Answer should be c....
the stem says that x+y+ z is odd , so for the sum of 3 number should odd , two of there should be odd and other should be even OR ,all of 3 numbers should be odd ...
Data 1 ) says |x| = .5 Or : x= .5 , x= -.5 this is clearly insufficient as we don't know any info about y & z , so options A & D are ruled out...
Data 2 ) says that z= 3x , as we don't know neither the value of z nor x , this data is not sufficient alone. notice here if we knew the x is integer , this data would be sufficient . because in the
x+y + z , we would have 4x+ y = an odd number and as 4x is even , so even + y = odd , therefore y has to be odd . But we don't know whether x is integer , so this option is not sufficient .
Combining both data , we have 2 cases ;
case 1 ) : if x=.5 and z=3x , so z= 1.5 and x+z = .5 +1.5 = 2 and , 2+y = odd integer so, y must be an odd integer,
case 2) : if x= -.5 and z= 3x , so z= -1.5 and x+z = -.5 + -1.5 = -2 , and , -2 +y = odd integer so, y must be an odd integer
as we see both cases satisfy that y must be an odd integer , so, the answer to the question is Surly : NO therefore is sufficient and answer is : C....