800score.comhttp://www.800score.com/forum/ GMAT Algebrahttp://www.800score.com/forum/viewtopic.php?f=3&t=15349 Page 1 of 1

 Author: questioner [ Mon Apr 29, 2013 11:34 am ] Post subject: GMAT Algebra If 1/3 + 1/2 + 1/x = 4, then x =A. 5/18B. 6/19C. 24/11D. 19/6E. 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 = 24x5x + 6 = 24x6 = 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!

 Author: Gennadiy [ Mon Apr 29, 2013 11:35 am ] Post subject: Re: GMAT Algebra 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 = 5/6The original equation becomes:5/6 + 1/x = 4There 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) ?= 4If 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 ?= 4The remaining step is to sum the fractions and see if we get 4.

 Page 1 of 1 All times are UTC - 5 hours [ DST ] Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Grouphttp://www.phpbb.com/