inequality question...

Question

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 ?

joshi.komal · Answer

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.

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its_me07 · Answer

Komal: Disable the HTML code to avoid confusions in ur post. Paresa.

hemanth28 · Answer

komal i am sorry..i couldnt get a bit of what you explained [:(]

joshi.komal · Answer

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

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www.Cityinapage.com

m7373 · Answer

How does - x | x | > 0 result in x<0 ? I don't understand.

Stuart@KaplanGMAT · Answer

m7373 wrote:How does - x | x | > 0 result in x<0 ? I don't understand.

The only way to get a positive product is to multiply 2 positives or 2 negatives.

We know that |x| is positive; therefore, -x must also be positive.

If -x is positive, then x must be negative.

hemanth28 · Answer

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.

GMAT First take :- 680
Getting the guns ready for second shot !!!
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horizonx29 · Answer

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.

Stuart@KaplanGMAT · Answer

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.

Actually, that's not true.

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.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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