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# is ((x-3)^2)^0.5 = 3-x ? A)x is not equal to 3 B)-x|x| >

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Manager
Joined: 29 Jul 2009
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is ((x-3)^2)^0.5 = 3-x ? A)x is not equal to 3 B)-x|x| > [#permalink]

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05 Aug 2009, 07:51
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is ((x-3)^2)^0.5 = 3-x ?

A)x is not equal to 3
B)-x|x| > 0
Retired Moderator
Joined: 05 Jul 2006
Posts: 1747
Re: is ((x-3)^2)^0.5 = 3-x ? [#permalink]

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05 Aug 2009, 08:24
apoorvasrivastva wrote:
is ((x-3)^2)^0.5 = 3-x ?

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

the question is asking wheter x = 3

from one.......suff

from 2

x is -ve insuff

A
Manager
Joined: 07 Apr 2009
Posts: 145
Re: is ((x-3)^2)^0.5 = 3-x ? [#permalink]

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05 Aug 2009, 10:33

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

statement 1: NOT SUFF
it just says x<>3, what abt x > 3 the inequality holds good

Statement 2:
the given equality holds good for all negative values

-x|x|> 0

x>0 --> -x^2 > 0 -> a negative number cant be > 0 so x cant be > 0
x < 0 --> x2 > 0 --> yes so x is negative

for all negative values this holds good.

hence B
Manager
Joined: 29 Jul 2009
Posts: 114
Re: is ((x-3)^2)^0.5 = 3-x ? [#permalink]

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05 Aug 2009, 11:57
skpMatcha wrote:

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

statement 1: NOT SUFF
it just says x<>3, what abt x > 3 the inequality holds good

Statement 2:
the given equality holds good for all negative values

-x|x|> 0

x>0 --> -x^2 > 0 -> a negative number cant be > 0 so x cant be > 0
x < 0 --> x2 > 0 --> yes so x is negative

for all negative values this holds good.

hence B

well can the question be written as is |x-3| = 3-x?
Senior Manager
Joined: 17 Jul 2009
Posts: 285
Concentration: Nonprofit, Strategy
GPA: 3.42
WE: Engineering (Computer Hardware)
Re: is ((x-3)^2)^0.5 = 3-x ? [#permalink]

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05 Aug 2009, 12:22
apoorvasrivastva wrote:
skpMatcha wrote:

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

statement 1: NOT SUFF
it just says x<>3, what abt x > 3 the inequality holds good

Statement 2:
the given equality holds good for all negative values

-x|x|> 0

x>0 --> -x^2 > 0 -> a negative number cant be > 0 so x cant be > 0
x < 0 --> x2 > 0 --> yes so x is negative

for all negative values this holds good.

hence B

well can the question be written as is |x-3| = 3-x?

yeah you can, answer is b, as 0 escapes statement 1, and statement 2 includes statement 1's situation....
SVP
Joined: 29 Aug 2007
Posts: 2467
Re: is ((x-3)^2)^0.5 = 3-x ? [#permalink]

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05 Aug 2009, 14:25
apoorvasrivastva wrote:
skpMatcha wrote:

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

statement 1: NOT SUFF
it just says x<>3, what abt x > 3 the inequality holds good

Statement 2: the given equality holds good for all negative values

-x|x|> 0

x>0 --> -x^2 > 0 -> a negative number cant be > 0 so x cant be > 0
x < 0 --> x2 > 0 --> yes so x is negative

for all negative values this holds good.

hence B

well can the question be written as is |x-3| = 3-x?

Thats what the question is.

[(x-3)^2]^0.5 = (3-x) ?
Irrespective of x's value, (x-3)^2 is always +ve. Sqrt of (x-3)^2 is always +ve (x - 3).
Therefore ((x-3)^2)^0.5 = |x - 3|. Hence |x - 3| = (3-x) ?

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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Director
Joined: 13 Nov 2003
Posts: 788
Location: BULGARIA
Re: is ((x-3)^2)^0.5 = 3-x ? [#permalink]

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05 Aug 2009, 22:19
Hi,

What will happen if we square both sides of the equation?

Thanks
Manager
Joined: 18 Jul 2009
Posts: 167
Location: India
Schools: South Asian B-schools
Re: is ((x-3)^2)^0.5 = 3-x ? [#permalink]

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06 Aug 2009, 02:35
OA B

S(1) asking if x=3 or 0 or any -ve number ...as these are the only possible solutions ( plz substitute n chk)....as x is not equal to 3 ...x can be 0 or any other number... hence insufficient

S(2) -x|x| > 0...this means for left hand side to be +ve .... |x| = always +ve so to negate negative sign of -x => x has to ve -ve thus..... x < 0....hence sufficient

if u likr my post...consider it for Kudos
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Bhushan S.
If you like my post....Consider it for Kudos

Manager
Joined: 15 Jun 2009
Posts: 151
Re: is ((x-3)^2)^0.5 = 3-x ? [#permalink]

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06 Aug 2009, 02:54
imo b....

1) is insuff as equnation can be equal or unequal.....
Ex. put x=4 ...not equal

x=2 ..equal...

2) -x|x| > 0 ..implies x<0 ....

the equation satisifes for all values of neagtive x.....
Manager
Joined: 29 Jul 2009
Posts: 114
Re: is ((x-3)^2)^0.5 = 3-x ? [#permalink]

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06 Aug 2009, 04:37
The OA is B...great solutions guys
Re: is ((x-3)^2)^0.5 = 3-x ?   [#permalink] 06 Aug 2009, 04:37
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