What is the value of x?

Question

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

(2)  x(x-1)=0

New question !!

AnirudhaS · Answer

(1) Either, 6-2x = x-6; Here x = 4, but this is not valid as 6-2x>=0
Therefore, 6-2x = -(x-6); Here x = 0
Sufficient

(2) x=0, or 1
Insufficient

(1) + (2)
x=0
Sufficient

Answer:  A

*Edited, thanks  uchihaitachi  you are right!

uchihaitachi · Answer

Statement B :
  x(x-1)=0 
x = 0 or x = 1
 Insufficient

Statement A :
Since we have a modulus, so there will be two cases.

Case 1  x  <  6
 6 - 2x = -(x-6) 
 6-2x = -x + 6 
 3x = 0 
 x=0  Since x should be  <  6. This satisfies.

Case 1  x > 6
 6 - 2x = (x-6) 
 6-2x = x - 6 
 3x = 12 
 x=4  Since x should be greater than 6 This does not satisfy.

Sufficient

OA, A

GMATinsight · Answer

Question: x = ?

STatement 1 :  6-2x=|x-6|

SInce |x-6| is always ≥ 0

therefore, 6-2x ≥0 i.e. x ≤ 3

For x≤3, |x-6| = 6-x

i.e.  6-2x=|x-6|    is same as  6-2x=6-x  
ie. x = 0

SUFFICIENT

STatement 2 :  x(x-1)=0

i.e. x is either 0 or 1 hence

NOT SUFFICIENT

ANswer: Option A

Kinshook · Answer

Asked: What is the value of x? (1) 6-2x=|x-6| Case 1: x>=6 6-2x = x-6 3x = 12 x = 4; NOT VALIED since x>=6 Case 2: x<6 6-2x = 6-x x = 0; VALID since x<6 x = 0 SUFFICIENT (2) x(x-1)=0 x = 0 or 1 NOT SUFFICIENT IMO A

Archit3110 · Answer

#1
 6-2x=|x-6| 
solve we get 
x= 4 and x=0 
since lx-6l will always be +ve so x=4 is not valid
x=0 sufficient
#2
  x(x-1)=0 
x=1 & 0 
insufficient
OPTION A

harshbirajdar · Answer

How do you avoid such traps?

What is the value of x?

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