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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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Joined: 22 Aug 2013
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x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0  [#permalink]

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New post 26 Jul 2018, 22:13
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E

Difficulty:

  45% (medium)

Question Stats:

63% (01:28) correct 37% (01:00) wrong based on 34 sessions

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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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Re: x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0  [#permalink]

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New post 26 Jul 2018, 22:48
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]

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New post 26 Jul 2018, 23:16
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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