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...

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.

Users browsing this forum: No registered users and 1 guest

You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum

GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.