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 Post subject: GMAT Algebra
PostPosted: Mon Apr 29, 2013 11:34 am 
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Joined: Sun May 30, 2010 3:15 am
Posts: 424
If 1/3 + 1/2 + 1/x = 4, then x =
A. 5/18
B. 6/19
C. 24/11
D. 19/6
E. 18/5

(B) To solve this equation, we first need to find a common denominator to simplify the equation. The lowest common denominator is 3 × 2 × x = 6x. If we multiply the both sides of the equation by 6x, we can get rid of all of the fractions.

Multiplying 1/3 + 1/2 + 1/x = 4 by 6x, we get:
6x/3 + 6x/2 + 6x/x = 4(6x).

Reducing this, we get:
2x + 3x + 6 = 24x
5x + 6 = 24x
6 = 19x, or x = 6/19.

Now you might be tempted to stop there, but if you have extra time you can double check by backsolving in for x. You can plug in 6/19 for x. 1/(6/19) is the same as 19/6.
1/2 = 3/6 and 1/3 = 2/6 so you can put everything in terms of 6ths and get:
2/6 + 3/6 + 19/6 = 24/6 = 4.

So, you can see with 100% certainty that the answer of 6/19 is correct.

The correct answer is choice (B).
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Hi.
I didn't understand why we have to multiply both sides of the equation.
What I did is finding LCD that is 6, and I did not multiply 4 by 6...

Also, I didn't understand what is 19/6 ?

Thanks!


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 Post subject: Re: GMAT Algebra
PostPosted: Mon Apr 29, 2013 11:35 am 
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