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Algebra Attack !

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by tabsang » Tue Sep 24, 2013 10:34 am
Okay this will look ugly but it's an interesting question.
Is it possible to nail this within 2 minutes?

a^2(b-c) + b^2(c-a) + c^2(a-b)
----------------------------------------xxxxxxis the same as:
xxxxxxxxxxabc

(a) (a^2+b^2+c^2)(a+b+c)

(b) (a+b(b+c)(c+a)

(c) (a-b)(c-a)

(d) (a-b)/c + (b-c)/a + (c-a)/b

(e) b/a + c/b + a/c

OA: [spoiler](d)[/spoiler]

I picked numbers (a=b=c=1) & got it down to (C) & (D) but then got stuck :(
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by Brent@GMATPrepNow » Tue Sep 24, 2013 11:03 am
tabsang wrote:Okay this will look ugly but it's an interesting question.
Is it possible to nail this within 2 minutes?

a^2(b-c) + b^2(c-a) + c^2(a-b)
----------------------------------------xxxxxxis the same as:
xxxxxxxxxxabc

(a) (a^2+b^2+c^2)(a+b+c)

(b) (a+b(b+c)(c+a)

(c) (a-b)(c-a)

(d) (a-b)/c + (b-c)/a + (c-a)/b

(e) b/a + c/b + a/c

OA: [spoiler](d)[/spoiler]

I picked numbers (a=b=c=1) & got it down to (C) & (D) but then got stuck :(
Plugging in some nice numbers is a great approach.
From here, you might eliminate C or D by plugging in another set of values.


Alternatively, now that you've eliminated the correct answer to either C or D, take a look at each remaining option.

C) (a-b)(c-a)
The ORIGINAL expression has a lot of symmetry, as well as even distribution of a's, b's and c's. HOWEVER, answer choice C does not have symmetry, and it does not have even distribution of a's, b's and c's.
Instead, answer choice C has one b, one c and two a's.
The symmetrical original expression would NOT simplify to have a greater emphasis on one variable.
Based on this, we can eliminate C.

D) (a-b)/c + (b-c)/a + (c-a)/b
Answer choice D retains symmetry AND has an even distribution of a's, b's and c's.
So, the correct answer must be D.

Cheers,
Brent
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by Brent@GMATPrepNow » Tue Sep 24, 2013 11:04 am
tabsang wrote:Okay this will look ugly but it's an interesting question.
Is it possible to nail this within 2 minutes?

a^2(b-c) + b^2(c-a) + c^2(a-b)
----------------------------------------xxxxxxis the same as:
xxxxxxxxxxabc

(a) (a^2+b^2+c^2)(a+b+c)

(b) (a+b(b+c)(c+a)

(c) (a-b)(c-a)

(d) (a-b)/c + (b-c)/a + (c-a)/b

(e) b/a + c/b + a/c

OA: [spoiler](d)[/spoiler]

I picked numbers (a=b=c=1) & got it down to (C) & (D) but then got stuck :(
Here's an algebraic approach:
Image

Correct answer = D

Cheers,
Brent
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by vinay1983 » Tue Sep 24, 2013 5:03 pm
Brent@GMATPrepNow wrote:
tabsang wrote:Okay this will look ugly but it's an interesting question.
Is it possible to nail this within 2 minutes?

a^2(b-c) + b^2(c-a) + c^2(a-b)
----------------------------------------xxxxxxis the same as:
xxxxxxxxxxabc

(a) (a^2+b^2+c^2)(a+b+c)

(b) (a+b(b+c)(c+a)

(c) (a-b)(c-a)

(d) (a-b)/c + (b-c)/a + (c-a)/b

(e) b/a + c/b + a/c

OA: [spoiler](d)[/spoiler]

I picked numbers (a=b=c=1) & got it down to (C) & (D) but then got stuck :(
Here's an algebraic approach:
Image

Correct answer = D

Cheers,
Brent
The algebraic approach works best here I presume!
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by Brent@GMATPrepNow » Tue Sep 24, 2013 6:25 pm
vinay1983 wrote:
The algebraic approach works best here I presume!
I think the algebraic approach is slightly better (i.e., faster) for this question.
It can be quite time consuming to plug 3 different variables into 6 expressions.
AND if the first round fails to eliminate 4 answer choices, you'll probably need to plug in another set of numbers (and possibly ANOTHER set, if you choose your numbers poorly).

Cheers,
Brent
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by ganeshrkamath » Tue Sep 24, 2013 8:50 pm
tabsang wrote:Okay this will look ugly but it's an interesting question.
Is it possible to nail this within 2 minutes?

a^2(b-c) + b^2(c-a) + c^2(a-b)
----------------------------------------xxxxxxis the same as:
xxxxxxxxxxabc

(a) (a^2+b^2+c^2)(a+b+c)

(b) (a+b(b+c)(c+a)

(c) (a-b)(c-a)

(d) (a-b)/c + (b-c)/a + (c-a)/b

(e) b/a + c/b + a/c

OA: [spoiler](d)[/spoiler]

I picked numbers (a=b=c=1) & got it down to (C) & (D) but then got stuck :(
a^2(b-c) + b^2(c-a) + c^2(a-b) = (a^2)b - (a^2)c + (b^2)c - (b^2)a + (c^2)a - (c^2)b
= ab(a-b) + ac(c-a) + bc(b-c)
Divide this by abc.

Choose d

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by tabsang » Thu Sep 26, 2013 5:28 am
Thanks Brent !

Thanks for detailing the various methods and for illustrating the algebraic approach.
Really appreciate it, this helps :) :)

Cheers,
Taz
Brent@GMATPrepNow wrote:
tabsang wrote:Okay this will look ugly but it's an interesting question.
Is it possible to nail this within 2 minutes?

a^2(b-c) + b^2(c-a) + c^2(a-b)
----------------------------------------xxxxxxis the same as:
xxxxxxxxxxabc

(a) (a^2+b^2+c^2)(a+b+c)

(b) (a+b(b+c)(c+a)

(c) (a-b)(c-a)

(d) (a-b)/c + (b-c)/a + (c-a)/b

(e) b/a + c/b + a/c

OA: [spoiler](d)[/spoiler]

I picked numbers (a=b=c=1) & got it down to (C) & (D) but then got stuck :(
Here's an algebraic approach:
Image

Correct answer = D

Cheers,
Brent
If this post helped you in your GMAT prep, please take a moment and hit the "thanks" button. It'll make my day :) :)
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by [email protected] » Thu Sep 26, 2013 11:31 am
Hi tabsang,

If you're going to TEST values in this type of situation, you should TEST three DIFFERENT numbers.

If you try
A = 1
B = 2
C = 3

The math is really fast and easy AND you can eliminate most of the answers based on formatting alone. Here's how:

Plugging in the above values to the original equation will give you an end result of -1/3
Notice how we need a NEGATIVE FRACTION as an answer:

You can eliminate B and C because they're not fractions and you can eliminate E because it can't be negative. This means you just have to plug in your values into A and D. This is a HUGE time saver.

Final Answer: D

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