Last visit was: 29 Apr 2026, 23:51 It is currently 29 Apr 2026, 23:51
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 29 Apr 2026
Posts: 109,994
Own Kudos:
812,022
 [8]
Given Kudos: 105,957
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,994
Kudos: 812,022
 [8]
How many distinct solutions does the equation |1 - |x - 215|| = 1 have 21 Feb 2023, 04:03
1
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

64% (01:31) correct 36% (01:34) wrong based on 374 sessions

History

Date
Time
Result
Not Attempted Yet
How many distinct solutions does the equation |1 - |x - 215|| = 1 have?

A. None

B. One

C. Two

D. Three

E. Four
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 29 Apr 2026
Posts: 109,994
Own Kudos:
812,022
 [4]
Given Kudos: 105,957
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,994
Kudos: 812,022
 [4]
How many distinct solutions does the equation |1 - |x - 215|| = 1 have 24 Feb 2023, 01:58
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
BusinessAdmin
Can someone please explain why there are three solutions and not two?
Show more

How many distinct solutions does the equation |1 - |x - 215|| = 1 have?

A. None

B. One

C. Two

D. Three

E. Four

|1 - |x - 215|| = 1:

Case 1:
1 - |x - 215| = 1
|x - 215| = 0
x = 215.

Case 2:
1 - |x - 215| = -1
|x - 215| = 2
x - 215 = 2 or x - 215 = -2
x = 217 or x = 213.

So, x can be 213, 215, and 217.

Answer: D.

Hope it helps.
General Discussion
User avatar
Rabab36
User avatar
Joined: 17 Jun 2022
Last visit: 23 Aug 2024
Posts: 243
Own Kudos:
158
Given Kudos: 67
Posts: 243
Kudos: 158
How many distinct solutions does the equation |1 - |x - 215|| = 1 have 21 Feb 2023, 10:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
|1 - |x - 215|| = 1
solving we get 4 values of x

only 2 values of x satisfy equation
x=215 and x=217

thereofre option c correct
User avatar
BusinessAdmin
User avatar
Joined: 25 Aug 2020
Last visit: 26 Aug 2024
Posts: 12
Own Kudos:
3
 [1]
Given Kudos: 9
Location: India
Concentration: General Management, Strategy
Schools: Kellogg (A)
GPA: 3.8
Schools: Kellogg (A)
Posts: 12
Kudos: 3
 [1]
How many distinct solutions does the equation |1 - |x - 215|| = 1 have 23 Feb 2023, 19:25
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Can someone please explain why there are three solutions and not two?
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 27 Apr 2026
Posts: 2,287
Own Kudos:
2,684
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,287
Kudos: 2,684
How many distinct solutions does the equation |1 - |x - 215|| = 1 have Updated on: 10 Jan 2025, 06:31
Originally posted by BrushMyQuant on 10 Oct 2024, 22:39.
Last edited by BrushMyQuant on 10 Jan 2025, 06:31, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
↧↧↧ Detailed Video Solution to the Problem ↧↧↧


We need to find how many distinct solutions does the equation |1 - |x - 215|| = 1 have?

Now, | 1 - Something | = 1
=> Something = 0 or 2
Making 1 - Something = 1 or -1 and | 1 - Something | = 1
=> | x - 215| = 0 or 2

We have two cases
-Case 1: | x - 215| = 0
=> x - 215 = 0
=> x = 215		-Case 2: | x - 215 | = 2
=> x - 215 = 2 or x - 215 = -2
=> x = 217 or 213

So, there are three solutions x = 213, 215, 217

So, Answer will be D
Hope it helps!

Watch the following video to MASTER Absolute Values

User avatar
adityapal1989
User avatar
Joined: 18 Jun 2020
Last visit: 08 Oct 2025
Posts: 1
Given Kudos: 149
Posts: 1
Kudos: 0
How many distinct solutions does the equation |1 - |x - 215|| = 1 have 13 Oct 2024, 10:46
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Rabab36
|1 - |x - 215|| = 1
solving we get 4 values of x

only 2 values of x satisfy equation
x=215 and x=217

thereofre option c correct
Show more


213 is also a possibile solution

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,000
Own Kudos:
1,121
Posts: 39,000
Kudos: 1,121
How many distinct solutions does the equation |1 - |x - 215|| = 1 have 15 Dec 2025, 03:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109994 posts
Krunaal
Tuck School Moderator
852 posts