It is currently Sun Oct 21, 2018 3:05 am

 All times are UTC - 5 hours [ DST ]

 Page 1 of 1 [ 4 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: GMAT SymbolsPosted: Thu Aug 11, 2011 5:17 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
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 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

 Post subject: Re: math (t.1, qt.5): algebra, sumbolsPosted: Thu Aug 11, 2011 5:21 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
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

 Post subject: Re: math (t.1, qt.5): algebra, sumbolsPosted: Thu Dec 08, 2011 2:46 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
What happened to 8ab when you solved 4a² + 4b² + 8ab = 100 to (2a+ 2b)² = 100?
The 8ab was just dropped?

Top

 Post subject: Re: math (t.1, qt.5): algebra, sumbolsPosted: Thu Dec 08, 2011 2:50 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
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

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 4 posts ]

 All times are UTC - 5 hours [ DST ]

#### Who is online

Users browsing this forum: No registered users and 5 guests

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

Search for:
 Jump to:  Select a forum ------------------ GMAT    GMAT: Quantitative Section (Math)    GMAT: Verbal Section    GMAT: Integrated Reasoning    GMAT: General Questions GRE    GRE: Quantitative Reasoning (Math)    GRE: Verbal Reasoning    GRE: General Questions General questions    Other questions