OA: C ?

cans wrote:X,Y,W and Z are all integers
X-Y-Z is even and Y-Z-W is odd. If X is even, what must be true?
a)Y-Z must be odd
b)W must be even
c)W must be odd
d)Z must be odd
e) Y must be even
OA later

Ans is C.
if X is even then Y and Z both are either odd or even.(First condition X-Y-Z is even)
and hence W should be odd (Second condition Y-Z-W is odd)

cans wrote:X,Y,W and Z are all integers
X-Y-Z is even and Y-Z-W is odd. If X is even, what must be true?
a)Y-Z must be odd
b)W must be even
c)W must be odd
d)Z must be odd
e) Y must be even
OA later

x-(y+z) is even; also x is even;
therefore y+z must be even because Even-Even=Even;
y+z will be even if y is even and z is even or if y is odd and z is odd,-----1)

Y-Z-W is odd; y-(z+w) is odd, from 1) we have that y,z both will either be even or odd,
y,z even
Even-(Even+odd)= Even-odd=odd,
ie w is odd for both y,z to be even,
when y,z are odd
odd-(odd+odd)= odd-even=odd;
ie w is odd for both y,z to be odd,
hence w must be odd, C

OA C