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PEMDAS clarification needed...

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Joined: 14 Apr 2015
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Location: United States
Concentration: Nonprofit, Entrepreneurship
GMAT Date: 06-14-2015
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WE: Marketing (Non-Profit and Government)
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Kudos [?]: 6 [0], given: 12

PEMDAS clarification needed... [#permalink] New post 05 Jul 2015, 19:12
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!
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Posts: 904
Concentration: Finance, Strategy
GMAT 1: 650 Q49 V30
GMAT 2: 690 Q49 V34
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PEMDAS clarification needed... [#permalink] New post 05 Jul 2015, 19:20
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meshackb wrote:
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!


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.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-87417.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Intern
Intern
avatar
Joined: 14 Apr 2015
Posts: 20
Location: United States
Concentration: Nonprofit, Entrepreneurship
GMAT Date: 06-14-2015
GPA: 3.93
WE: Marketing (Non-Profit and Government)
Followers: 0

Kudos [?]: 6 [0], given: 12

PEMDAS clarification needed... [#permalink] New post 05 Jul 2015, 19:57
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 =
1 KUDOS received
Math Forum Moderator
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Joined: 20 Mar 2014
Posts: 904
Concentration: Finance, Strategy
GMAT 1: 650 Q49 V30
GMAT 2: 690 Q49 V34
GMAT 3: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 19

Kudos [?]: 282 [1] , given: 134

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PEMDAS clarification needed... [#permalink] New post 06 Jul 2015, 02:11
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meshackb wrote:
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 =


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.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-87417.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

PEMDAS clarification needed...   [#permalink] 06 Jul 2015, 02:11
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