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Re: Odds and Evens.. [#permalink]
04 Apr 2006, 13:22

lhotseface wrote:

If x,y and z are integers and xy + z is odd, is x even ?

1. xy + xz is even 2. y + xz is odd

I think it is A.

Given
xy+z = Odd -(I)
xy+xz = Even -(II)

Subtract (I) from (II)

z(x-1) = Even-Odd = Odd
=> z(x-1) must be Odd
=> both z and x-1 are odd.

If x-1 is Odd => x is Even

A it is! _________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

i think its C ... ywilfred is right from the stem z could be anything even or odd i f thats the case and x(y+z) is even ... x could be even or odd ... you need II) also ... good job

I posted answer C. I have read giddi's reply but I do not understand OAs answer. I don't understand if we use both equations to reach a solution, how come answer is A. Any help is appreciated.

I posted answer C. I have read giddi's reply but I do not understand OAs answer. I don't understand if we use both equations to reach a solution, how come answer is A. Any help is appreciated.

May be you could put some values and check the equations.
Remember:

O+/-E = O
O+/-O = E
E+/-E = E

and

O*O = O
O*E = E
E*E = E

if X is even and we are given that X-Y is odd, then Y has be odd.
Eg: If 10 - Y = ODD (say 3), then Y has to be ODD (= 7 in this eg).. HTH _________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

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