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

 It is currently 14 Jul 2020, 15:24

### 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

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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 65290
If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

### Show Tags

28 May 2020, 05:01
00:00

Difficulty:

65% (hard)

Question Stats:

57% (01:55) correct 43% (02:19) wrong based on 60 sessions

### HideShow timer Statistics

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

Are You Up For the Challenge: 700 Level Questions

_________________
GMAT Club Legend
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4372
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

### Show Tags

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

_________________
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
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
Joined: 18 Jan 2020
Posts: 1194
Location: India
GPA: 4
Re: If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

### Show Tags

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

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

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
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

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

GMAT Club Legend
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 4372
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

### Show Tags

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

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

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
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
Joined: 16 Jan 2019
Posts: 660
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

28 May 2020, 08:35
3
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

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 $$|m-n| = |9-(-9)| = 18$$

Senior Manager
Joined: 05 Aug 2019
Posts: 301
Location: India
GMAT 1: 600 Q50 V22
GPA: 4
Re: If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu  [#permalink]

### Show Tags

29 May 2020, 10:18
1
See the attachment.
E - 18
Attachments

1.PNG [ 21.32 KiB | Viewed 366 times ]

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