• Board contributors include instructors with "800" GMAT scores.
  • 95% of posts have replies within 24 hours.
  • Join for discounts with 800score, VeritasPrep and ManhattanGMAT


FAQ  - Register  - Search - Login 

All times are UTC - 7 hours




Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: GMAT Algebra
PostPosted: Mon Aug 20, 2012 7:22 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 481
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!


Top
 Profile  
 
 Post subject: Re: GMAT Algebra
PostPosted: Mon Aug 20, 2012 7:48 am 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 457
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.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

All times are UTC - 7 hours


Who is online

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

Search for:
Jump to:  
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group
Template made by DEVPPL -
phpBB SEO
 
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.