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Director  Joined: 03 Sep 2006
Posts: 767
What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 69% (02:05) correct 31% (02:17) wrong based on 142 sessions

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What is the value of $$\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}$$?

A. a+b-c
B. a-b+c
C. -a+b+c
D. a-b-c
E. -a+b-c
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Joined: 27 Dec 2012
Posts: 1812
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What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab  [#permalink]

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1
$$\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}$$

This also means that $$a^2+b^2+c^2+ac+bc-ab$$ when multiplied with any one of the 5 options, gives answer $$a^3+b^3-c^3+3abc$$

Just focus on $$a^2, b^2, c^2$$ in the LHS & $$a^3+b^3-c^3$$ on RHS

$$a^2$$ has to be multiplied by "a" to give $$a^3$$

Similarly,$$b^{2} * b = b^3$$

$$c^{2} * -c = -c^3$$

Answer = a+b-c

Answer = A
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Kindly press "+1 Kudos" to appreciate ##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 55271
Re: Simplest form of expression  [#permalink]

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3
LM wrote:
What is the value of $$\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}?$$

A) a+b-c

B) a-b+c

C) -a+b+c

D) a-b-c

E) -a+b-c

Plug-in method would be the most efficient way to deal with this problem.

Let $$a=2$$, $$b=1$$ and $$c=0$$. Then $$\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}=3$$. Now let's see which answer choice yields 3:

A. a+b-c=3 --> correct;
B. a-b+c=1 --> discard;
C. -a+b+c=-1 --> discard;
D. a-b-c=1 --> discard;
E. -a+b-c=-1 --> discard.

Answer: A.

P.S. For plug-in method it might happen that for some particular numbers more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

Hope it helps.
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Re: What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab  [#permalink]

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PareshGmat wrote:
$$\frac{a^3+b^3-c^3+3abc}{a^2+b^2+c^2+ac+bc-ab}$$

This also means that $$a^2+b^2+c^2+ac+bc-ab$$ when multiplied with any one of the 5 options, gives answer $$a^3+b^3-c^3+3abc$$

Just focus on $$a^2, b^2, c^2$$ in the LHS & $$a^3+b^3-c^3$$ on RHS

$$a^2$$ has to be multiplied by "a" to give $$a^3$$

Similarly,$$b^{2} * b = b^3$$

$$c^{2} * -c = -c^3$$

Answer = a+b-c

Answer = A

This is such a smart and "simple" approach, kudos mate!
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https://gmatclub.com/forum/verbal-strategies-268700.html#p2082192

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On the mission to improve my quant score, all help is appreciated!  Re: What is the value of a^3+b^3-c^3+3abc/a^2+b^2+c^2+ac+bc-ab   [#permalink] 01 Dec 2018, 10:17
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