Is | x | <1?
(1) x / | x | <x
(2) x <| x |
OA C
Is | x | <1?
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|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.
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
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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
[/i]
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
[/i]
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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
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
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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
(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
Last edited by apex231 on Mon Dec 12, 2011 10:09 pm, edited 1 time in total.
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colakumarfanta wrote:Is | x | <1?
(1) x / | x | <x
(2) x <| x |
OA C
Statement 1: x/|x| < x
If x is positive, 1/|x| < 1 => |x| > 1
If x is negative, 1/|x| > 1 => |x| < 1
Not sufficient
Statement 2: |x| > x
Only if x is negative, then |x| = -x > x
So we know x is negative, but we don't have enough information to conclude whether |x| less than 1 or not.
Not sufficient
1 & 2 Together: From statement 2, x is negative.
From statement 1, if x is negative then, 1/|x| > 1 => |x| < 1
Sufficient
The correct answer is C.
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