Last visit was: 22 May 2024, 19:55 It is currently 22 May 2024, 19:55
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4461
Own Kudos [?]: 28669 [13]
Given Kudos: 130
If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink] If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +   Updated on: 17 Oct 2012, 04:32
2
Kudos
11
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

77% (02:02) correct 23% (03:01) wrong based on 259 sessions
Hide Show timer Statistics
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/
ShowHide Answer
Official Answer
B

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.
Most Helpful Reply
User avatar
SOURH7WK
Manager
Manager
Joined: 15 Jun 2010
Posts: 242
Own Kudos [?]: 1177 [6]
Given Kudos: 50
Concentration: Marketing
Schools:IE'14, ISB'14, Kellogg'15
 Q47  V26 GMAT 2: 540  Q45  V19 GMAT 3: 580  Q48  V23
GPA: 3.2
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Send PM
Reviews Badge
Re: hard factoring problem [#permalink] If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +   16 Oct 2012, 11:21
5
Kudos
1
Bookmarks
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

Answer B.
General Discussion
User avatar
reto
Retired Moderator
Joined: 29 Apr 2015
Posts: 717
Own Kudos [?]: 4229 [0]
Given Kudos: 302
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE:Asset Management (Investment Banking)
Send PM
GMAT ToolKit User
Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink] If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +   24 Jul 2015, 04:21
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:
https://magoosh.com/gmat/2012/algebra-on ... to-factor/


mikemcgarry
This should be 700+ as you describe in your blog right?
User avatar
B
TimeTraveller
Senior Manager
Senior Manager
Joined: 28 Jun 2015
Posts: 250
Own Kudos [?]: 294 [0]
Given Kudos: 47
Concentration: Finance
GPA: 3.5
Send PM
Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink] If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +   24 Jul 2015, 05:04
\(6x^2 + x - 12 = 6x^2 + 9x - 8x - 12 = 3x(2x+3) - 4(2x+3) = (3x-4) (2x+3)\)

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

therefore, \(a = 3, b = -4, c = 2, d = 3\).

\(|a| + |b| + |c| + |d| = |3| +|-4| +|2| +|3| = 3+4+2+3 = 12\). Ans (B).
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4461
Own Kudos [?]: 28669 [0]
Given Kudos: 130
Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink] If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +   24 Jul 2015, 11:22
Expert Reply
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:
https://magoosh.com/gmat/2014/is-this-a- ... -question/

Does this make sense?
Mike :-)
avatar
B
NeedThatScore1694
Intern
Intern
Joined: 05 Apr 2020
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 16
Send PM
GMAT ToolKit User
Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink] If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +   22 May 2021, 03:40
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
User avatar
B
arbre
Intern
Intern
Joined: 19 Aug 2021
Posts: 44
Own Kudos [?]: 0 [0]
Given Kudos: 3
Send PM
Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink] If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| +   09 May 2022, 01:49
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 ! :)
+1
GMAT Club Bot
gmatclubot
Re: If 6x^2 + x - 12 = (ax + b)(cx + d), then |a| + |b| + |c| + [#permalink]
09 May 2022, 01:49
Moderator:
Bunuel
Math Expert
93405 posts