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 Post subject: GMAT AlgebraPosted: Mon Apr 29, 2013 11:34 am

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).
----------
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 AlgebraPosted: Mon Apr 29, 2013 11:35 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
I didn't understand why we have to multiply both sides of the equation.
We do that to get rid of the denominators.

Quote:
What I did is finding LCD that is 6, and I did not multiply 4 by 6...
6 is the LCD of the first two fractions only. Knowing it you can add 1/3 and 1/2 .

1/2 + 1/3 = 3/6 + 2/6 = (3 + 2)/6 = 5/6

The original equation becomes:
5/6 + 1/x = 4

There is still a way to go. There will be a multiplication of 4 by 6 somewhere along it.

Quote:
Also, I didn't understand what is 19/6 ?
We got the answer x = 6/19 . If we want to check that we did no mistakes along the way and this answer is in fact the correct one, we can plug x = 6/19 in the original equation.

1/3 + 1/2 + 1/(6/19) ?= 4

If this equality is true, then the solution x = 6/19 is correct.
The third term, 1/(6/19) , equals 19/6 . This is where we get 19/6.

1/3 + 1/2 + 19/6 ?= 4

The remaining step is to sum the fractions and see if we get 4.

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