Why do reverse PEMDAS

[veronica1]

Question: Why not distribute
the 8?
Problem:
8(x - 7) + 20 = 4

x =

Answer:

Do "reverse PEMDAS" to solve the equation:

Problem 8(x - 7) + 20 = 4
A/S 8(x - 7) = -16
M/D (x - 7) = -2
E
P x = 5

The correct answer is C.

[veronica1]

Another example:
Do "reverse PEMDAS" to solve the equation:


problem: 5(3x + 1) - 1 = 7
A/S 5(3x + 1) = 8
M/D 3x + 1) = 8/5
E
P 3x = 3/5
x = 1/5

[tim]

there's nothing wrong with your method. it's a good idea to practice this question both ways so you can be prepared for whichever is more effective on actual GMAT questions..

[michaelbrettgonzalez]

BUMP
I have the same question and I don't really find Tim's reply helpful. I understand that both methods will get the right answer but as I am reviewing the Math Foundations I tests, I can see that "reverse PEMDAS" is often times much faster. So is there a hard and fast rule on when to use PEMDAS and when to use ASMDEP?

[RonPurewal]

BUMP
I have the same question and I don't really find Tim's reply helpful. I understand that both methods will get the right answer but as I am reviewing the Math Foundations I tests, I can see that "reverse PEMDAS" is often times much faster. So is there a hard and fast rule on when to use PEMDAS and when to use ASMDEP?

this whole "looking for hard and fast rules" thing is your biggest enemy on the gmat exam; don't slip into this mentality (and, if you're already there, try to break out of it!).
the biggest point of the gmat exam is to require mental flexibility. you don't have to master a ton of mathematical concepts -- in fact, the exam doesn't test anything that comes after first-year algebra and geometry in an American school -- but you do have to be able to manipulate those concepts in all kinds of different ways.
so, the important point here is just to be able to play around with the expressions/equations in as many (workable) ways as possible.

most importantly, there's no point at all in worrying about "efficiency" when it comes to basic algebra.
even if there are time savings involved in one method over the other, we're talking about a savings of ... two seconds? three?
the procedures shown here don't even take more than 10-15 seconds from start to finish, so it should be clear that thinking about "efficiency" here is just a distraction.

[tim]

On top of everything Ron said, I would emphasize that one of the problems in looking for a hard and fast rule for which method to use is useless precisely because different people may find different methods better in different situations. Without practicing both methods as often as you can anytime you have two potential methods, you will never learn to get a sense of which methods work better for you in which situations. I'm sorry that you didn't find helpful my earlier answer suggesting an open mind and a variety of approaches; as Ron mentioned, if you can break out of the rigid mindset that traps you into looking for hard and fast rules, you will be doing yourself the best possible favor you can in preparing for the GMAT.

[michaelbrettgonzalez]

Tim and Ron,
Thank you both for your replies. I think I my question was misleading when I said "hard and fast". The bottom line is that I am confused by the fact that both PEMDAS and ASMDEP work properly. I understand that MDEASP (or any other random combination) will not work but I have been struggling to understand why both PEMDAS and ASMDEP do. Sounds like on this one I just need to push the "I believe" button and drive on.

I know myself and I know that I will perform better on the GMAT if I understand the WHY.

[RonPurewal]

I have been struggling to understand why both PEMDAS and ASMDEP do.

one thing it seems you're overlooking here is the difference between doing math operations and undoing them.

when you talk about "PEMDAS", that's a tool for evaluating expressions involving numbers. e.g., if i give you an expression like 7 - 4 x 3 + 2, then you use "PEMDAS" to evaluate that expression.
note, in particular, that you are not solving anything here; you are just simplifying/evaluating a numerical expression.

on the other hand, when you talk about solving an algebraic equation for a variable, you aren't talking about "PEMDAS" anymore. instead, you're talking about UNdoing the mathematical steps, to "strip down" the equation to the bare variable you want to solve for.

in other words, here's an analogy:
* when you get dressed, you put your underwear on before your pants.
* when you get UNdressed, you don't try to take them off in the same order! that wouldn't work out so well.
viewed in this light, what's wrong with your question should be a lot easier to see. in other words, saying "i'm not sure when to use PEMDAS and when not to" is a lot like saying, in this example, "i'm not sure when the underwear is first".
hope that helps.