Is sqrt of (x-3)^2 = 3-x
(1) x is not equal to 3
(2) - x | x | > 0
Answer is B:
This is how i solved it..
You can reduce the left side of the equation to |x-3|. The question is asking if |x-3| = 3-x
(2) implies that x is negative and the above statement would be true for any negative number...
B is the OA too..
But there is another way to look at it.. Dont redude the left side to modulus form. Take -5 as an example.
Left side = sqrt [ (-5 -3) ^ 2 ] = sqrt 64 = 8 or -8
Right side = 3 - (-5) = 8
Anyone has any explanation ?
inequality question...
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Hi Tkneo,
I must say this is a very good question: I would solve it in this manner
Is sqrt of (x-3)^2 = 3-x
Getting to the kernel: sqrt of (x-3)^2
=> +/- (x-3)
But (x-3)^2 will be = 3-x only when when sqrt(x-3)^2 = - (x-3)
sqrt(x-3)^2 = - (x-3)
=> x-3 <0> x < 3
So our rephrased question:
Is x <3> x can be > 3 or <3> 0
=> x < 0
Since x <0> x < 3
Hence sufficient.
I must say this is a very good question: I would solve it in this manner
Is sqrt of (x-3)^2 = 3-x
Getting to the kernel: sqrt of (x-3)^2
=> +/- (x-3)
But (x-3)^2 will be = 3-x only when when sqrt(x-3)^2 = - (x-3)
sqrt(x-3)^2 = - (x-3)
=> x-3 <0> x < 3
So our rephrased question:
Is x <3> x can be > 3 or <3> 0
=> x < 0
Since x <0> x < 3
Hence sufficient.
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Hi Hemanth,
Which part you did not understand? ...
I see some confusions let me try again :
Question : Is sqrt of (x-3)^2 = 3-x ?
Solution: Since we know sqrt of (x-3)^2 = either +(x-3) or - (x-3)
But sqrt of (x-3)^2 will be = 3-x only when when sqrt(x-3)^2 = - (x-3)
Now simplify the question:
sqrt(x-3)^2 = - (x-3) (It is a negative root of the no so use the inequality)
or x-3 < 0
or x < 3
So our rephrased question:
Is x <3 ?
Now look at the statements:
(1) x is not equal to 3: Since this statement is not giving us any info about whether x < 3 so INSUFFICIENT. Eliminate A, D
(2) - x | x | > 0
From this we can say x < 0
Since 0(Zero) < 3
So we can say x < 3
Hence this answer choice is sufficient.
Hope now it is clear
Thanks
Komal
Which part you did not understand? ...
I see some confusions let me try again :
Question : Is sqrt of (x-3)^2 = 3-x ?
Solution: Since we know sqrt of (x-3)^2 = either +(x-3) or - (x-3)
But sqrt of (x-3)^2 will be = 3-x only when when sqrt(x-3)^2 = - (x-3)
Now simplify the question:
sqrt(x-3)^2 = - (x-3) (It is a negative root of the no so use the inequality)
or x-3 < 0
or x < 3
So our rephrased question:
Is x <3 ?
Now look at the statements:
(1) x is not equal to 3: Since this statement is not giving us any info about whether x < 3 so INSUFFICIENT. Eliminate A, D
(2) - x | x | > 0
From this we can say x < 0
Since 0(Zero) < 3
So we can say x < 3
Hence this answer choice is sufficient.
Hope now it is clear
Thanks
Komal
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The only way to get a positive product is to multiply 2 positives or 2 negatives.m7373 wrote:How does - x | x | > 0 result in x<0 ? I don't understand.
We know that |x| is positive; therefore, -x must also be positive.
If -x is positive, then x must be negative.
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- hemanth28
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joshi.komal wrote:Hi Hemanth,
Which part you did not understand? ...
I see some confusions let me try again :
Question : Is sqrt of (x-3)^2 = 3-x ?
Solution: Since we know sqrt of (x-3)^2 = either +(x-3) or - (x-3)
But sqrt of (x-3)^2 will be = 3-x only when when sqrt(x-3)^2 = - (x-3)
Now simplify the question:
sqrt(x-3)^2 = - (x-3) (It is a negative root of the no so use the inequality)
or x-3 < 0
or x < 3
So our rephrased question:
Is x <3 ?
Now look at the statements:
(1) x is not equal to 3: Since this statement is not giving us any info about whether x <3> 0
From this we can say x < 0
Since 0(Zero) < 3
So we can say x <3>0
2)Sqrt of (x-3)^2 =-(x-3) if x-3<0
i am not sure if your assumption is right or i am not sure if i am missing something.
becasue sqrt of (16) =+4 or -4.
and there is no condition attached to it.Thinking in similar terms,
Sqrt of (x-3)^2 can be always be either +(x-3) or -(x-3).
Thanks,
Hemant Maddineni.
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The answer is A.
x = 3 is the only value for x that makes the question true. So A tells x can't equal three. Therefore if we take A to be true, that sufficient to tell us that the answer to their question is no.
The prior responses forget that the sqrt has +/- roots. You're assuming the roots are + only.
x = 3 is the only value for x that makes the question true. So A tells x can't equal three. Therefore if we take A to be true, that sufficient to tell us that the answer to their question is no.
The prior responses forget that the sqrt has +/- roots. You're assuming the roots are + only.
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Actually, that's not true.horizonx29 wrote:The answer is A.
x = 3 is the only value for x that makes the question true. So A tells x can't equal three. Therefore if we take A to be true, that sufficient to tell us that the answer to their question is no.
The prior responses forget that the sqrt has +/- roots. You're assuming the roots are + only.
The square root symbol literally means "the positive square root of", so if you see an x surrounded by that symbol, you don't have to worry about negative roots.
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