If |x| 0, is x^y

Question

If  |x| > 0 , is  x^y < 1 ?

(1)  x = 1/2

(2)  y = 0

chetan2u · Answer

|x| > 0  tells us that  x
eq 0 ,

(1)  x = 1/2 
If y>0, then yes......y=2, then  x^y=\frac{1}{4} 
If y<0, then no......y=-2, then  x^y=(\frac{1}{2})^{-2}=2^2=4

(2)  y = 0 
Irrespective of the value of x,  x^y=x^0=1 
Thus answer is NO.
Sufficient

B

Sushen · Answer

B 
Q: Is x^y<1 
Given: |x|>0 So, x≠0 
If x^y<1,then 
x is positive and greater than one, and y is negative,
or 0<x<1 and y is pos 
or x is neg and y is odd, 
or others

(1) x=1/2  Not Sufficient.  If y is positive then the answer is yes. If y is negative the answer is no. I am unable to answer the question with the data supplied.
(2) y=0  Sufficient   Anything to the zero power is one, thus I can answer the question. The answer is NO. x^y is NOT less than zero, but the data is sufficient for me to answer this.

prakashb2497 · Answer

I got the answer correct. But in the pre-solving is it correct to infer that if |x| > 0; then |x| is positive only?

chetan2u

chetan2u · Answer

Yes, |x| is non negative. |x| > 0 means |x| is positive but the same cannot be said about x.

prakashb2497 · Answer

I understood partly. If |x| is non negative and |x| >0 then |x| will be positive and same will be for x right?

How would you plot it on the number line visually? Essentially absolute value of a number is either positive or negative. And if it's non negative and >0 then it will be positive correct?

What am I missing here?

chetan2u

Posted from my mobile device

chetan2u · Answer

ABSOLUTE VALUE means |x|, and is the positive value of x.
Say, you say distance between Delhi and Pune is 1500km, so if D is at 0 and P is at 1500, the distance will always be 1500.
It cannot be D-P=0-1500=-1500, so we will write |D-P|=|P-D|=1500.

coming to |x|.
It is NON-NEGATIVE, that is like distance, |x| will never be negative, even though x itself, similar to D-P can be negative.
|x|>0 does not tell anything about x except that x is not zero. Rest, it could eb anything.

prakashb2497 · Answer

This makes sense and put things in perspective. Thanks a lot!  chetan2u

If |x| > 0, is x^y < 1? (1) x = 1/2 (2) y = 0

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