \ \ or\ \ \ \ \ \ \ x=4$$ $$\Rightarrow\ x=-\frac{1}{3}\ \ \ \ \ \ or\ \ \ \ \ \ \ x=4$$ But on the other hand, we are told that $x$ does not equal to $4$, then we have that $x=-\frac{1}{3}.$

So, the correct answer is the option [spoiler]C) -1/3[/spoiler].

I hope it is clear. <i class="em em-sunglasses"></i>

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