• 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  [ 4 posts ] 
Author Message
 Post subject: GMAT Symbols
PostPosted: Mon Apr 08, 2013 7:54 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 477
Operation # is defined as: a # b = 4a² + 4b² + 8ab for all non-negative integers. What is the value of (a + b) + 3, when a # b = 100?
A. 5
B. 8
C. 10
D. 13
E. 17

(B) We know that a # b = 100 and a # b = 4a² + 4b² + 8ab. So
4a² + 4b² + 8ab = 100

We can see that 4a² + 4b² + 8ab is a well-known formula for (2a + 2b)². Therefore (2a + 2b)² = 100.
(2a + 2b) is non-negative number, since both a and b are non-negative numbers. So we can conclude that 2(a + b) = 10.

(a + b) + 3 = 10/2 + 3 = 8.

The correct answer is B.
----------
The only question I have about this problem is the transition from (2a + 2b)² = 100 to 2(a + b) = 10. Obviously the square root was taken but only of the (a + b)?


Top
 Profile  
 
 Post subject: Re: GMAT Symbols
PostPosted: Mon Apr 08, 2013 7:56 am 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 453
questioner wrote:
The only question I have about this problem is the transition from (2a + 2b)² = 100 to 2(a + b) = 10. Obviously the square root was taken but only of the (a + b)?
The square root was taken of the whole expression within the brackets, 2a + 2b.

So (2a + 2b)² = 100 yields 2a + 2b = 10. Then we just factor out 2: 2a + 2b = 2(a + b).


Top
 Profile  
 
 Post subject: Re: GMAT Symbols
PostPosted: Mon Apr 08, 2013 7:56 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 477
What happened to 8ab when you solved 4a² + 4b² + 8ab = 100 to (2a+ 2b)² = 100?
The 8ab was just dropped?


Top
 Profile  
 
 Post subject: Re: GMAT Symbols
PostPosted: Mon Apr 08, 2013 7:57 am 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 453
questioner wrote:
The 8ab was just dropped?
No, we've used the well-known formula x² + 2xy + y² = (x + y)².

In our case it is:
4a² + 8ab + 4b² = 100
(2a)² + 2 × (2a) × (2b) + (2b)² = 100
So we apply the formula for x = 2a and y = 2b.
(2a + 2b)² = 100


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 4 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:  
cron
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.