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# Is root{(x-3)^2}=3-x?

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16 Jan 2013, 03:04
vaivish1723 wrote:
Is $$\sqrt{(x-3)^2}=3-x$$?

(1) $$x\neq{3}$$
(2) $$-x|x| >0$$

$$\sqrt{(x-3)^2} = 3-x$$
$$|x-3| = 3-x$$
$$3-x >= 0$$
$$3>=x$$ x is less than or equal to 3
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Re: [square_root](X-3)^2[/square_root][/m] = 3 -X ? [#permalink]

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06 Mar 2013, 20:19
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sujit2k7 wrote:
This is a DS question ..

Is $$\sqrt{(X-3)^2}$$ = 3 -X ?

1) X # 3
2) -X|X| > 0

Only thing which the question is asking is 3-X positive
As Sqrt (X-3)^2
= X-3 if X-3 is positive
= 3-X if 3-X is positive

STAT1
is INSUFFICIENT as X# 3 doesn't tell anything about whether 3-X is positive or not.

STAT2
-X|X| > 0
since |X| is positive so
-X > 0
=> X <0
and if X< 0 then 3-X will be positive.
Hope it helps!
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Re: [square_root](X-3)^2[/square_root][/m] = 3 -X ? [#permalink]

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06 Mar 2013, 20:43
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sujit2k7 wrote:
This is a DS question ..

Is $$\sqrt{(X-3)^2}$$ = 3 -X ?

1) X # 3
2) -X|X| > 0

We know that $$\sqrt{X^2}$$ = |X|. Thus, the question stem is asking whether |X-3| = 3-X. This is possible only if (X-3) is negative or X<3.

From F.S 1, we have x is not equal to 3. Clearly Insufficient.

From F.S 2, we have -X|X|>0. Thus, as |X| is always positive, X has to be negative. Thus, if X is negative, it will always be less than 3. Sufficient.

B.
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18 Apr 2013, 15:04
vaivish1723 wrote:
Is $$\sqrt{(x-3)^2}=3-x$$?

(1) $$x\neq{3}$$
(2) $$-x|x| >0$$

Here is how i solved it:

1) x [/s]=[/s] 3. Not sufficient
2) -x|x|>0 => x<0 only then the given inequality holds

so [/square_root](s-3)^2[/square_root] => -(x-3) (as we know [/square_root]x^2[/square_root] = - (x) if x<0) and 3-x = -(x-3) so sufficient.

IMO B.
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16 May 2014, 00:01
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24 Dec 2014, 01:13
vaivish1723 wrote:
Is $$\sqrt{(x-3)^2}=3-x$$?

(1) $$x\neq{3}$$
(2) $$-x|x| >0$$

Hi Bunuel,

When x\leq{3}, then LHS=|x-3|=-x+3=3-x=RHS, hence in this case equation holds true. Should the part in red not just be "<"?
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24 Dec 2014, 06:24
dmgmat2014 wrote:
vaivish1723 wrote:
Is $$\sqrt{(x-3)^2}=3-x$$?

(1) $$x\neq{3}$$
(2) $$-x|x| >0$$

Hi Bunuel,

When x\leq{3}, then LHS=|x-3|=-x+3=3-x=RHS, hence in this case equation holds true. Should the part in red not just be "<"?

No, because x=3 also satisfies $$\sqrt{(x-3)^2}=3-x$$.
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07 Jan 2016, 00:29
HI understand the square root concept.

But I ended up squaring both sides of equation and got the question as |x-3|=|3-x|.

Can someone explain why cant we square both the sides of equation to eliminate square root on lefthand side?
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10 Jan 2016, 06:01
seemachandran wrote:
HI understand the square root concept.

But I ended up squaring both sides of equation and got the question as |x-3|=|3-x|.

Can someone explain why cant we square both the sides of equation to eliminate square root on lefthand side?

Hope it helps.
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10 Jan 2016, 13:03
Thanks a lot Bunuel!!
I got the concept, i forgot to apply the concept i.e not to square when not sure about the sign.
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11 Jan 2016, 18:22
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is root{(x-3)^2}=3-x?

(1) x≠3
(2) −x|x|>0

When you modify the original condition and the question, it becomes n-th power root (A^n)=|A| when n=even, and |A|=A when A>=0, |A|=-A when A<0. So, |x-3|=3-x=-(x-3)? becomes x-3<0?, x<3?. There is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), x=/3-> x=2 yes, x=4 no, which is not sufficient.
For 2), -x|x|>0 -> x<0<3, which is yes and sufficient. Therefore, the answer is B.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: Is root{(x-3)^2}=3-x?   [#permalink] 11 Jan 2016, 18:22

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