Dividing Equations

Question

I was working in Book 3 of MGMAT and one of the problems confused me, I was able to solve for it, but the explanation the book gave was confusing but looked like something I may be able to add to my repertoire if I learn it. Can you provide any assistance?

Solve for A using these two equations

\frac{B+A}{2A} =2
 a+b=8

I was able to solve for this but MGMAT gave an interesting answer for it, and was wondering if someone could help me understand it. They gave their answer as Divide the first equation by the second
 \frac{B+A}{2A/A+B}  = \frac{2}{8}  Sorry for the mess, couldn't get this to post neatly

Which reduces to 
 \frac{B+A}{2A(a+b)} = \frac{2}{8}

Which when reduced ends up 2A=4 and A=2

Should you divide equations like that and any suggestions to avoid that in the future?

whiplash2411 · Answer

It really depends on each individual equation. Another way of thinking about the solution the book has is to think about substituting the value of a + b, which you know, into the first equation, thereby leaving only one unknown variable. Hence you can easily solve for a.

Bigred2008 · Answer

Thanks, you're a pretty big source of knowledge for my math problems in these forums. But your response makes sense, I was just wondering.

whiplash2411 · Answer

There is no set way to attack a given problem. The GMAT is a timed test and ultimately, all the test-takers will be able to figure out a problem given infinite time. You're trying to train your mind to identify the tricks and substitutions that would eventually help you to solve a problem in time, if not actually gain time to use on another problem from something like this. Practice is the only way of really getting through. If you're able to solve something your way in under 2 minutes, it's fine. But keep an alternate idea in mind because it might come in handy in another situation where your method is infeasible for some reason.

Bigred2008 · Answer

That's exactly the reason I posted, I was able to solve it in about a minute. I just thought the method the book gave me may be something I could learn in case my method did not work.

parker · Answer

In general, honing your pattern recognition skills to seek out "chunks" of information can be quite useful, as it often saves time and brain space

Here, the (a+b) chunk is common to both, and if you saw that you could combine the equations that way to eliminate variables (the book solution is the multiplication version of the stack & add/subtract method for systems of equation), awesome. If not-- no worries--substitution will still work, and it's a waste of time to pull your hair out if you don't ID a "cool" way to do a problem quickly. Whenever you have the option, though, some elegant stacking-and-eliminating (or chunking to allow you to eliminate) will cut out a few steps; substitution tends to take longer. To zoom out to the bigger picture, that ability to ID chunks/patterns in unfamiliar info is what will speed you along on the GMAT, and something that all of the highest scorers do. (Splitting/resplitting on Sentence Correction questions is an example of this. And at the heart of it, that's what all the test prep companies are trying to do-- prepare you to recognize patterns in new material-- GMAT questions on your test day-- by analyzing patterns in old material--retired GMAT questions). Bigred, you already seem to be aware of this; bravo to you for recognizing that a solution might contain a future-applicable tool rather than being content with a simple explanation. Good luck with your prep!

Dividing Equations

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