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29 Jan 2012, 08:29
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
45% (02:09) correct
55%
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wrong
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If x is different from 0, is |x| < 1 ?
(1) x*|x| < x
(2) |x| > x
(1) x*|x| < x
(2) |x| > x
I think in this way.
From stat 1 : |x| < 1 and so we have 2 solution INSUFF
From stat 2: the same INSUFF.
At this point I'm lost how to evaluate together ????
Thanks
From stat 1 : |x| < 1 and so we have 2 solution INSUFF
From stat 2: the same INSUFF.
At this point I'm lost how to evaluate together ????
Thanks
29 Jan 2012, 08:42
Kudos
Bookmarks
carcass
If x is different from 0, is |x| < 1 ?
(1) x |x| < x
(2) |x| > x
I think in this way.
From stat 1 : |x| < 1 and so we have 2 solution INSUFF
From stat 2: the same INSUFF.
At this point I'm lost how to evaluate together ????
Thanks
(1) x |x| < x
(2) |x| > x
I think in this way.
From stat 1 : |x| < 1 and so we have 2 solution INSUFF
From stat 2: the same INSUFF.
At this point I'm lost how to evaluate together ????
Thanks
If x is different from 0, is |x| < 1 ?
(1) x*|x|<x --> if \(x>0\) then we can divide both parts by it and we'l get \(|x|<1\) (so we would have an YES answer. Complete range for this case would be: \(0<x<1\)) BUT if \(x<0\) then we can also divide both parts by it though this time we should switch the sign of the inequality as we are dividing by negative value: \(|x|>1\) (so we would have a NO answer. Complete range for this case would be: \(x<-1\)). Not sufficient. (Basically we should know whether \(x\) is positive or negative).
(2) |x| > x --> well this basically tells that \(x\) is negative, as if \(x\) were positive (or zero) then \(|x|\) would be equal to \(x\). Still insufficient to say whether \(|x|<1\).
(1)+(2) From (2) \(x<0\) thus from (1) \(|x|>1\) and the answer to the question is NO (solution based on both statements is \(x<-1\)). Sufficient.
Answer: C.
Similar question: if-x-is-not-equal-to-0-is-x-less-than-1-1-x-x-x-86140.html
Hope it helps.
29 Jan 2012, 09:58
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carcass
I suppose that you have put in red my logic on stat 1 because not so clear.
Stat (1) : x > 1 or -x > 1.........x < -1
Stat (2) : x < x or -x > x.........x < -x
This is the logic that conduct me to say that the 2 stats are insufficient. I don't understand completely why in the 2 one |x| > x ........ x is < 0 ??'
I also read the topic that you suggested; your third reply is very helpful but the doubt remain on stat ( 2)
Thanks
OK. First of all: I marked "|x|<1" in red for (1), because you don't get that |x| < 1 from this statement. If it were so then then you'd have an YES answer right away (as the question asks exactly about the same thing "is |x|<1")Stat (1) : x > 1 or -x > 1.........x < -1
Stat (2) : x < x or -x > x.........x < -x
This is the logic that conduct me to say that the 2 stats are insufficient. I don't understand completely why in the 2 one |x| > x ........ x is < 0 ??'
I also read the topic that you suggested; your third reply is very helpful but the doubt remain on stat ( 2)
Thanks
Next, "is \(|x|<1\)?" means "is \(-1<x<1\)?"
(1) x*|x|<x holds true in two cases for \(x<-1\) and \(0<x<1\):
-----(-1)----(0)----(1)----
So as you can see this one is not sufficient to answer the question.
(2) |x| > x. Absolute value property: when \(x\geq{0}\) then \(|x|=x\) and when \(x<{0}\) (so when \(x\) is negative) then \(|x|=-x\). For the second case \(|x|=positive>x=negative\). That' why \(|x|>x\) means that \(x<0\) (or as I wrote if \(x\) were positive we would have \(|x|=x\) not \(|x|>x\)). You can also consider a simple example: \(|-3|>-3\) --> \(-3<0\). Thus the range for (2) is:
-------------(0)--------
Also insufficient to answer the question.
(1)+(2) Intersection of the ranges from (1) and (2) is:
----(-1)----(0)----(1)---- --> \(x<-1\). Which makes the answer to the question "is \(-1<x<1\)?" NO.
Check Absolute Value chapter of Math Book for more on this topic: math-absolute-value-modulus-86462.html
Hope it's clear.
