Last visit was: 20 Nov 2025, 03:33 It is currently 20 Nov 2025, 03:33
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,464
 [2]
Given Kudos: 99,987
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: 105,408
Kudos: 778,464
 [2]
What is the value of x? (1) |6 - 3x| = x - 2 (2) |5x + 3| = 2x + 9 25 Jul 2018, 03:41
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

71% (01:41) correct 29% (01:46) wrong based on 182 sessions

History

Date
Time
Result
Not Attempted Yet
What is the value of x?


(1) |6 - 3x| = x - 2

(2) |5x + 3| = 2x + 9
ShowHide Answer
Official Answer
A
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 15 Nov 2025
Posts: 11,238
Own Kudos:
43,707
 [3]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,238
Kudos: 43,707
 [3]
What is the value of x? (1) |6 - 3x| = x - 2 (2) |5x + 3| = 2x + 9 25 Jul 2018, 03:49
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
What is the value of x?


(1) |6 - 3x| = x - 2......
Two cases..
a) 6-3x=x-2........4x=8.....X=2
b) -(6-3x)=x-2........3x-6=x-2.....2x=4.....X=2
Sufficient

(2) |5x + 3| = 2x + 9
Two cases
a) 5x+3=2x+9.......3x=6......X=2
b) -(5x+3)=2x+9.......5x+2x=-3-9......x=-12/7
So two values possible
Insufficient

A
User avatar
D3N0
User avatar
Joined: 21 Jan 2015
Last visit: 19 Nov 2025
Posts: 587
Own Kudos:
572
Given Kudos: 132
Location: India
Concentration: Operations, Technology
Schools: Smeal'21 (WD) Arizona State'21 (A$) Simon '21 (WD)
GMAT 1: 620 Q48 V28
GMAT 2: 690 Q49 V35
WE:Operations (Retail: E-commerce)
Products:
My Reviews
Schools: Smeal'21 (WD) Arizona State'21 (A$) Simon '21 (WD)
GMAT 2: 690 Q49 V35
Posts: 587
Kudos: 572
What is the value of x? (1) |6 - 3x| = x - 2 (2) |5x + 3| = 2x + 9 25 Jul 2018, 05:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I have one silly question here/..
When look for the sign of |x-n| we always use these two conditions:
if x>n : |x-n| is positive so = x-n
If x<n then |x-n| is negative = -x+n
but what if x=n then ??
I am asking this because in statement one i got confused. when i took x>2, I got x=2 and again when x<2 solution was x=2 but thought there is no slution because in both the cases x=2 is not satifying the conditions i too for deciding the sign.
Please elaborate...

chetan2u
What is the value of x?
|6 - 3x| = x - 2


A
Show more
User avatar
KrishnakumarKA1
User avatar
Joined: 05 Jan 2017
Last visit: 13 Oct 2020
Posts: 403
Own Kudos:
310
Given Kudos: 15
Location: India
Posts: 403
Kudos: 310
What is the value of x? (1) |6 - 3x| = x - 2 (2) |5x + 3| = 2x + 9 25 Jul 2018, 05:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi,
If this question has been asked like,
Is x > 0?
Then the solving part would have been very easy,
Because here statement are equations with one side modulus, so we can consider one side non-negative.
Say, for example, in the statement I here given is,
|6-3x| = x -2
We should have equated this to,
x-2 > = 0
Because modulus of anything will be non-negative.
But here the question asks the value of x,
So, we have to do it, either using the number line or by the definition of modulus,
Statement I is sufficient:
|6 - 3x| = x – 2
By the definition of modulus,
6 – 3x = x -2, whenever (6-3x) >= 0 i.e., whenever, x <= 2
Solving this we get,
x = 2
Which works according to the condition of x,
Now,
6-3x = -x +2, whenever (6-3x) <= 0 i.e., whenever, x > = 2
Solving this we get,
x = 2.
So only one x value works here.
So statement I is sufficient.

Statement II is insufficient:
|5x + 3| = 2x + 9
By the definition of modulus,
5x + 3 = 2x +9, whenever (5x+3) >= 0 i.e., whenever, x >= -3/5
Solving this we get,
x = 2
Which works according to the condition of x,
Now,
5x+3 = -2x-9, whenever (5x+3) <= 0 i.e., whenever, x < = -3/5
Solving this we get,
7x = 6.
x = -12/7
Which also works according to the condition of x,
Hence there are two values of x.
So statement II is insufficient.
So the answer is A(I alone).
Key to solving the modulus question, knowing the definition of modulus.
Hope this helps.
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 15 Nov 2025
Posts: 11,238
Own Kudos:
43,707
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,238
Kudos: 43,707
What is the value of x? (1) |6 - 3x| = x - 2 (2) |5x + 3| = 2x + 9 25 Jul 2018, 05:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dkumar2012
I have one silly question here/..
When look for the sign of |x-n| we always use these two conditions:
if x>n : |x-n| is positive so = x-n
If x<n then |x-n| is negative = -x+n
but what if x=n then ??
I am asking this because in statement one i got confused. when i took x>2, I got x=2 and again when x<2 solution was x=2 but thought there is no slution because in both the cases x=2 is not satifying the conditions i too for deciding the sign.
Please elaborate...

chetan2u
What is the value of x?
|6 - 3x| = x - 2


A
Show more


When opening modulus, you can take equal to with any of the inequality signs.
And the value you get then should fall in that range..
Say here you took X<=2..
So |6-3x|=x-2......so 3x-6=x-2.....X=2
So this value X=2 is within the range X<=2, so OK
Otherwise |6-3x|=x-2 it self means x-2 is 0 or >0 as left side is Modulus

Also if you had to solve this
|6-3x|=x-2......
3|2-x|=x-2....
Only possible of 2-x=0...X=2
Moderators:
Bunuel
Math Expert
105408 posts
kingbucky
496 posts