Confusing absolute value problem

[netigen]

If x = ± |x| , then which one of the following statements could be true?

I. x=0
II. x<0
III. x>0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

[smar83]

is the answer E ?

[netigen]

is the answer E ?

Ans is actually [D]

[ash g]

Can you also provide explanation for answer choice [D]. It will be very interesting to understand the explantion. I think it will have to do something with the wording "could be true".

From OG11 DS explanation, what I understand is that
If |x| = +x, then x is zero or positive i.e. x >= 0
If |x| = -x , then x is zero or negative i.e. x <= 0
If both are true, then obviously x=0.

I think answer should be .

[netigen]

Can you also provide explanation for answer choice [D]. It will be very interesting to understand the explantion. I think it will have to do something with the wording "could be true".

From OG11 DS explanation, what I understand is that
If |x| = +x, then x is zero or positive i.e. x >= 0
If |x| = -x , then x is zero or negative i.e. x <= 0
If both are true, then obviously x=0.

I think answer should be .

|x| is always positive for all x (thats the absolute value concept)

The explanation is given below but I was not able to make it out and hence the posting here:


Example: If x = ±|x| , then which one of the following statements could be true?
I. x = 0
II. x < 0
III. x > 0
(A) None (B) I only (C) III only (D) I and II (E) II and III
Statement I could be true because ±|0| = -(+0)= -(0) = 0 . Statement II could be true because the
right side of the equation is always negative [ ±|x| = –(a positive number) = a negative number].
Now, if one side of an equation is always negative, then the other side must always be negative,
otherwise the opposite sides of the equation would not be equal. Since Statement III is the
opposite of Statement II, it must be false. But let’s show this explicitly: Suppose x were positive.
Then |x| = x, and the equation x = ±|x| becomes x = –x. Dividing both sides of this equation by x
yields 1 = –1. This is contradiction. Hence, x cannot be positive. The answer is (D).

[Stuart@KaplanGMAT]

Can you also provide explanation for answer choice [D]. It will be very interesting to understand the explantion. I think it will have to do something with the wording "could be true".

From OG11 DS explanation, what I understand is that
If |x| = +x, then x is zero or positive i.e. x >= 0
If |x| = -x , then x is zero or negative i.e. x <= 0
If both are true, then obviously x=0.

I think answer should be .

|x| is always positive for all x (thats the absolute value concept)

The explanation is given below but I was not able to make it out and hence the posting here:


Example: If x = ±|x| , then which one of the following statements could be true?
I. x = 0
II. x < 0
III. x > 0
(A) None (B) I only (C) III only (D) I and II (E) II and III
Statement I could be true because ±|0| = -(+0)= -(0) = 0 . Statement II could be true because the
right side of the equation is always negative [ ±|x| = –(a positive number) = a negative number].
Now, if one side of an equation is always negative, then the other side must always be negative,
otherwise the opposite sides of the equation would not be equal. Since Statement III is the
opposite of Statement II, it must be false. But let’s show this explicitly: Suppose x were positive.
Then |x| = x, and the equation x = ±|x| becomes x = –x. Dividing both sides of this equation by x
yields 1 = –1. This is contradiction. Hence, x cannot be positive. The answer is (D).

I have to confess, I understand neither the question nor the explanation.

My main question is:

what does the original information mean?

I could mean:

x = + OR - |x|

or it could mean

x = + AND - |x|

If the former is true, then x could be positive or negative and the answer should be all of the above.

If the latter is true, then the only possible value for x is 0 and (b) should be the right answer.

Anyone else as confused as I am?

[ash g]

okee. Thanks for posting the explanation. If the sign ± actually mean multiplying by (1)(-1) i.e by (-1), [as per the explanation provided, this is what they mean]
then the statement x=±|x| can be simplified into:
x = -|x|
or
|x| = -x.

which according to my statement before
=> If |x| = -x , then x is zero or negative i.e. x <= 0
makes I and II correct.

+ in ± is redundant.
I said initially because I took the statement x=±|x| to mean 2 sub statements x = +|x| AND x = -|x|.

Can I ask where did you get this problem from ?

[netigen]

Nova's GMAT prep course page 76

somehow the author is evaluating equation x = ±|x| becomes x = –x

which sounds like a mistake because in my opinion it should be

equation x = ±|x| becomes x = ±(+x) = ±x

So from my perspective all three cases suffice as a valid answer.