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 Post subject: GMAT AlgebraPosted: Wed Apr 17, 2013 7:41 am

Joined: Sun May 30, 2010 3:15 am
Posts: 424
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:3ab = 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:
(3ab = 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:
(3ab = 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.

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 Post subject: Re: GMAT AlgebraPosted: Wed Apr 17, 2013 7:41 am

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