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21 Sep 2019, 19:06
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Difficulty:
5%
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Question Stats:
89% (01:05) correct
11%
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wrong
based on 609
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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
(1) x is odd and z is even.
(2) x – z is odd.
DS85100.01
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
21 Sep 2019, 22:07
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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
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
26 Sep 2019, 04:45
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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.
(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.
