Sovittalgmat wrote:X / |X| < X.
Which of the following must be true about X ( X <> 0 )
A. X >1
B. X > -1
C. |X| < 1
D. |X| = 1
E. |X|^2 = 1
[spoiler]OA: B[/spoiler]
So X>1 and -1<x<0 are the two ranges we are talking about and clearly
0<X<1 will not satisfy this equation and B can not be the correct answer.
To test this, plug 1/2
1 < 1/2 ? I don't think so!
Cramya, this is a must be true question. So MUST is a MUST. I dont mess around when a question uses that term, so should not you!cramya wrote:So X>1 and -1<x<0 are the two ranges we are talking about and clearly
0<X<1 will not satisfy this equation and B can not be the correct answer.
To test this, plug 1/2
1 < 1/2 ? I don't think so!
The reason why B must be true is because it covers the maximum possible range for x/|x| < x condition to be true. IMO this does not mean all values >-1 this is true
This question may be a little ambigous but out of the answer choices given x>-1 covers the maximum possible range. Again the question does not say that all x's that we choose in the answer choice have to satisfy this either so it really ambigous????.
Regards,
Cramya
I agree to a certain extent and may be the experts may weigh in on this and dismiss it.Cramya, this is a must be true question. So MUST is a MUST. I dont mess around when a question uses that term, so should not you
Agreed!cramya wrote:
I am sure in the real test there would be no room for such ambiguity or arguments in questions .
Regards,
CR
You can't just divide both sides by x here, at least not without analyzing two cases; if x is negative, you'd need to reverse the inequality after you divide by x. In addition, you've made a mistake going from the second last line above to the last; if you ever do conclude that 1 < |x|, that means that x > 1 or x < -1.welcome wrote:Here is my solution.
X/|X| <X
=> 1/|X| < 1
=> 1<|X|
=> -1<x<1
=> Ans B.
Oh Ian..now you changed my entire paradigm for must be true question...hmmIan Stewart wrote:There is nothing ambiguous about the question, and I've seen questions with a similar type of logic on the real test. Let's look at a simpler question:
If 0 < x < 10, what must be true?
I) x > 5
II) x > -5
III) 2 < x < 10
The answer here is II) only. The question does *not* ask "which of the following gives all possible values of x, and only those values?" It only asks "what must be true?". If we know that x is greater than 0, we can be absolutely certain that x is greater than -5.
The same is true in the question in the original post, above. From the inequality given, X/|X| < X, we can determine that X is either between -1 and 0 or X is greater than 1. Well, regardless, X is certainly greater than -1; that must be true. It isn't important that X can't be equal to 0.5. What is important is that the only possible solutions for X are all larger than -1.
Even if we had been given different information and had reached the conclusion that X = 18, we'd still know that it must be true that X > -1, since 18 is greater than -1.
