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555-605 (Medium)|   Algebra|      
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mikemcgarry
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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + Updated on: 17 Oct 2012, 04:32
Originally posted by mikemcgarry on 16 Oct 2012, 11:07.
Last edited by Bunuel on 17 Oct 2012, 04:32, edited 1 time in total.
Renamed the topic.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

75% (02:08) correct 25% (02:58) wrong based on 373 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:
https://magoosh.com/gmat/2012/algebra-on ... to-factor/
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B
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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + 16 Oct 2012, 11:21
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mikemcgarry
If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + |d| =
(A) 10
(B) 12
(C) 15
(D) 18
(E) 20
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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

Answer B.
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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + 24 Jul 2015, 04:21
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mikemcgarry
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:
https://magoosh.com/gmat/2012/algebra-on ... to-factor/
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mikemcgarry
This should be 700+ as you describe in your blog right?
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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + 24 Jul 2015, 05:04
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\(6x^2 + x - 12 = 6x^2 + 9x - 8x - 12 = 3x(2x+3) - 4(2x+3) = (3x-4) (2x+3)\)

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

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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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + 24 Jul 2015, 11:22
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reto
This should be 700+ as you describe in your blog right?
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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:
https://magoosh.com/gmat/2014/is-this-a- ... -question/

Does this make sense?
Mike :-)
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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + 22 May 2021, 03:40
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I think a major information missing here is that a,b,c and d are integers. The reason being, if you don’t consider them to be integers then 4/3 and -3/2 are also roots which will give an answer of 29/6.

Posted from my mobile device
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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + 09 May 2022, 01:49
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Hello !

If 6𝑥2+𝑥–12=(𝑎𝑥+𝑏)(𝑐𝑥+𝑑), then |a| + |b| + |c| + |d|

(A) 10

(B) 12

(C) 15

(D) 18

(E) 20


i have successfully found out possible group for a and c, b and d but there are so many possibilities to get ad+bc=1 it took a very long time and still no matches . how to solve this ?

thanks in advance ! :)
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If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + 07 Sep 2024, 06:52
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