Is √((x-3)^2) = 3 - x?

(1) x ≠ 3
(2) -x |x| > 0

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Is √((x-3)^2) = 3 - x?

(1) x ≠ 3
(2) -x |x| > 0

Rephrasing:-

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

applying squares on both the sides,
(x-3)^2= (3-x)^2 ( --> x^2+9-6x= 9+x^2-6x)



using ADBCE Grid,

1) x notequal to 3.

Say x=-3,x=0,x=1/2, is sufficient to answer the question.

2) -x|x| >0.
x=-1,-2,-3,-1/2 is sufficient to answer the question.

Hence D

Is √((x-3)^2) = 3 - x?

(1) x ≠ 3
(2) -x |x| > 0

Rephrase Is |x-3| = 3 -x
if x-3 >=0 ; x >=3
x-3 = 3-x So x=3;
if x-3 < 0; i.e. x < 3
-x +3 = 3-x for all values of x

So Q is is x =3 or is x < 3

St1 Insuff

St2 tells us that x is negative. Sufficient.

Ans B

Pathik
i.e. is 3-x >= 0 => 3 >= x

Excellent. Thanks.

OA: B

perfect explanation.

to the general audience: note the general fact that motivates the initial rephrase: if you square a number and then take the square root, you get the absolute value of the original number.

great