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GMAT Symbols http://www.800score.com/forum/viewtopic.php?f=3&t=379 
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Author:  questioner [ Thu Aug 11, 2011 5:17 pm ] 
Post subject:  GMAT Symbols 
Operation # is defined as: a # b = 4a² + 4b² + 8ab for all nonnegative 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 wellknown formula for (2a + 2b)². Therefore (2a + 2b)² = 100. (2a + 2b) is nonnegative number, since both a and b are nonnegative 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)? 
Author:  Gennadiy [ Thu Aug 11, 2011 5:21 pm ] 
Post subject:  Re: math (t.1, qt.5): algebra, sumbols 
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). 
Author:  questioner [ Thu Dec 08, 2011 2:46 pm ] 
Post subject:  Re: math (t.1, qt.5): algebra, sumbols 
What happened to 8ab when you solved 4a² + 4b² + 8ab = 100 to (2a+ 2b)² = 100? The 8ab was just dropped? 
Author:  Gennadiy [ Thu Dec 08, 2011 2:50 pm ] 
Post subject:  Re: math (t.1, qt.5): algebra, sumbols 
questioner wrote: The 8ab was just dropped? No, we've used the wellknown 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 
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