PEMDAS clarification needed...

Question

So I'm working on this problem:

2013^2 + 2014 − 2014^2 + 2013= ?

The official solution rearranges the terms to get:

2013^2 + 2013 + 2014 − 2014^2=

Is this legal? I thought PEMDAS for addition and subtraction said you should work left to right, in which case, this would be illegal? Is there some mathematical explanation for this move? Thanks!

ENGRTOMBA2018 · Answer

You are correct about your PEMDAS work order but you also need to remember a couple of things about addition:

A+B = B+A, thus 2014+2013 = 2013+2014. It is merely a rearrangement of terms and nothing else. This is very much 'legal! Also for given question, rearrangement as mentioned in the official solution will aid in the next step of taking the similar terms common in the form below:

2013^2 + 2013 + 2014 − 2014^2 = 2013(2013+1)+ 2014(1-2014) = 2013*2014+2014*(-2013) = 0

In GMAT, you should always try to find ways to simplify equations. This can be done by taking terms common, cancelling same factors out of numerator and denominator etc. Rearrangment is only a 'pre processing ' step before you actually simplify an equation

For the sake of completeness,

A+B= B+A (always)
A*B= B*A (always)
A-B may or may not be equal to B-A 
Finally, A/B may or may not be equal to B/A

You can see the above 'rules' by plugging in a few values for A and B.

meshackb · Answer

Ok, I think I get it... jeez, all these finer points of math that they never taught in high school are killing me. I knew I had to do factoring somewhere in this problem, but I was stuck on thinking I couldn't rearrange the terms.

So if I understand, this is what you are saying.

In this problem we basically have

a + b - c + d =

as long as we keep (b - c), we can rearrange the other terms around that however we like correct?

So the next step is basically

a + d + b - c = { b-c still in same order }

But to do this would be illegal, correct?:

a - c + d + b =

ENGRTOMBA2018 · Answer

No, you are looking at it incorrectly. You can rearrange terms in an equation as long as you keep the 'signs' before the terms.

Example, if you are given a+b-c+d , then you can also write it as a+d+b-c or a+d-c+b or -c+b+d+a as long as you keep + sign in front of a,b and d and - sign before c.

Finally any number 'a' is actually +a as 'a'= 0+a.

This is all you need to remember for rearranging the terms. You can rearrange all you want but make sure to keep the signs intact.

Side note, a- c + d + b is completely legal as you are still maintaining the correct signs before the variables. It does not matter if you write a+b-c+d or -c+a+b+d or d-c+a+b as we are still maintaining the signs. Another way to look at it is this: If we write b-c, we can also write it as : b+(-c). This does not violate any rule.

Now, as I stated above that a+b = b+a, thus b-c = b+(-c)= -c+b

Hope this helps.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

PEMDAS clarification needed...

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards