arjunshn wrote:If X, Y and Z are non-zero numbers, is X2- Y3- 2Z odd?
(1) X and Y are odd
(2) Z is even

(1) If X = 1, Y = 1, Z = 2, then X² - Y^3 - 2Z = 1 - 1 - 4 = -4, which is even.
If X = 1, Y = 1, Z = 3/2, then X² - Y^3 - 2Z = 1 - 1 - 3 = -3, which is odd.
No unique answer, which implies X² - Y^3 - 2Z may or may not be odd.
So, (1) is NOT SUFFICIENT.

(2) If X = 1, Y = 2, Z = 2, then X² - Y^3 - 2Z = 1 - 8 - 4 = -11, which is odd.
If X = 1, Y = 1, Z = 2, then X² - Y^3 - 2Z = 1 - 1 - 4 = -4, which is even.
No unique answer, which implies X² - Y^3 - 2Z may or may not be odd.
So, (2) is NOT SUFFICIENT.

Combining (1) and (2), X, Y are odd and Z is even.
So, X² - Y^3 - 2Z = (ODD)² - (ODD)^3 - 2(EVEN) = ODD - ODD - EVEN = EVEN
Hence, X² - Y^3 - 2Z is even.

The correct answer is C.

arjunshn wrote:in the first option it is 2z and when you are taking z=3 it has to be 6..hence even..a sufficient

Thanks for pointing, that was a typo. In statement 1, it is Z = 3/2. I have edited the previous post.

arjunshn wrote:it is X^2-y^3-2z and when you put x=1, y=1 and z=3..it is 1-1-6=-6 even..
i think the answer is A

We are given that X and Y are odd, but Z is a non-zero number, which means Z can take fractional values as well.

arjunshn wrote:thank you..i forgot that its not mentioned they are integers..

Thanks and Welcome!