GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 05 Jul 2020, 18:06

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.

Close

Request Expert Reply

Confirm Cancel

If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64951
If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

Show Tags

New post 28 May 2020, 05:01
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (01:55) correct 42% (02:16) wrong based on 57 sessions

HideShow timer Statistics

GMAT Club Legend
GMAT Club Legend
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4313
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

Show Tags

New post Updated on: 28 May 2020, 22:22
1
1
Bunuel wrote:
If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the value of |m - n| ?

A. 0
B. 1
C. 2
D. 9
E. 18




i.e. x^2 - 7|x| - 18 = 0

i.e. lxl^2 - 7|x| - 18 = 0

i.e. |x|(|x|-9)+2(|x|-9)=0

i.e. (|x|-9)(|x|+2)=0

i.e. |x|=9 or -2

But lxl is never negative hence lxl = 9

i.e. x = -9 and +9 which are the values of m and n hence

lm-nl = l-9-9l = 18



Answer: Option E
_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Click for FREE Demo on VERBAL & QUANT
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.

Originally posted by GMATinsight on 28 May 2020, 05:18.
Last edited by GMATinsight on 28 May 2020, 22:22, edited 1 time in total.
PS Forum Moderator
User avatar
G
Joined: 18 Jan 2020
Posts: 1018
Location: India
GPA: 4
CAT Tests
Re: If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

Show Tags

New post 28 May 2020, 05:40
GMATinsight wrote:
Bunuel wrote:
If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the value of |m - n| ?

A. 0
B. 1
C. 2
D. 9
E. 18

Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS


Are You Up For the Challenge: 700 Level Questions



SUm of the roots = -b/a
Product of the roots = c/a

i.e. x^2 - 7|x| - 18 = 0

i.e. Roots = -9 and +9

lm-nl = l-9-9l = 18

Answer: Option E


Sir, shouldn't roots be -9,&2 or -2&9
Because (x+9)(x-9) quadratic equation is x^2-81
Kindly Revert

Posted from my mobile device
Manager
Manager
avatar
S
Joined: 10 Jun 2018
Posts: 59
Re: If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

Show Tags

New post 28 May 2020, 06:06
2
1
\(x^2\)-7|x|-18=0
\(|x|^2\)-7|x|-18=0 --> (\(x^2\) can be written as \(|x|^2\))
\(|x|^2\)-9|x|+2|x|-18=0
|x|(|x|-9)+2(|x|-9)=0
(|x|-9)(|x|+2)=0
|x|=9 or -2

Since modulus value is never negative, discard |x|=-2
Solution of equation:
|x|=9
x=9 or x=-9

Sum of solutions of the above equation = |9-(-9)|=18

Answer: E
GMAT Club Legend
GMAT Club Legend
User avatar
V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4313
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Reviews Badge
Re: If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

Show Tags

New post 28 May 2020, 06:11
1
yashikaaggarwal wrote:
GMATinsight wrote:
Bunuel wrote:
If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the value of |m - n| ?

A. 0
B. 1
C. 2
D. 9
E. 18

Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS


Are You Up For the Challenge: 700 Level Questions



SUm of the roots = -b/a
Product of the roots = c/a

i.e. x^2 - 7|x| - 18 = 0

i.e. Roots = -9 and +9

lm-nl = l-9-9l = 18

Answer: Option E


Sir, shouldn't roots be -9,&2 or -2&9
Because (x+9)(x-9) quadratic equation is x^2-81
Kindly Revert

Posted from my mobile device


yashikaaggarwal

-2&9 are the values of lxl and not of x

but lxl can not be -ve so -2 is out anyway 2 and -2 do NOT satisfy the equation

so we are left with

lxl = 9

ie.. x = +9 or -9

I hope that help
_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting

Most affordable l Comprehensive l 2000+ Qn ALL with Video explanations l LINK: Courses and Pricing
Click for FREE Demo on VERBAL & QUANT
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
FREE GMAT Resource: 22 FREE (FULL LENGTH) GMAT CATs LINKS l NEW OG QUANT 50 Qn+VIDEO Sol.
Director
Director
User avatar
D
Joined: 16 Jan 2019
Posts: 650
Location: India
Concentration: General Management
WE: Sales (Other)
Re: If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

Show Tags

New post 28 May 2020, 08:35
2
1
Bunuel wrote:
If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the value of |m - n| ?

A. 0
B. 1
C. 2
D. 9
E. 18

Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS



Are You Up For the Challenge: 700 Level Questions


\(x^2 - 7|x| - 18 = 0\)

\(x=0\) is obviously not a solution so \(x\) is either positive or negative

Case 1: When \(x\) is positive (\(|x|=x\)),

\(x^2 - 7|x| - 18 = 0\) becomes \(x^2 - 7x - 18 = 0\)

Or \((x-9)(x+2)=0\) so \(x=9\) or \(-2\)

But since in this case \(x\) is positive, \(x=9\) is only possible root

\(m=9\)

Case 2: When \(x\) is negative (\(|x|=-x\)),

\(x^2 - 7|x| - 18 = 0\) becomes \(x^2 + 7x - 18 = 0\)

Or \((x+9)(x-2)=0\), so \(x=-9\) or \(2\)

But since in this case \(x\) is negative, \(x=-9\) is only possible root

\(n=-9\)

Therefore \(|m-n| = |9-(-9)| = 18\)

Answer is (E)
Senior Manager
Senior Manager
User avatar
G
Joined: 05 Aug 2019
Posts: 293
Location: India
Concentration: Leadership, Technology
GMAT 1: 600 Q50 V22
GPA: 4
CAT Tests
Re: If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

Show Tags

New post 29 May 2020, 10:18
See the attachment.
E - 18
Attachments

1.PNG
1.PNG [ 21.32 KiB | Viewed 336 times ]

GMAT Club Bot
Re: If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu   [#permalink] 29 May 2020, 10:18

If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne