Last visit was: 19 Nov 2025, 12:37 It is currently 19 Nov 2025, 12:37
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
   1   2 
User avatar
dave13
User avatar
Joined: 09 Mar 2016
Last visit: 12 Aug 2025
Posts: 1,108
Own Kudos:
1,113
Given Kudos: 3,851
Posts: 1,108
Kudos: 1,113
What is the value of integer x? 18 May 2021, 04:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
jashshah
What is the value of integer x?

(1) |1 - x| - |x + 1| = 0

(2) |7 - x| + |3 + x| = 10
Show more

VeritasKarishma for st 1 as per graph below i get following reults:

Attachment:
veritas (2).jpg
veritas (2).jpg [ 72.15 KiB | Viewed 1299 times ]


For range x ≥ 1

-(1-x)-x+1 = 0
-1+x-x+1 =0
0=0 (doesn`t it mean infinite number of solutions ?


For range -1≤x<1

1-x-x+1=0
2-2x=0
2x=2
x =1

For range x<-1

1-x- -(x+1) =0
1-x- -x-1 =0
1-x+x-1=0
again 0=0 :?

so i get either 0=0 or x=1 whats wrong with my solution / reasoning.... i see others get x=0 but 0=0 is not the same as x=0 and how about x=1 :?
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
77,000
 [1]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 77,000
 [1]
What is the value of integer x? 19 May 2021, 00:15
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dave13
jashshah
What is the value of integer x?

(1) |1 - x| - |x + 1| = 0

(2) |7 - x| + |3 + x| = 10

VeritasKarishma for st 1 as per graph below i get following reults:

Attachment:
veritas (2).jpg


For range x ≥ 1

-(1-x)-x+1 = 0
-1+x-x+1 =0
0=0 (doesn`t it mean infinite number of solutions ?


For range -1≤x<1

1-x-x+1=0
2-2x=0
2x=2
x =1

For range x<-1


1-x- -(x+1) =0
1-x- -x-1 =0
1-x+x-1=0
again 0=0 :?

so i get either 0=0 or x=1 whats wrong with my solution / reasoning.... i see others get x=0 but 0=0 is not the same as x=0 and how about x=1 :?
Show more

You are forgetting the bracket of the expression.

For range x ≥ 1
-(1-x) - (x+1) = 0
The negative sign is outside the entire expression of (x + 1). See stmnt 1: |1 - x| - |x + 1| = 0

You get -2 = 0 which is not valid.

Now check other equations too.
User avatar
dave13
User avatar
Joined: 09 Mar 2016
Last visit: 12 Aug 2025
Posts: 1,108
Own Kudos:
1,113
Given Kudos: 3,851
Posts: 1,108
Kudos: 1,113
What is the value of integer x? 19 May 2021, 05:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VeritasKarishma
dave13
jashshah
What is the value of integer x?

(1) |1 - x| - |x + 1| = 0

(2) |7 - x| + |3 + x| = 10

VeritasKarishma for st 1 as per graph below i get following reults:

Attachment:
veritas (2).jpg


For range x ≥ 1

-(1-x)-x+1 = 0
-1+x-x+1 =0
0=0 (doesn`t it mean infinite number of solutions ?


For range -1≤x<1

1-x-x+1=0
2-2x=0
2x=2
x =1

For range x<-1


1-x- -(x+1) =0
1-x- -x-1 =0
1-x+x-1=0
again 0=0 :?

so i get either 0=0 or x=1 whats wrong with my solution / reasoning.... i see others get x=0 but 0=0 is not the same as x=0 and how about x=1 :?

You are forgetting the bracket of the expression.

For range x ≥ 1
-(1-x) - (x+1) = 0
The negative sign is outside the entire expression of (x + 1). See stmnt 1: |1 - x| - |x + 1| = 0

You get -2 = 0 which is not valid.

Now check other equations too.
Show more

VeritasKarishma thanks.

For range x<-1

i get this

(1-x)-(-x-1) = 0

1-x+x+1=0

2=0 is this result correct ? i ask this question because as per other posts two ranges yield the same value of 0

as per one post in this thread when we have |1 - x| - |x + 1| = 0 we need to change from|1 - x| to | x -1| Is it a must to switch places? And Why? And when ?

so in this case |x-1| - |x + 1| = 0
For range x<-1
I get (x-1) - (-x-1) = 0
x-1+x+1 = 0
2x=0
x=0





As For range -1≤x<1

i get (1-x)-(x+1) =0
1-x-x-1=0
-2x=0
x = 0
solution for this range looks correct ...hopefully :)
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 19 Nov 2025
Posts: 16,267
Own Kudos:
77,000
 [1]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 77,000
 [1]
What is the value of integer x? 20 May 2021, 01:37
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dave13


For range x<-1

i get this

(1-x)-(-x-1) = 0

1-x+x+1=0

2=0 is this result correct ? i ask this question because as per other posts two ranges yield the same value of 0

as per one post in this thread when we have |1 - x| - |x + 1| = 0 we need to change from|1 - x| to | x -1| Is it a must to switch places? And Why? And when ?

so in this case |x-1| - |x + 1| = 0
For range x<-1
I get (x-1) - (-x-1) = 0
x-1+x+1 = 0
2x=0
x=0





As For range -1≤x<1

i get (1-x)-(x+1) =0
1-x-x-1=0
-2x=0
x = 0
solution for this range looks correct ...hopefully :)
Show more

|x - 1| = |1 - x|

You can use it in either format but to avoid confusion and give a consistent method, I suggest to always convert. We are familiar with expressions such as (x + a) or (x - a) and know that the transition points are at -a or a. The overall process just gets a bit more intuitive.

Try to solve the question using both expressions separately and see how things vary.

Fro example,
When x < -1,
|x - 1| = - (x - 1)
But |1 - x| = (1 - x)

So your equations will change accordingly but of course you will get the same answer in either case.


"For range x<-1
I get (x-1) - (-x-1) = 0
x-1+x+1 = 0
2x=0
x=0
"

You are solving for x < -1 and you get x = 0. So there is NO value of x in the range x < -1.
User avatar
adityaganjoo
User avatar
Joined: 10 Jan 2021
Last visit: 04 Oct 2022
Posts: 148
Own Kudos:
32
Given Kudos: 154
Posts: 148
Kudos: 32
What is the value of integer x? 27 Jun 2021, 05:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunuel
Please tell me where am I going wrong?

(2) |7-x| + |3+x| = 10
=> |-(x-7)| + |3+x| = 10;
=> |x-7| + |3+x| = 10
For x>=7,
x - 7 + 3 + x = 10
=> 2x = 14
=> x = 7
This falls within the interval of x>=7, thus is an acceptable solution

Please help!


Bunuel
What is the value of integer x?

(1) |1 - x| - |x + 1| = 0

|1 - x| = |x + 1| --> square: 1 - 2x + x^2 = x^2 + 2x +1 --> x = 0. Sufficient.

(2) |7 - x| + |3 + x| = 10.

When both 7 - x and 3 + x are positive (so when -3 <= x <= 7), then |7 - x| + |3 + x| = 10 expands as 7 - x + 3 + x = 10 --> 10 = 10, which is true. This means that any x where -3 <= x <= 7 satisfies the equation. Not sufficient.

Answer: A.
Show more
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,588
Own Kudos:
1,079
Posts: 38,588
Kudos: 1,079
What is the value of integer x? 20 Sep 2025, 01:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
   1   2 
Moderators:
Bunuel
Math Expert
105390 posts
kingbucky
496 posts