What is the value of x?

Question

(1)  \sqrt{x^4} = 9 
(2)  \sqrt{x^2}=-x

Bunuel · Accepted Answer

What is the value of x?

(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.

shrive555 · Answer

Number 2 Here i got stuck.
Thanks B

MacFauz · Answer

1)  x^2 = 9 . So x = +3 or -3. Insufficient

2)  \sqrt{x^2} = -x  x can be 0 or any negative number. Insufficient

1 & 2 together. x is negative and is either +3 or -3. So x is -3.

Answer C

Bunuel · Answer

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KarishmaB · Answer

Responding to a pm:

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)

keenys · Answer

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.

Bunuel · Answer

Please check again: where did we get negative result?

blueseas · Answer

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

keenys · Answer

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 again.

Bunuel · Answer

That's because |x^2|=x^2.

shashankism · Answer

Given : variable x
DS : value of x

Statement 1 :  \sqrt{x^4} = 9 
x^4 = 81 
x = +/-3
putting in the same equation we find both +3,-3 are valid soln.
 NOT SUFFICIENT

Statement 2 :  \sqrt{x^2}=-x 
|x| = -x 
so x<0
 NOT SUFFICIENT

Combined : x = -3

Answer C

Saundarya · Answer

Hi Experts,

I completely understand the above explanation but can you tell me why i cannot apply the below process,

statement ii.

x^(2x1/2)= x = -x
2x=0
x=0
Hence B.

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What is the value of x?

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