is ((x-3)^2)^0.5 = 3-x ?

[apoorva_srivastva]

is ((x-3)^2)^0.5 = 3-x ?

A)x is not equal to 3
B)-x|x| > 0


Kindly explain!!!

[sd]

Is the answer D?

With all these ^ carat symbols, not sure if I interpreted the question right...but here is my explanation -

((x-3)^2)^0.5 = 3-x
can be simplified to
Is x-3=3-x???

(1) The above statement will only be true if x=3. But stmt 1 says x <> 3. Hence take any value of x (fraction, number, integer, 0 etc) x-3 is not equal to 3-x. SUFF

(2) -x|x| > 0. |x| is always greater than 0. -x|x| will be greater than 0 only if x is negative number. So take any negative number, x-3 will be negatibe, while 3-x will be positive. Hence even in this case x-3 is not equal to 3-x. SUFF.

Hence answer is D. what is the OA?

[apoorva_srivastva]

OA is B..I am able to understand ur explanation for st 2

St 1: is insufficient for the very fact that X can take any value other than 3

[sd]

Apoorva, I am still not getting how the OA can be B.

(1) x is not equal to 3.

Statement 1 gives us that x cannot be 3. Take any value of x other than 3. We always get x-3 <> 3-x. So we are able to answer the question, using stmt 1 alone. The answer is that x-3 cannot equal 3-x for any value of x.

So statement 1 must be SUFF by itself alone. What am I missing?

[apoorva_srivastva]

Apoorva, I am still not getting how the OA can be B.

(1) x is not equal to 3.

Statement 1 gives us that x cannot be 3. Take any value of x other than 3. We always get x-3 <> 3-x. So we are able to answer the question, using stmt 1 alone. The answer is that x-3 cannot equal 3-x for any value of x.

So statement 1 must be SUFF by itself alone. What am I missing?

the question is:

is ((x-3)^2)^0.5 = 3-x. since 3-x=-(x-3). the question basically asks you whether (x-3) is negative

1)x is not equal to 3 . X can be greater than or less than 3. not sufficient

it just says x<>3, what abt x > 3 the inequality holds good

For example: x = -4, 0 , 1, 5
If x = -4, [(x-3)^2]^0.5 = [(-4-3)^2]^0.5 = [(-7)^2]^0.5 = (49)^0.5 = 7, which is equal to |-4 - 3| = |7| = 7
If x = 0, [(x-3)^2]^0.5 = [(-0-3)^2]^0.5 = [(-3)^2]^0.5 = (9)^0.5 = 3, which is equal to |0 - 3|= |3| = 3
If x = 1, [(x-3)^2]^0.5 = [(1-3)^2]^0.5 = [(-2)^2]^0.5 = (4)^0.5 = 2, which is equal to |1 - 3| = |2| = 2
If x = 5, [(x-3)^2]^0.5 = [(5-3)^2]^0.5 = [(2)^2]^0.5 = (4)^0.5 = 2, which is equal to |5 - 3| = |2| = 2

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[Ben Ku]

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