Confusing absolute value problem

smar83 wrote:is the answer E ?

ash g wrote: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 wrote:

ash g wrote: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).