NEW HERE? LEARN MORE
closeclose
Last visit was: 13 May 2024, 21:26 It is currently 13 May 2024, 21:26
Decision Tracker
My Rewards
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

HOT Competition 4 Sep/8PM: What is the median of all the values of x

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93243
Own Kudos [?]: 623541 [15]
Given Kudos: 81851
Send PM
CAT Tests Forum Quiz Mode
HOT Competition 4 Sep/8PM: What is the median of all the values of x [#permalink] New post   04 Sep 2020, 20:00
2
Kudos
13
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

69% (01:47) correct 31% (02:04) wrong based on 643 sessions
Hide Show timer Statistics
What is the median of all the values of x, which satisfy \(||x – 3| – 5| = 3\) ?

A. 1
B. 2
C. 3
D. 5
E. 6


 

This question was provided by GMAT Club
for the Heroes of Timers Competition

 



M37-85

Experience a GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93243
Own Kudos [?]: 623541 [1]
Given Kudos: 81851
Send PM
CAT Tests Forum Quiz Mode
Re: HOT Competition 4 Sep/8PM: What is the median of all the values of x [#permalink] New post   03 Dec 2021, 02:39
1
Bookmarks
Expert Reply
Official Solution:

What is the median of all the values of \(x\), which satisfy \(||x – 3| – 5| = 3\) ?

A. \(1\)
B. \(2\)
C. \(3\)
D. \(5\)
E. \(6\)


\(||x – 3| – 5| = 3\) means that \(|x – 3| – 5 = 3\) or \(|x – 3| – 5 = -3\).

CASE 1:

\(|x – 3| – 5 = 3\);

\(|x – 3| = 8\);

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

CASE 2:

\(|x – 3| – 5 = -3\);

\(|x – 3| = 2\);

\(x=5\) or \(x=1\)

So, \(x\) can be (in ascending order): -5, 1, 5, or 11. The median of the values is \(\frac{1+5}{2}=3\).


Answer: C
General Discussion
User avatar
D
minustark
Senior Manager
Senior Manager
Joined: 14 Jul 2019
Status:Student
Posts: 476
Own Kudos [?]: 370 [4]
Given Kudos: 52
Location: United States
Concentration: Accounting, Finance
Schools: Zicklin Baruch "22
GMAT 1: 650 Q45 V35
GPA: 3.9
WE:Education (Accounting)
Send PM
Reviews Badge
Re: HOT Competition 4 Sep/8PM: What is the median of all the values of x [#permalink] New post   04 Sep 2020, 20:07
1
Kudos
3
Bookmarks
What is the median of all the values of x, which satisfy ?

||X -3|-5| = 3
|X-3-5|=3
|X -8| = 3
-3 = x -8 = 3
5 = x = 11

Now, |-x + 3 -5| = 3
-3 = -x -2 = 3
-1 = -x = 5
1 = x = -5

The four values of x are : -5, 1, 5, 11

Median is 3.

A. 1
B. 2
C. 3
D. 5
E. 6

C is the answer.

Posted from my mobile device
User avatar
P
BenjaminS
Manager
Manager
Joined: 28 Aug 2018
Posts: 71
Own Kudos [?]: 109 [2]
Given Kudos: 196
Location: Thailand
Schools: Sloan '23 Anderson '24 Booth '24 Broad Carlson Carroll CEIBS '24 Columbia CBS '24 Darden '24 Goizueta '24 ESADE Foster '24 Fuqua '24 Haas '24 Harvard '24 HKUST IESE '24 IMD '22 ISB '23 Johnson '24 Jones Judge '23 Katz Kelley '24 Kellogg '24 Kenan-Flagler '24 LBS '24 Madison Marshall '24 Mays McCombs '24 McDonough '24 Mendoza Merage NTU NUS Owen '24 Said '23 BU Ross '24 Rotman '24 Erasmus Scheller Bocconi Simon '24 Smeal Stanford '24 Tuck '24 Warwick "23 Wharton '24 Yale '24 Tepper '24
GMAT 1: 610 Q48 V27
Send PM
Re: HOT Competition 4 Sep/8PM: What is the median of all the values of x [#permalink] New post   04 Sep 2020, 20:08
1
Kudos
1
Bookmarks
What is the median of all the values of x, which satisfy ||x–3|–5|=3 ?

