earth@work wrote:If x = ± ıxı , 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
ıxı stands for absolute value of x
Ans:[spoiler](D)[/spoiler]
yeah, the writing of this question is a bit ridiculous.
the users above have this one pretty much covered, but here's a recap:
* preliminary observations:
if x > 0, then |x| is just x; therefore, x = |x|.
if x < 0, then |x|, which is positive, is the opposite of x; therefore, x = -|x|.
if x = 0, then everything is 0, and so x equals
both |x| and -|x|.
* we're not sure whether "±" means "EITHER + or -" or "BOTH + and -". the answer to the problem will differ according to which of these meanings was intended.
* CASE 1: take "±" to mean "EITHER + or -".
in this case,
every possible value of x will solve the equation, because, as noted in the preliminary observations,
every possible value of x is equal to at least one of |x| and -|x|.
in this case the answer is "i, ii, and iii," which isn't one of the choices.
one of the previous posters called this "choice (f)". i like.
* CASE 2: take "±" to mean "BOTH + and -".
in this case, the only value of x that works is 0, as noted in the preliminary observations.
this is choice (b).
* since only one of the cases above appears in the answer choices, we may as well go with that one, so let's pick (b).
--
the official test will NEVER feature this sort of notational ambiguity, so rest easy. instead, concentrate on the takeaways ("preliminary observations") posted above regarding the absolute value, since those are what you'll actually be able to apply to other problems.
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