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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?
(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
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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