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# x and y are non-zero integers. Is x^y a positive number?

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Manager
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x and y are non-zero integers. Is x^y a positive number?  [#permalink]

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11 Apr 2019, 23:09
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Difficulty:

65% (hard)

Question Stats:

18% (00:41) correct 82% (01:25) wrong based on 17 sessions

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x and y are non-zero integers. Is x^y a positive number?

(1) $$y = - x$$
(2) $$y = (2k + 1)^2$$ where k is a non-zero integer

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Re: x and y are non-zero integers. Is x^y a positive number?  [#permalink]

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12 Apr 2019, 05:21
1
themindful wrote:
x and y are non-zero integers. Is x^y a positive number?

(1) $$y = - x$$
(2) $$y = (2k + 1)2$$ where k is a non-zero integer

Question: Is $$x^y$$ a positive number?

$$x^y$$ will be positive only if x is positive irrespective of y

Question REPHRASED: Is x > 0?

Statement 1: $$y = - x$$

i.e. x and y have opposite signs but we don't know whether x is +ve or -ve hence

NOT SUFFICIENT

Statement 2: $$y = (2k + 1)^2$$ where k is a non-zero integer

i.e. y is +ve (a perfect square) odd integer (2k+1=odd) but since sign of x is unknown hence
NOT SUFFICIENT

Combining the two statements

Since y is positive odd integer and y = -x therefore x is -ve and

$$x^y = (-ve)^{odd} = -ve$$ hence answer to question is NO hence

SUFFICIENT

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Re: x and y are non-zero integers. Is x^y a positive number?  [#permalink]

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12 Apr 2019, 10:16
1
themindful wrote:
x and y are non-zero integers. Is x^y a positive number?

(1) $$y = - x$$
(2) $$y = (2k + 1)2$$ where k is a non-zero integer

#1
$$y = - x$$
so x^y a positive number
yes when both x& y are even
and no when odd both; insufficient

#2
$$y = (2k + 1)2$$ where k is a non-zero integer[/quote]
this will be true for all odd values only ; y =1 at k=0 ; y= 9 at k = 1 ; y=25 at k= 2
but x not know insufficeint
from 1 & 2
we know y= odd so x has to be odd also
therefore x^y is not +ve number
sufficient
IMO C
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Re: x and y are non-zero integers. Is x^y a positive number?  [#permalink]

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13 Apr 2019, 09:40
1
can you please make the question a bit more clear. option B looks like y=(2k+1)x2 . I thought it to be even always.
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Re: x and y are non-zero integers. Is x^y a positive number?  [#permalink]

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14 Apr 2019, 02:55
1
HAPPYatHARVARD wrote:
can you please make the question a bit more clear. option B looks like y=(2k+1)x2 . I thought it to be even always.

Sorry to hear that, But I wrote pretty clearly in the mathematical notation as per gmatclub guidelines $$y=(2k+1)^2$$
Maybe you viewed it on a platform which could not render the mathematical notation. Try on Chrome or gmatclub app on mobile
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Re: x and y are non-zero integers. Is x^y a positive number?   [#permalink] 14 Apr 2019, 02:55
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