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# If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
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Kudos [?]: 9271 [1], given: 117

If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink]

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16 Oct 2012, 10:07
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Difficulty:

25% (medium)

Question Stats:

78% (01:36) correct 22% (02:28) wrong based on 131 sessions

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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + |d| =
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20

For a complete solution and more practice problems, see this blog:
http://magoosh.com/gmat/2012/algebra-on ... to-factor/
[Reveal] Spoiler: OA

_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Last edited by Bunuel on 17 Oct 2012, 03:32, edited 1 time in total.
Renamed the topic.

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16 Oct 2012, 10:21
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mikemcgarry wrote:
If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + |d| =
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20

6x^2+x-12 = 6x^2 + 9x -8x -12
=> 3x(2x+3) -4(2x+3)
=> (2x+3)(3x-4) = (ax+b)(cx+d)
Hence a=2, b=c=3, d=-4

So, 2+3+3+ |-4| = 2+3+3+4 = 12

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Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink]

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24 Jul 2015, 03:21
mikemcgarry wrote:
If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + |d| =
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20

For a complete solution and more practice problems, see this blog:
http://magoosh.com/gmat/2012/algebra-on ... to-factor/

mikemcgarry
This should be 700+ as you describe in your blog right?
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Senior Manager
Joined: 28 Jun 2015
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Concentration: Finance
GPA: 3.5
Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink]

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24 Jul 2015, 04:04
$$6x^2 + x - 12 = 6x^2 + 9x - 8x - 12 = 3x(2x+3) - 4(2x+3) = (3x-4) (2x+3)$$

$$(3x-4) (2x+3) = (ax+b) (cx+d)$$

therefore, $$a = 3, b = -4, c = 2, d = 3$$.

$$|a| + |b| + |c| + |d| = |3| +|-4| +|2| +|3| = 3+4+2+3 = 12$$. Ans (B).
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Kudos [?]: 115 [0], given: 47

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4643

Kudos [?]: 9271 [0], given: 117

Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink]

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24 Jul 2015, 10:22
reto wrote:
This should be 700+ as you describe in your blog right?

Dear reto,
I'm happy to respond. This is a rather challenging question, about as hard as the GMAT Quant would ever ask. It's rare that they would ask you to factor a quadratic with a lead coefficient other than 1.

Nevertheless, I am of the opinion that the idea of a "700+ question" is suspect and possibly flawed. See this blog article:
http://magoosh.com/gmat/2014/is-this-a- ... -question/

Does this make sense?
Mike
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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink]

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05 Oct 2017, 12:08
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +   [#permalink] 05 Oct 2017, 12:08
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