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how to solve second statement? i did 2nd statement squaring on both sides then got same x^2 = x^2. then what to do after this?? and also how to solve combining both 1 and 2 statement??

Squaring is not the solution for every problem. When you square both sides you sometimes lose valuable information. e.g. x = -5 Square -> x^2 = 25

If you are given x^2 = 25, all you can say is that x is 5 or -5. You cannot say which one. So you lost information here.

As for this question, there is a concept that you need to use here \(\sqrt{x^2}= |x|\) \(\sqrt{9} = 3\). It is not 3 or -3. Only the positive value is considered for square roots. Hence, the mod is used when dealing with a variable.

So from the second statement, you get |x| = -x Now, we know that |x| = -x when x is negative. So the only thing that the second statement tells us is that x is negative. Statement 1 tells you that x is 3 or -3. Statement 2 tells you that x is negative. SO using both statements, you can say that x = -3. Sufficient. Answer (C)
_________________

(1) \(\sqrt{x^4} = 9\) --> \(x^2=9\) --> \(x=3\) or \(x=-3\). Not sufficient.

(2) \(\sqrt{x^2}=-x\) --> \(|x|=-x\) --> just says that \(x\) is not positive (\(x\) could be 0 or any negative number). Not sufficient.

(1)+(2) As from (2) \(x\) is not positive then from (1) \(x=-3\). Sufficient.

Answer: C.

HI Bunnel,

I am slightly confuse here. Isnt it true that when the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root?

How is A and B different here? If x can be negative according to A then it could be negative according to B as well. Could you please help clarify this rule?

(1) \(\sqrt{x^4} = 9\) --> \(x^2=9\) --> \(x=3\) or \(x=-3\). Not sufficient.

(2) \(\sqrt{x^2}=-x\) --> \(|x|=-x\) --> just says that \(x\) is not positive (\(x\) could be 0 or any negative number). Not sufficient.

(1)+(2) As from (2) \(x\) is not positive then from (1) \(x=-3\). Sufficient.

Answer: C.

HI Bunnel,

I am slightly confuse here. Isnt it true that when the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root?

How is A and B different here? If x can be negative according to A then it could be negative according to B as well. Could you please help clarify this rule?

Thanks.

Please check again: where did we get negative result?
_________________

I am slightly confuse here. Isnt it true that when the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root?

How is A and B different here? If x can be negative according to A then it could be negative according to B as well. Could you please help clarify this rule?

Thanks.

whatever value comes after square root ...put a modulus over it..and then you will not get confused.... as you said..square root gives positive value..hence modulus does the same thing.. example: \sqrt{x^4}=modulus x^2==>since x^2 is always positive(or equal to zero) we can remove mod hence it becomes==>x^2=9....now no more square root ...hence whatever value will satisfy ...it can be positive or negative. hence x=+3..or -3========>insufficient.

in option 2 \sqrt{x^2}=-x remove square root and put a mod hence mod x= -x===>this conditions is correct only when X IS NEGATIVE...==>NOT SUFFICIENT

NOW COMBINING WE CAN ANSWER X=3==>SINCE X IS NEGATIVE..HENCE C
_________________

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I am slightly confuse here. Isnt it true that when the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root?

How is A and B different here? If x can be negative according to A then it could be negative according to B as well. Could you please help clarify this rule?

Thanks.

Please check again: where did we get negative result?

I am referring to this statement - (1) \(\sqrt{x^4} = 9\) --> \(x^2=9\) --> \(x=3\) or \(x=-3\). Not sufficient.

As per your explanation in this statement, x could be 3 or -3. However, in the second statement, the explanation says

\sqrt{x^2}= |x|

My question is why in the first statement, \sqrt{x^4} not equal to |x^2|.

I am slightly confuse here. Isnt it true that when the GMAT provides the square root sign for an even root, then the only accepted answer is the positive root?

How is A and B different here? If x can be negative according to A then it could be negative according to B as well. Could you please help clarify this rule?

Thanks.

Please check again: where did we get negative result?

I am referring to this statement - (1) \(\sqrt{x^4} = 9\) --> \(x^2=9\) --> \(x=3\) or \(x=-3\). Not sufficient.

As per your explanation in this statement, x could be 3 or -3. However, in the second statement, the explanation says

\sqrt{x^2}= |x|

My question is why in the first statement, \sqrt{x^4} not equal to |x^2|.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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_________________

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

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