Can the experts please help me with this question?
If x is not equal to 0, is |x| less than 1?
a) x/|x|<x
b) |x|>x
Thanks!!
If x is not equal to 0, is |x| less than 1?
a) x/|x|<x
b) |x|>x
Thanks!!
Hi safina,
The question essentially asks - is -1<x<1 (excluding 0)?
Choice A: the left hand side will be 1 when x>0 and -1 when x<0. Let's look at the possibilities:
x>1 --> Statement will be TRUE because left hand side is 1 whereas x>1.
0<x<1 --> Statement will be FALSE because left hand side is 1 whereas x is a small positive number
-1<x<0 --> Statement will be TRUE because left hand side is -1 whereas x is a smaller negative number
x<-1: Statement will be FALSE because left hand side is -1 whereas x<-1
Since the statement is TRUE for x>1 and -1<x<0, it is INSUFFICIENT to determine if |x|<1.
Choice B: |x|>x only when x is negative, otherwise they'll be equal. However, this means any negative number would work. So B is INSUFFICIENT on its own.
Together: Test out both cases for choice A being true.
x>1 - makes choice A true but makes choice B false - does not work
-1<x<0 - makes choice A true and choice B true.
Therefore for A and B to be true, -1<x<0 must be true as well. The answer is C
