Data Sufficiency

Is sqrt(x-3)^2 = 3-x ?

1. x not equal to 3
2. -x|x| >0

My approach :

Simplifying given statement -> x-3 = 3-x -> x=3
Hence, question is Is x=3? ( Am I wrong till now ? )

Option 1 : x not equal to 3.... it gives me answer as NO.
Option 2 : -x|x| > 0 means x is negative => not equal to 3.

Since, both gives me an answer E should be right.
But OA is B

Please help me understand this.[/list]

6983manish wrote:Is sqrt(x-3)^2 = 3-x ?

1. x not equal to 3
2. -x|x| >0

My approach :

Simplifying given statement -> x-3 = 3-x -> x=3
Hence, question is Is x=3? ( Am I wrong till now ? )

Option 1 : x not equal to 3.... it gives me answer as NO.
Option 2 : -x|x| > 0 means x is negative => not equal to 3.

Since, both gives me an answer E should be right.
But OA is B

Please help me understand this.[/list]

the part in boldface is wrong ;

sqrt(x-3)^2 SHOULD NOT BE NEGATIVE and the question asks if it is 3-x that means 3-x >=0 i.e. x <=3

hence the question is ;
Is x <=3 ?

statement 1) INSUFF

statement 2)
for x>0
-x^2>0 not possible

for x<0
x^2 >0 true

=> x<0 i.e. x<3

SUFFICIENT

HENCE B

hope this helps..!!

6983manish wrote:Is sqrt(x-3)^2 = 3-x ?

1. x not equal to 3
2. -x|x| >0

My approach :

Simplifying given statement -> x-3 = 3-x -> x=3
Hence, question is Is x=3? ( Am I wrong till now ? )

Option 1 : x not equal to 3.... it gives me answer as NO.
Option 2 : -x|x| > 0 means x is negative => not equal to 3.

Since, both gives me an answer E should be right.
But OA is B

Please help me understand this.[/list]

i think that this problem should be simplified as

=> Is |x-3| = 3-x ?

Stat. 1...

x can surely have 0 value, but it does not help in concluding |x-3| = 3-x or not. Not Suff.

Stat. 2...

by observing |x-3| = 3-x, we can say that if x takes values less than 3, then |x-3| = 3-x holds true. If x > 3, then its not.

Pl. plug in few extreme values of x such as x = 4, 3, -4 etc. in -x|x| >0, we can conclude that stat. 2 if suff.

Ans. B.