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Is root{(x3)^2}=3x? [#permalink]
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09 Dec 2006, 00:46
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Is \(\sqrt{(x3)^2} = 3x\) (1) x is not equal to 3 (2)  x  x  > 0 OPEN DISCUSSION OF THIS QUESTION IS HERE: isrootx323x92204.html
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Re: Is root{(x3)^2}=3x? [#permalink]
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09 Dec 2006, 01:40
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Is sqrt of (x3)^2 = 3x
(1) x is not equal to 3
(2)  x  x  > 0
REPHRASE STEM
SQRT(X3)^2 = / X3/ = 3X
/X3/ = 3X ONLY IF X< = 3
FROM ONE
INSUFF COULD BE < OR > 3
FROM TWO
X/X/ >0 WE ARE SURE /X/ IS +VE THUS X IS +VE TOO
ie: x is ve this staisfys x<=3 thus suff
answer is B



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Re: Is root{(x3)^2}=3x? [#permalink]
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09 Dec 2006, 01:43
Same logic as Yezz .... (B)



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Re: Is root{(x3)^2}=3x? [#permalink]
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09 Dec 2006, 05:07
Yezz, Fig, please help me out Showing you below how I solved it but it seems I have a different approach, which I think is wrong...
stem is asking if x3 = 3  x
if x>0 then x3 = x3 > you're left with nothing
if x<0 then x3 = 3x > 2x=6 > x=3
is this the correct way???
so frustrating these absolute value problems!!!
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Re: Is root{(x3)^2}=3x? [#permalink]
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09 Dec 2006, 06:26
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A kind of rule to remember is to search the roots of the expression in each absolute value. It's similar to what I said in my response to u on another topic
As we have x3, so we search the roots of x3. Hence,
x3 = 0 <=> x = 3
Thus, the domains to consider are x > 3 and x < 3.
Each domain implies a simplified equation that removes the absolute.
We do not consider x > 0 or x < 0 because nothing in the equation asks for it



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Re: Is root{(x3)^2}=3x? [#permalink]
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09 Dec 2006, 07:04
Hermione wrote: I remember seeing this problem before but I cannot find it anymore in the posts.
Is sqrt of (x3)^2 = 3x (1) x is not equal to 3 (2)  x  x  > 0
Please explain your answers!
The q asked here is if the sq root is ve
So if x = x
From (1) we do not know anything
From (2)
xx > 0 means
since x is positive for the eq xx to be > 0 x should be ve
So B



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Re: Is root{(x3)^2}=3x? [#permalink]
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09 Dec 2006, 07:41
Thanks Fig! I got it!
Thank you for your help!!
Will keep that in mind for test day
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Re: Is root{(x3)^2}=3x? [#permalink]
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04 Jun 2009, 21:45
hey guys was wondering if anyone could offer a way to solve this problem:
Is \(\sqrt{(X3)^2} = 3X\)?
(1) X is not equal to 3
(2) X*X is greater than 0
answer: B.



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Re: Is root{(x3)^2}=3x? [#permalink]
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05 Jun 2009, 02:34
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Is square root (X3)^2= 3X ? (1) X is not equal to 3 Since for +ve valuues of x , (X3)^2= 3X and for negative values of x., (X3)^2!= 3X INSUFFICIENT (2) XX is greater than 0 XX > 0 this clearly means x <0 for x<0, (X3)^2!= 3X SUFFICIENT IMO B
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Re: Is root{(x3)^2}=3x? [#permalink]
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05 Jun 2009, 02:35
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And yes , I assumed "(X3)*2" as "square of (x3)" I have seen this problem before , I guess its GmatPrep one...
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Re: Is root{(x3)^2}=3x? [#permalink]
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22 Jun 2010, 17:41
WE have [x3]=3x [] is absolute value if x>= 3 we have x3 = 3x. Solve x3 = 3x by itself we have x = 3. Put togethere with x>= 3 we have x= 3
if x=<3 we have 3x = 3x. it if right with all x =<3 ==> the solution without any additional condition is x =< 3
Let use the condition 1 only we can have x> 3 doesn't belong to the area x=<3==> insufficient Let use the condition 2 only we have x< 0 belong to area x=< 3 ==> sufficient
SO I think the answer is B



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Re: Is root{(x3)^2}=3x? [#permalink]
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28 Jun 2010, 01:15
i. Equality in question is TRUE if x is negative and FALSE if x is positive. Dual solution, hence NOT SUFFICIENT ii. x always positive. For x to be greater than 0, x has to be negative. Single solution, hence SUFFICIENT.



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Re: Is root{(x3)^2}=3x? [#permalink]
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