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If x, y and z are integers and xy + z is an odd integer, is

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If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 28 Jul 2009, 21:25
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Question Stats:

39% (03:31) correct 61% (02:24) wrong based on 297 sessions
If x, y and z are integers and xy + z is an odd integer, is x an even integer?

(1) xy + xz is an even integer
(2) y + xz is an odd integer
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Mar 2013, 01:10, edited 1 time in total.
Edited the question and added the OA.
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Re: DS - Is x even? [#permalink] New post 28 Jul 2009, 22:14
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IMO A

1. xy + xz is an even integer - SUFFICIENT
Given:
xy + z is odd ...(i)
xy + xz is even ...(ii)

subtracting (ii) from (i)
we get xz - z, which should be odd (* since odd - even = odd)
=> z(x-1) is odd
=> both z and (x-1) is odd
=> since (x-1) is odd, x must be even.

2. y + xz is an odd integer -INSUFFICIENT
Given:
xy + z is odd ...(i)
y + xz is odd ...(ii)

subtracting (ii) from (i)
we get xy + z - y - xz
= (x-1)(y-z) , which should be even
=> either (x-1) is even or (y-z) is even ....insufficient to determine
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Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 20 Mar 2014, 05:09
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Expert's post
Mountain14 wrote:
jlgdr wrote:
Aleehsgonji wrote:
If x, y and z are integers and xy + z is an odd integer, is x an even integer?

(1) xy + xz is an even integer
(2) y + xz is an odd integer



Odd/Even questions can be usually solved quite easily if one tries some operations with the statements

We want to know if x is even integer

We are given that xy+z is odd

Statement 1

xq + xz is even

Subtracting

z(x+1) is odd

Therefore, x+1 should be odd and x should be even


Sufficient

Statement 2

Not sufficient

Answer is A

Just my 2c

Cheers
J



I am not clear with the red part.


When you subtract xy + z=odd from xy+xz=even you'll get: xz-z=even-odd=odd --> z(x-1)=odd. For the product of two integers to be odd, both of them must be odd --> z and x-1 are odd. If x-1=odd, then x must be even: x-1=x-odd=odd --> x=odd+odd=even.

Hope it's clear.
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Re: If x,y and z are integers and xy + z is an odd integer, is x [#permalink] New post 06 Mar 2013, 20:55
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This question took forever to solve great strategy. Plugging numbers won't work all the time.
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Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 31 Jan 2014, 08:31
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Aleehsgonji wrote:
If x, y and z are integers and xy + z is an odd integer, is x an even integer?

(1) xy + xz is an even integer
(2) y + xz is an odd integer



Odd/Even questions can be usually solved quite easily if one tries some operations with the statements

We want to know if x is even integer

We are given that xy+z is odd

Statement 1

xq + xz is even

Subtracting

z(x+1) is odd

Therefore, x+1 should be odd and x should be even

Sufficient

Statement 2

Not sufficient

Answer is A

Just my 2c

Cheers
J
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Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 20 Mar 2014, 04:09
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jlgdr wrote:
Aleehsgonji wrote:
If x, y and z are integers and xy + z is an odd integer, is x an even integer?

(1) xy + xz is an even integer
(2) y + xz is an odd integer



Odd/Even questions can be usually solved quite easily if one tries some operations with the statements

We want to know if x is even integer

We are given that xy+z is odd

Statement 1

xq + xz is even

Subtracting

z(x+1) is odd

Therefore, x+1 should be odd and x should be even


Sufficient

Statement 2

Not sufficient

Answer is A

Just my 2c

Cheers
J



I am not clear with the red part.
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Re: DS - Is x even? [#permalink] New post 29 Jul 2009, 03:00
great explanation bigoyal...+1 kudos from my side...:)
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Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 19 Mar 2014, 18:41
Given condition:
xy + z = odd
implies either xy = odd (x =odd and y = odd) and z = even or xy = even (x or y can be odd and even respectively and vice versa) and z = odd

condition 1:

xy + xz = even; Implies x(y+z) = even which again implies the following:

i) x even and y+z = odd - where again y or z can be odd and even respectively and vice versa
ii) x odd and y +z = even - where again y and z has to be both odd or both even

inconclusive

condition 2:

y + xz = odd

again inconclusive
1 + 2:
Add xy + z + y + xz = odd + odd
implies: (x + 1)(y+z) = even
and x (y+z) is also even according to 2.. so y + z = even <y and z both even or y + z both odd>, x can be odd or even
but by 1 xy + z = odd which means y and z both odd, so x is even.

C is the answer
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Re: If x, y and z are integers and xy + z is an odd integer, is [#permalink] New post 21 Mar 2014, 19:46
Odd(O) Even (E)
given:
x,y,z integers
xy+z=O
so only the following scenarios can fulfill the constraints
a) EO+O
b) EE+O
c) OE+O
d) OO+E

question:
x=E?

1) x(y+z)=E
i. (E)(O+O) --> fits scenario a -->yes, x can be even
ii. (O)(E+E) --> n/a - doesn't fit any scenarios
iii. (O)(O+O) --> n/a - doesn't fit any scenarios

stop testing, x can't be odd, sufficient

2) y+xz = O
i. E+(O)(O) --> fits scenario a -->yes, x can be even
ii. O+(E)(E) --> n/a - doesn't fit any scenarios
iii. O+(O)(E) --> fits scenario d -->no, x can be odd

stop testing, x can be either even or odd

insufficient

A
Re: If x, y and z are integers and xy + z is an odd integer, is   [#permalink] 21 Mar 2014, 19:46
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