Stumped

[muzali]

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

Correct OA=A

Would appreciate a detailed solution.

[cramya]

Stumped would be right! Can u please confirm OA and source?

My approach

I am getting [spoiler]A)[/spoiler] (may be I am missing something and doing something incorrect in Stmt I ) but the OA is different

Given:- xy+z is an odd integer

Stmt I

xy+xz is an even integer

even integer - odd integer = odd integer
(xy+xz) - (xy+z) = odd integer
xy+xz-xy-z =odd
xz-z = odd
z(x-1) = odd

Both z and x-1 have to be odd

x-1 is odd then x has to be even

Definite YES

SUFF


Given: xy+z is an odd integer 1)
Stmt II

y+xz is an odd integer 2)
odd integer + odd intger = even integer

xy+z +y+xz = even
x(y+z) + y + z = even 3)
x->odd y->odd z->even

x-> even y->odd z->odd

2 possibilites still 1), 2) and 3) hold good

INSUFF

[muzali]

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

OA=A

Would appreciate a detailed solution.

[muzali]

Cramya, you are right. I had unwittingly put the incorrect OA. Source is GMATPrep.

[cramya]

Cramya, you are right. I had unwittingly put the incorrect OA. Source is GMATPrep.

No problem, Muzali!

IMO it could have got a little trickier and time consumung if u looked at it as x,y,z seperately without manipulations.

I am sure there are other better/equally good approaches and mine being just one of them.

Good question!

[ronniecoleman]

IMO A

Cramya..
buddy nice explanation!!!

[muzali]

Totally agree, very methodical approach.

[ravikirancheni]

Cramya,
Just amazed by your comprehending skills....
How on the earth could you get the idea of solving this monster ...kudos !!!

[pbanavara]

Stumped would be right! Can u please confirm OA and source?

My approach

I am getting [spoiler]A)[/spoiler] (may be I am missing something and doing something incorrect in Stmt I ) but the OA is different

Given:- xy+z is an odd integer

Stmt I

xy+xz is an even integer

even integer - odd integer = odd integer
(xy+xz) - (xy+z) = odd integer
xy+xz-xy-z =odd
xz-z = odd
z(x-1) = odd

Both z and x-1 have to be odd

x-1 is odd then x has to be even

Definite YES

SUFF


Given: xy+z is an odd integer 1)
Stmt II

y+xz is an odd integer 2)
odd integer + odd intger = even integer

xy+z +y+xz = even
x(y+z) + y + z = even 3)
x->odd y->odd z->even

x-> even y->odd z->odd

2 possibilites still 1), 2) and 3) hold good

INSUFF

Bingo same approach same answer.