|x|<1? Is -1<x<1?
st(1) x/|x|<x implies x<x|x|, if x>0 then 1<|x|. If x<0, then 1>|x| Not Sufficient
st(2) x<|x| implies x is negative only. Not Sufficient
combined st(1&2): st(2) x is -ve and x<0 with st(1) 1>|x| Sufficient, as we answer No to this question.

colakumarfanta wrote:Is | x | <1?
(1) x / | x | <x
(2) x <| x |
OA C

I stink at these!

I had to test values.

Is -1 < x < 1 ?

(1)
x / |x| < x
x < x * |x| <---- Plug in values inside and outside the range

2: 2 < 4 TRUE
-1/2: -1/2 < -1/4 TRUE

So x can be inside or outside the range, can't answer yes or no.

INSUFFICIENT

(2)
x < |x| --> x < 0

x is therefore inside and outside the range. Can't answer yes or no.

INSUFFICIENT

(1+2)
x < x*|x| <---- Plug in values for x<0

-1/2: -1/2 < -1/4 TRUE

-1 < -1 FALSE

-3/2: -3/2 < -9/4 FALSE

Therefore it seems with statements 1&2 combined, the answer is yes.

SUFFICIENT

So we choose C


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option 1
says that x is always positive. But x can be fraction or integer i.e it can be less than or greater than 1

option 2
says that x is always negative. But x can be fraction or integer i.e it can be less than or greater than 1

option 1 and 2 combined

x / | x | <x <| x |

only negative fraction values can satisfy the condition. hence C

Is | x | <1?
(1) x / | x | <x
x < |x| x - means x is positive but can't say whether its greater than or less than one.
Not sufficient

(2) x <| x | - means x is negative i.e. x < 0 but can't say whether x is less than or greater than -1.

1+2
x < |x| x , and x is negative i.e. negative x multiplied by positive x is less than negative x. this is only possible if -1<x<0.

Hence, C