(1) X = -Y

=> XYZ = - Y x Y x Z

this gives us a negative number, and negative numbers cannot be prime. Hence, sufficient to answer the question

(2) Z = 1

XYZ = XY x 1

A prime number is one with 2 factors, one of them being 1 and the other being the number itself

In this case, it has 3 factors, 1, X and Y.
If X = Y = 1, then the answer is 1 which is not a prime number, and for any other values of X and Y, the number has more than 2 factors. so it cannot be prime. Hence, sufficient to answer the question

Answer should be (D), can you give the OA please?

to me the answer is C, but not sure
(1) x=-y,
(-y)(y)*z=-y^2*z, y=1, z=2, -1*2=-2 not prime
y=1, z=-2, -1*-2=2 prime
so 1 st not sufficient
(2)z=1, not sufficient as x,y not mentioned
both
-y^2*1 it can`t be prime as possible factors 1,-1 y
so my pick for C

clock60 wrote:to me the answer is C, but not sure
(1) x=-y,
(-y)(y)*z=-y^2*z, y=1, z=2, -1*2=-2 not prime
y=1, z=-2, -1*-2=2 prime
so 1 st not sufficient
(2)z=1, not sufficient as x,y not mentioned
both
-y^2*1 it can`t be prime as possible factors 1,-1 y
so my pick for C

Ah, you are right clock60.

In my reasoning for (1), I missed out on the fact that Z could also be negative...

So yes, (1) is not sufficient.

However, with (2), even if X and Y are not mentioned, we still know that the number has 3 factors (1, X and Y), so it cant be prime... right?

not completely agree z=1, (given) x=1, y=2 1*1*2=2 prime
z=1, x=2, y=2 1*2*2 =not prime

clock60 wrote:not completely agree z=1, (given) x=1, y=2 1*1*2=2 prime
z=1, x=2, y=2 1*2*2 =not prime

Great, thanks for pointing that out (god I hate DS! )

kmittal82 wrote:

clock60 wrote:not completely agree z=1, (given) x=1, y=2 1*1*2=2 prime
z=1, x=2, y=2 1*2*2 =not prime

Great, thanks for pointing that out (god I hate DS! )

i hate it even greater!

right answer is C.

Thanks guys!