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GMAT Algebra http://www.800score.com/forum/viewtopic.php?f=3&t=15330 
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Author:  questioner [ Wed Apr 17, 2013 7:41 am ] 
Post subject:  GMAT Algebra 
If a – (b/3) = 1/3 and a + (b/4) = 3/2, then what is the value of a + b? A. 1 B. 2 C. 3 D. 4 E. 5 (C) Whenever we have fractions in algebra, it is usually a good idea to eliminate them. Let’s multiply the first equation by 3, yielding:3a – b = 1.Then let’s multiply the second equation by 4, yielding:4a + b = 6. If we add the equations, the b terms cancel out, yielding: (3a – b = 1) + (4a + b = 6) 7a = 7 a = 1. Now, we can substitute the value of a into either of the equations to determine that b = 2.Therefore, a + b = 1 + 2 = 3.The correct answer is choice (C). If we add the equations, the b terms cancel out, yielding: (3a – b = 1) + (4a + b = 6) 7a = 7 a = 1 My question is how do you know when you should be adding equations together (The step referenced above). I know there has to be a fundamental concept I am forgetting. I think I tried the solving for a and then substituting the answer into the other equation, therefore treating each equation as if they are mutually exclusive. Please explain the correct approach/rationale and how to make the correct determination. Thanks. 
Author:  Gennadiy [ Wed Apr 17, 2013 7:41 am ] 
Post subject:  Re: GMAT Algebra 
The most obvious reason to add equations together or subtract one from another is having one of the variables with the same constant multiplier (or opposite, e.g. 3 and 3). a + 3b = 7 2a – 3b = 7 or a + 3b = 7 2a + 3b = 7 If we consider this specific question then you can see that we could subtract one from another right from the beginning : a – (b/3) = 1/3 – a + (b/4) = 3/2 a – (b/3) – a – (b/4) = 1/3 – 3/2 – (b/3) – (b/4) = 1/3 – 3/2 We got rid of variable a, though we have to deal with fractions. (7b/12) = (1/6) b = 2 
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