1/3(x - 2) + 1/x - 2 - 1/2(x - 2) = -5/6. What is the value of x?

Question

\frac{1}{3(x - 2)} + \frac{1}{x - 2} - \frac{1}{2(x - 2)} = \frac{-5}{6}.  What is the value of  x ?

A.  1 
 
B.  4 
 
C.  7  
 
D.  8 
 
E.  9

Rabab36 · Answer

option A s correct

1/3(x−2)+1/(x−2)−1/2(x−2)=−5/6.

taking 1/x-2 common and solving we get 
x=1

gmatophobia · Answer

We can take 6(x-2) as the LCM of the three fractions

\frac{2}{6(x-2)} + \frac{6}{6(x-2)} - \frac{3}{6(x-2)} = \frac{-5}{6}

\frac{2 + 6 - 3}{6(x-2)} = \frac{-5}{6}

\frac{5}{6(x-2)} = \frac{-5}{6}

Cross multiplying

30 = -30(x-2)

30 = -30x + 60

30x = 30

x = 1

Option A

ThatDudeKnows · Answer

Three  ways.

First, focusing on the REASONING part of Quantitative Reasoning: 
We need a negative output. For all values greater than 2, the first and second terms are both going to be positive. If x were greater than 2, we would need the third term to have a bigger absolute value than the first two terms combined, but the denominator of the third term will be larger than that of the second term, making it closer to zero than the second term. Therefore, x must be less than 2.
Answer choice A.

Second, Plugging In The Answers (PITA) (probably the way I'd do it):
 I normally like trying B and D, but A looks really easy to work with, so I'd likely just start there.
A:  \frac{1}{3(1 - 2)} + \frac{1}{1 - 2} - \frac{1}{2(1 - 2)} = \frac{-5}{6}.

\frac{1}{-3} + \frac{1}{-1} - \frac{1}{-2} = \frac{-5}{6}.

\frac{-2}{6} - \frac{6}{-6} + \frac{3}{6} = \frac{-5}{6}.

Yay!
Answer choice A.

Third, the "real" math: 
 \frac{1}{3(x - 2)} + \frac{1}{x - 2} - \frac{1}{2(x - 2)} = \frac{-5}{6}

\frac{1}{x-2}*(\frac{1}{3} + \frac{1}{1} - \frac{1}{2}) = \frac{-5}{6}

\frac{1}{x-2}*(\frac{2}{6} + \frac{6}{6} - \frac{3}{6}) = \frac{-5}{6}

\frac{1}{x-2}*\frac{5}{6} = \frac{-5}{6}

\frac{1}{x-2} = -1

1 = -1(x-2)

-1 = x-2

1 = x

Answer choice A.

1/3(x - 2) + 1/x - 2 - 1/2(x - 2) = -5/6. What is the value of x?

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GMAT Problem Solving (PS) Questions

1/3(x - 2) + 1/x - 2 - 1/2(x - 2) = -5/6. What is the value of x?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards