If x ≠ 0, is x^2/|x| < 1?
(1) x < 1
(2) x > −1
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C?
Statement: x<1
say x=1/2
or (1/4)/(1/2)=1/2 <1 yes
say x=-1
or 1/1=1<1 no not sufficient
Statement: x>-1
say x=-1/2
or (1/4)/(1/2)=1/2<1 yes
say x=1
or 1/1=1<1 no not sufficient
combining 1 and 2 , -1<x<1 or x must be some fraction either positive or negative (x cannot be 0)
x=-1/2 or x=1/2 gives (1/4)/(1/2)=1/2<1
hence C
Statement: x<1
say x=1/2
or (1/4)/(1/2)=1/2 <1 yes
say x=-1
or 1/1=1<1 no not sufficient
Statement: x>-1
say x=-1/2
or (1/4)/(1/2)=1/2<1 yes
say x=1
or 1/1=1<1 no not sufficient
combining 1 and 2 , -1<x<1 or x must be some fraction either positive or negative (x cannot be 0)
x=-1/2 or x=1/2 gives (1/4)/(1/2)=1/2<1
hence C
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Question stem:
x^2 / |x| < 1 can be rewritten as x^2 < |x| since we know |x| is always positive (so dont have to worry about affecting the inequality)
This is true is for fractions between -1 and +1
Stmt I
x<1
If x=-2 for eg x^2>|x|
If x=1/2 x^2<|x|
INSUFF
Stmt II
x>-1
If x=2 for eg x^2>|x|
If x=1/2 then x^2<|x|
INSUFF
Combining stmt I and II we get
-1<x<1
Therefore for all values within this range x^2<|x|
SUFF
C)
x^2 / |x| < 1 can be rewritten as x^2 < |x| since we know |x| is always positive (so dont have to worry about affecting the inequality)
This is true is for fractions between -1 and +1
Stmt I
x<1
If x=-2 for eg x^2>|x|
If x=1/2 x^2<|x|
INSUFF
Stmt II
x>-1
If x=2 for eg x^2>|x|
If x=1/2 then x^2<|x|
INSUFF
Combining stmt I and II we get
-1<x<1
Therefore for all values within this range x^2<|x|
SUFF
C)
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This is what I did -scoobydooby wrote:C?
Statement: x<1
say x=1/2
or (1/4)/(1/2)=1/2 <1 yes
say x=-1
or 1/1=1<1 no not sufficient
As the x in the denominator is |x|
so I assumed 2 cases
case 1: x>0
here your example is valid where you took x = 1/2
therefore, x^2/|x| < 1
But for x < 0
i.e. x is negative
if I take x = -1
I get
x^2/x = (-1)^2 / - (-1) = 1 ----- (ohh! I realize my mistake now. I didn't account for the negative sign of the negative number and took (-1)^2/(-1) instead)
Thanks Scoobydoo - sometimes another perspective is what you need to understand your own mistakes. [/quote]scoobydooby wrote: Statement: x>-1
say x=-1/2
or (1/4)/(1/2)=1/2<1 yes
say x=1
or 1/1=1<1 no not sufficient
combining 1 and 2 , -1<x<1 or x must be some fraction either positive or negative (x cannot be 0)
x=-1/2 or x=1/2 gives (1/4)/(1/2)=1/2<1
hence C
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Ok, for this question, I dint substitute any numbers..
so guys, please check and let me know if there's any flaw in my approach..
X^2/|X| < 1 can be written as
X^2/X < 1 and X^2/(-X) < 1
Or X < 1 and X > -1
So the given question can be re-written as if - 1 < x < 1
From A we know that X < 1, but it can be any value till - infinity.
From B we know that X > -1, similarly any value till infinity.
Combining both we surely know that - 1 < X < 1
Hence C is the answer.
so guys, please check and let me know if there's any flaw in my approach..
X^2/|X| < 1 can be written as
X^2/X < 1 and X^2/(-X) < 1
Or X < 1 and X > -1
So the given question can be re-written as if - 1 < x < 1
From A we know that X < 1, but it can be any value till - infinity.
From B we know that X > -1, similarly any value till infinity.
Combining both we surely know that - 1 < X < 1
Hence C is the answer.