Is sqrt((x-3)^2) = 3-x
1)x != 3
put x = 1
LHS = 2 or -2
RHS = 2
So LHS may be or may not be equal to RHS
INSUFF
2) -x|x|>0
when x>0,
-x(x)>0
-x^2>0
x^2<0
this is not possible.
Hence x should be less than 0.
When x<0, x-3<-3 and 3-x>3
sqrt((x-3)^2) has two roots in which one is positive and the other is negative.
since x-3 should always be less than -3, it has only one root now.
this root will always not equal to 3-x. since 3-x is always >3
Hence SUFF
pick B
DS
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Source: Beat The GMAT — Data Sufficiency |
