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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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DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1348
Location: India
x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0  [#permalink]

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26 Jul 2018, 22:13
3
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Difficulty:

45% (medium)

Question Stats:

64% (01:25) correct 36% (01:05) wrong based on 44 sessions

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x and y are real numbers. Is y negative?

(1) x^y > 0

(2) y^x > 0
Senior RC Moderator
Status: Perfecting myself for GMAT
Joined: 22 May 2017
Posts: 759
Concentration: Nonprofit
Schools: Haas '21
GPA: 4
WE: Engineering (Computer Software)
Re: x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0  [#permalink]

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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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Joined: 02 Aug 2009
Posts: 6957
x and y are real numbers. Is y negative? (1) x^y > 0 (2) y^x > 0  [#permalink]

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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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