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# If x and z are integers, is x + z^2 odd?

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Senior Manager
Joined: 04 Sep 2017
Posts: 318
If x and z are integers, is x + z^2 odd?  [#permalink]

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21 Sep 2019, 18:06
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83% (01:09) correct 17% (01:20) wrong based on 185 sessions

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If x and z are integers, is x + z^2 odd?

(1) x is odd and z is even.
(2) x – z is odd.

DS85100.01
Math Expert
Joined: 02 Aug 2009
Posts: 8755
Re: If x and z are integers, is x + z^2 odd?  [#permalink]

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21 Sep 2019, 21:07
If x and z are integers, is x + z^2 odd?

few points..
(A) x will have same property as $$x^2$$ or $$x^5$$ and so on
(B) x+z will have same property as x-z or z-x or z+x.

(1) x is odd and z is even.
$$x+z^2=odd+even^2=odd+even=odd$$
Suff

(2) x – z is odd.
x-z will have same property as x+z, which will have same property as $$x+z^2$$
So, $$x+z^2$$ is odd.
Suff

D
_________________
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Joined: 22 Jul 2013
Posts: 4
Re: If x and z are integers, is x + z^2 odd?  [#permalink]

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26 Sep 2019, 03:45
1
The only ways x + z^2 can be odd is: Either 'x is odd and z is even' or 'y is odd and z is even'.
(Since, O+O=E, E+E=E, E+O=O) & (O^2=O and E^2=E)

(1) x is odd and z is even.
It satisfies our condition. hence it's sufficient.

(2) x – z is odd
The only way X-Z can be odd is either of them is even and the other is odd.
(since: O-O=E, E-0=0, 0-E=0)
This satisfies our condition too. thus x + z^2 is odd.
Manager
Status: In last prep stage
Joined: 11 Jun 2017
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GMAT 1: 630 Q44 V33
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Re: If x and z are integers, is x + z^2 odd?  [#permalink]

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26 Oct 2019, 15:53
chetan2u wrote:
If x and z are integers, is x + z^2 odd?

few points..
(A) x will have same property as $$x^2$$ or $$x^5$$ and so on
(B) x+z will have same property as x-z or z-x or z+x.

(1) x is odd and z is even.
$$x+z^2=odd+even^2=odd+even=odd$$
Suff

(2) x – z is odd.
x-z will have same property as x+z, which will have same property as $$x+z^2$$
So, $$x+z^2$$ is odd.
Suff

D

Could you please further explain below statement:

x+z will have same property as x-z or z-x or z+x.
Re: If x and z are integers, is x + z^2 odd?   [#permalink] 26 Oct 2019, 15:53