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
Algebra Attack !
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Plugging in some nice numbers is a great approach.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
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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Here's an algebraic approach: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
Correct answer = D
Cheers,
Brent
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The algebraic approach works best here I presume!Brent@GMATPrepNow wrote:Here's an algebraic approach: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
Correct answer = D
Cheers,
Brent
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I think the algebraic approach is slightly better (i.e., faster) for this question.vinay1983 wrote:
The algebraic approach works best here I presume!
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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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)btabsang 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
= ab(a-b) + ac(c-a) + bc(b-c)
Divide this by abc.
Choose d
Cheers
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Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
Thanks Brent !
Thanks for detailing the various methods and for illustrating the algebraic approach.
Really appreciate it, this helps
Cheers,
Taz
Thanks for detailing the various methods and for illustrating the algebraic approach.
Really appreciate it, this helps
Cheers,
Taz
Brent@GMATPrepNow wrote:Here's an algebraic approach: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
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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich