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x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0

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amanvermagmat
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x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0 [#permalink] New post   26 Jul 2018, 22:13
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x and y are real numbers. Is y negative?

(1) x^y > 0

(2) y^x > 0
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E
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Nikhil
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Re: x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0 [#permalink] New post   26 Jul 2018, 22:48
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To determine if y is negative

x and y are real numbers

Statement 1

\(x^y\) > 0

x can be 10 and y can be 1 satisfying \(10^1 = 10 > 0\) and y is positive

x can be 10 and y can be -1 satisfying \(10^{-1} = \frac{1}{10} = 0.1 > 0\) and y is negative

Statement 1 is insufficient

Statement 2

\(y^x > 0\)

x can be 1 and y can be 10 satisfying \(10^1 = 10 > 0\) and y is positive

x can be 2 and y can be -10 satisfying \(-10^2 = 100 > 0\) and y is negative

Statement 2 is insufficient

Combining statements 1 and 2

x can be 10 and y can be 1 satisfying \(10^1 = 10 > 0\) and \(1^{10} = 1 > 0\) and y is positive

x can be 2 and y can be -1 satisfying \(2^{-1} = 0.5 > 0\) and \(-1^2 = 1 > 0\) and y is negative

Statements 1 and 2 together are insufficient

Hence option E
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x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0 [#permalink] New post   26 Jul 2018, 23:16
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x and y are real numbers. Is y negative?

(1) \(x^y > 0\)
this can happen irrespective of value of y..
y is -1 and x is 2....x^y=2^(-1) = 1/2>0
y is 1 and x is 2....2^1=2>0
insuff

(2) y^x > 0
this can also happen with any value of y..
(-1)^2=1>0
1^2=1>0
insuff

combined..
y = -1 will satisfy both statements
y= 1 will satisfy both equations
insuff

E
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Re: x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0 [#permalink] New post   03 Jun 2019, 23:44
amanvermagmat wrote:
x and y are real numbers. Is y negative?

(1) x^y > 0

(2) y^x > 0



The way i did
is y negetive?
1st says x^y >0,implying ylogx is undefined ,so y and x can have any value and same does option 2
combiningly x and y can take any value in the quant section.
so option E.

HINT:LOG(0) IS UNDEFINED.
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Re: x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0 [#permalink] New post   20 Oct 2021, 21:29
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Re: x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0 [#permalink]
20 Oct 2021, 21:29
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