It is currently 20 Jan 2018, 03:27

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many real numbers x satisfy ||x-3|-4|=4?

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

Hide Tags

Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 4692

Kudos [?]: 3320 [0], given: 0

GPA: 3.82
Premium Member
How many real numbers x satisfy ||x-3|-4|=4? [#permalink]

Show Tags

New post 04 Dec 2017, 00:36
Expert's post
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

41% (01:12) correct 59% (01:15) wrong based on 85 sessions

HideShow timer Statistics

[GMAT math practice question]

How many real numbers \(x\) satisfy \(||x-3|-4|=4\)?

A. 1
B. 2
C. 3
D. 4
E. 5
[Reveal] Spoiler: OA

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3320 [0], given: 0

1 KUDOS received
PS Forum Moderator
avatar
P
Joined: 25 Feb 2013
Posts: 815

Kudos [?]: 381 [1], given: 42

Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
How many real numbers x satisfy ||x-3|-4|=4? [#permalink]

Show Tags

New post 04 Dec 2017, 04:35
1
This post received
KUDOS
MathRevolution wrote:
[GMAT math practice question]

How many real numbers \(x\) satisfy \(||x-3|-4|=4\)?

A. 1
B. 2
C. 3
D. 4
E. 5


\(||x-3|-4|=4\)

\(=>|x-3|-4=4\) or \(|x-3|-4=-4\)

\(=>|x-3|=8\) or \(|x-3|=0\)

\(=>x-3=8\) or \(x-3=-8\) or \(x=3\)

\(=>x=11\) or \(x=-5\) or \(x=3\)

Hence \(3\) real values satisfy the equation

Option C

Kudos [?]: 381 [1], given: 42

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5534

Kudos [?]: 6439 [0], given: 122

Re: How many real numbers x satisfy ||x-3|-4|=4? [#permalink]

Show Tags

New post 04 Dec 2017, 05:14
MathRevolution wrote:
[GMAT math practice question]

How many real numbers \(x\) satisfy \(||x-3|-4|=4\)?

A. 1
B. 2
C. 3
D. 4
E. 5





if you have POSITIVE values on both sides, you can square both sides..


\(||x-3|-4|=4............(|x-3|-4)^2=4^2.........(x-3)^2+4^2-2*4*|x-3|=4^2.........(x-3)^2=8|x-3|\)
you can square both sides again
\((x-3)^2=8|x-3|.............(x-3)^4=8^2*(x-3)^2..............(x-3)^4-8^2*(x-3)^2=0.................(x-3)^2((x-3)^2-8^2)=0.....................(x-3)^2(x-3-8)(x-3+8)=0............(x-3)^2(x-11)(x+5)=0\)
so roots of equation or the different values of x are 3,11,-5
ans 3 different values
C
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

Kudos [?]: 6439 [0], given: 122

Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 4692

Kudos [?]: 3320 [0], given: 0

GPA: 3.82
Premium Member
How many real numbers x satisfy ||x-3|-4|=4? [#permalink]

Show Tags

New post 06 Dec 2017, 00:09
=>

\(| |x-3| - 4 | = 4\)
\(⇔ |x-3| - 4= ± 4\)
\(⇔ |x-3| = 4 ± 4\)
\(⇔ |x-3| = 8\) or \(|x-3| = 0\)
\(⇔ x-3 = ±8\) or \(x-3 = 0\)
\(⇔ x = 3 ± 8\) or \(x = 3\)
\(⇔ x = 11, x = -5\) or \(x = 3\)

The equation has 3 solutions.

Therefore, the answer is C.

Answer : C
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3320 [0], given: 0

How many real numbers x satisfy ||x-3|-4|=4?   [#permalink] 06 Dec 2017, 00:09
Display posts from previous: Sort by

How many real numbers x satisfy ||x-3|-4|=4?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.