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# Is sqrt{ (X- 3)^2 } = 3-X ? 1) X is not equal to 3 2) -X|X|

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Senior Manager
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Is sqrt{ (X- 3)^2 } = 3-X ? 1) X is not equal to 3 2) -X|X| [#permalink]  30 Jul 2006, 03:58
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Is sqrt{ (X- 3)^2 } = 3-X ?

1) X is not equal to 3

2) -X|X| =0

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient

My doubt:
Statement 1 should be sufficient on it's own since sqrt{ (X- 3)^2 } = 3-X
only when X =3.
Senior Manager
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sqrt{ (X- 3)^2 } = 3-X
=> + - (X- 3) = 3-X

Other then X=3, the above equation can statisy for infinite values.
depending on the sign of sqrt values.

Is it E ?
Senior Manager
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Re: DS: Gmat prep [#permalink]  30 Jul 2006, 07:33
given sqrt{ (X- 3)^2 } = |x-3|

S1 X!=3 insufficient. x-3 or -x+3
S2 X=0 sufficient
sqrt[(0- 3)^2] = 3

B it is.
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Senior Manager
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I'll go with B on this one..

St1. x<>3 is insufficient
for x=1, equation is satisfied (1=1)
for x=4, equation is not satisfied (1=-1)

St2. -X|X| = 0 => X=0
Then sqrt{(0-3)^2} = 3-0 which is satisfied...
which is SUFF
Senior Manager
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The OA is B.
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Joined: 30 Mar 2006
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Clear B.

1) Sqr {(x-3)^2}

when x <0
Sqr {(x-3)^2} = -(x-3) = 3-x

When x > 0 and != 3
Sqr {(x-3)^2} != 3-x

Not Suff

2) -x|x| = 0

Means x = 0
Suff.
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Re: DS: Gmat prep [#permalink]  05 Aug 2006, 06:03
zoom612 wrote:
Is sqrt{ (X- 3)^2 } = 3-X ?

1) X is not equal to 3

2) -X|X| =0

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient

My doubt:
Statement 1 should be sufficient on it's own since sqrt{ (X- 3)^2 } = 3-X
only when X =3.

I am not clear on this. I think the answer is D

It is a yes/no question.

from stem the question is x-3 = 3-x?

From (1) since x!=3 we can answer a definite no the above question. Whether 3 is negative or positive or 0, as long it is not 3, the LHS will be -1 times RHS. So, SUFF

From (2) x=0. So the question turns out to is -3=3 and again the answer is no in this case. So, SUFF.

Where am I going wrong here. Can anyone please explain?

Thanks.
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Re: DS: Gmat prep [#permalink]  05 Aug 2006, 12:57
sqrt{ (X- 3)^2 } = |x-3|
If x>= 3 , |x-3| = x-3
If x< 3, |x-3| = 3-x

1) x not equal to 3
|x-3| = x-3 for x>3
|x-3| = 3-x for x<3
Insuff

2) -X|X| =0
since |x| is always +ve
-x = 0
i.e x = 0
therfore x<3 implies |x-3| = 3-x
Suff

Hence B

Heman
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Re: DS: Gmat prep [#permalink]  05 Aug 2006, 13:39
heman wrote:
sqrt{ (X- 3)^2 } = |x-3|
If x>= 3 , |x-3| = x-3
If x< 3, |x-3| = 3-x

1) x not equal to 3
|x-3| = x-3 for x>3
|x-3| = 3-x for x<3
Insuff

2) -X|X| =0
since |x| is always +ve
-x = 0
i.e x = 0
therfore x<3 implies |x-3| = 3-x
Suff

Hence B

Heman

But sqrt { (x-3) ^2} is a radical. In that case only positive value can be taken. So, its just (x-3) and not (3-x). Am I not correct?
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Re: DS: Gmat prep [#permalink]  05 Aug 2006, 14:08
yessuresh wrote:
heman wrote:
sqrt{ (X- 3)^2 } = |x-3|
Hence B

Heman

But sqrt { (x-3) ^2} is a radical. In that case only positive value can be taken. So, its just (x-3) and not (3-x). Am I not correct?

Why dont you take examples
(1) When x>3 for eg x=4 then |x-3| = x-3
Lhs = 1 Rhs = -1 Not Equal --> No

When x<3 for eg x=2 then |x-3| = 3-x
Lhs = 1 Rhs = 1 Yes

So you get a Yes and a No for statement (1) hence insufficient

Hope that is clear

Heman
Re: DS: Gmat prep   [#permalink] 05 Aug 2006, 14:08
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