A. 1
B. 2
C. 3
D. 5
E. 6

Case 1: |x–3|–5=3
|x–3| = 8
Case 1.1: x-3 = 8
x = 11
Case 1.2: x-3 = -8
x = -5

Case 2: |x–3|–5=-3
|x–3| = 2
Case 2.1: x-3 = 2
x = 5
Case 2.2: x-3 = -2
x = 1

So all the values of x = -5, 1, 5, and 11.
Therefore, the median of all the values of x = \(\frac{1+5}{2}\) = 3.
I choose C.

Posted from my mobile device
User avatar
P
MrBaby
Intern
Intern
Joined: 28 Aug 2018
Posts: 48
Own Kudos [?]: 117 [3]
Given Kudos: 328
Concentration: Entrepreneurship, Healthcare
Schools: Babson Madison CBS '23 Kellogg '23 Sloan '23 Owen '24
Send PM
Re: HOT Competition 4 Sep/8PM: What is the median of all the values of x [#permalink] New post   04 Sep 2020, 20:09
1
Kudos
2
Bookmarks
Quote:
What is the median of all the values of x, which satisfy \(||x–3|–5|=3\) ?

A. 1
B. 2
C. 3
D. 5
E. 6


\(|x–3|–5=3\) , \(|x–3|–5=-3\)
\(|x–3|=8\) , \(|x–3|=2\)
\(x–3=8\) , \(x–3=-8\) , \(x–3=2\) , \(x–3=-2\)
\(x=11\) , \(x=-5\) , \(x=5\) , \(x=1\)

the median of -5,1,5,11 is 3.
ANS C.

Posted from my mobile device
User avatar
L
mSKR
VP
VP
Joined: 14 Aug 2019
Posts: 1373
Own Kudos [?]: 848 [1]
Given Kudos: 381
Location: Hong Kong
Concentration: Strategy, Marketing
Schools: IE (A) IIML-IPMX '22 (A) HKUST '22
GMAT 1: 650 Q49 V29
GPA: 3.81
Send PM
Re: HOT Competition 4 Sep/8PM: What is the median of all the values of x [#permalink] New post   04 Sep 2020, 20:22
1
Kudos
set1:
|x-3| -5 = 3
|x-3| = 8


set1a:
x-3= 8
x= 11


set1b:
x-3= -8
x= -5


or
set2:
|x-3| -5 = - 3
|x-3| = 2

set2a:
x-3= 2
x= 5

set2b:
x-3= -2
x= 1

values of x :


11,-5,5,1

median of (-5,1,5,11)
5+1/2= 3

hence c
avatar
S
AjitJangale
Intern
Intern
Joined: 25 Jun 2019
Posts: 38
Own Kudos [?]: 36 [1]
Given Kudos: 123
Send PM
Re: HOT Competition 4 Sep/8PM: What is the median of all the values of x [#permalink] New post   04 Sep 2020, 20:44
1
Kudos
What is the median of all the values of x, which satisfy ||x–3|–5|=3||x–3|–5|=3 ?

A. 1
B. 2
C. 3
D. 5
E. 6

Let |x–3| = a

||a|–5|=3

Case 1) |a|–5=3
|a|=3+5
|a|=8

Case 2) |a|–5=-3
|a|=-3+5
|a|=2

Now insert value of a

Case 1)
a) |x-3|=8
x-3=8
x=8+3
x=11

b)|x-3|=8
x-3=-8
x=-8+3
x=-5

Case 2)
a)|x-3|=2
x-3=2
x=2+3
x=5

b)|x-3|=2
x-3=-2
x=-2+3
x=1

Values of x are = -5,1,5,11

Median = (1+5)/2 = 3

IMO Answer is C.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32991
Own Kudos [?]: 828 [0]
Given Kudos: 0
Send PM
Re: HOT Competition 4 Sep/8PM: What is the median of all the values of x [#permalink] New post   10 Jun 2023, 21:41
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: HOT Competition 4 Sep/8PM: What is the median of all the values of x [#permalink]
10 Jun 2023, 21:41
Moderators:
Bunuel
Math Expert
93243 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3136 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions