If x does not equal 0, is x^2 / |x| < 1 ?

Given x is not equal to 0

IMO u can rewrite the question Is x^2 / |x| < 1 as:

Is x^2 < |x| ? The reason u can do this is beacuse |x| is always positive so you can multiply both sides by |x| without affecting the inequality

Also the statement would be true for any values between -1 and 1 (positive and negative fractions between -1 and 1)

Stmt I

x<1

x=-2 no
x=-1/2 yes

INSUFF

Stmt II

x=2 NO
x=1/2 YES

INSUFF

Stmt I and II

-1<x<1 so we can definitely say x^2 < |x|

SUFF

Hope this helps!

Choose C)

P.S : If the question was x^2 / x < 1 given x is not equal to 0 then we cannot rewrite the question as x^ 2 < x since we dont know the sign of x. If x is positive then yes but if x was negative then the inequality will change to >. Since we dont know we cant do this. This is where we could make a mistake.

Given x is not equal to 0

IMO u can rewrite the question Is x^2 / |x| < 1

as:

ALL well ramya,..... wasnt this too much of a assumption??

yes stem says nto equal to 0 .. cant it be greater than 0 ????

please kindly share ur thought processs

vishu

If x does not equal 0, is x^2 / |x| < 1 ?
(1 )x < 1
(2) x > &#8722;1


x2/|x| = |x|

combining 1 and 2

we see that -1<|x| <1

hence IMO C

Thanks Cramya for the reminder on dividing by a variable..
BTW I got C as well for this problem by plugging values.

cramya wrote:P.S : If the question was x^2 / x < 1 given x is not equal to 0 then we cannot rewrite the question as x^ 2 < x since we dont know the sign of x. If x is positive then yes but if x was negative then the inequality will change to >. Since we dont know we cant do this. This is where we could make a mistake.

Thanks for this

please kindly share ur thought processs

Vishu,
U r correct. I could not have done it if the problem just read x is non zero. As I said earlier:

The question can be rephrased as Is x^2 < |x|. The reason u can do this is beacuse |x| is always positive so you can multiply both sides by |x| without affecting the inequality

If the question was x^2 / x < 1 given x is not equal to 0 then we cannot rewrite the question as x^ 2 < x since we dont know the sign of x. If x is positive then yes but if x was negative then the inequality will change to >. Since we dont know we cant do this. This is where we could make a mistake


Let me know if u still have questions/concerns.

Regards,
Cramya