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

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Bunuel
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If |x| > 0, is x^y < 1? (1) x = 1/2 (2) y = 0 [#permalink] New post   09 Mar 2022, 09:00
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If \(|x| > 0\), is \(x^y < 1\)?


(1) \(x = 1/2\)

(2) \(y = 0\)
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chetan2u
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Re: If |x| > 0, is x^y < 1? (1) x = 1/2 (2) y = 0 [#permalink] New post   09 Mar 2022, 22:55
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Bunuel wrote:
If \(|x| > 0\), is \(x^y < 1\)?


(1) \(x = 1/2\)

(2) \(y = 0\)



\(|x| > 0\) tells us that \(x\neq 0\),

(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

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Re: If |x| > 0, is x^y < 1? (1) x = 1/2 (2) y = 0 [#permalink] New post   10 Mar 2022, 11:38
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.
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If |x| > 0, is x^y < 1? (1) x = 1/2 (2) y = 0 [#permalink] New post   28 Sep 2022, 10:32
chetan2u wrote:
Bunuel wrote:
If \(|x| > 0\), is \(x^y < 1\)?


(1) \(x = 1/2\)

(2) \(y = 0\)



\(|x| > 0\) tells us that \(x\neq 0\),

(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



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
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Re: If |x| > 0, is x^y < 1? (1) x = 1/2 (2) y = 0 [#permalink] New post   28 Sep 2022, 11:10
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prakashb2497 wrote:
chetan2u wrote:
Bunuel wrote:
If \(|x| > 0\), is \(x^y < 1\)?


(1) \(x = 1/2\)

(2) \(y = 0\)



\(|x| > 0\) tells us that \(x\neq 0\),

(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



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



Yes, |x| is non negative. |x| > 0 means |x| is positive but the same cannot be said about x.
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Re: If |x| > 0, is x^y < 1? (1) x = 1/2 (2) y = 0 [#permalink] New post   28 Sep 2022, 11:26
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

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Re: If |x| > 0, is x^y < 1? (1) x = 1/2 (2) y = 0 [#permalink] New post   30 Sep 2022, 04:10
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prakashb2497 wrote:
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



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.
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Re: If |x| > 0, is x^y < 1? (1) x = 1/2 (2) y = 0 [#permalink] New post   01 Oct 2022, 05:10
chetan2u wrote:
prakashb2497 wrote:
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



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.



This makes sense and put things in perspective. Thanks a lot! chetan2u
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Re: If |x| > 0, is x^y < 1? (1) x = 1/2 (2) y = 0 [#permalink]
01 Oct 2022, 05:10
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