Bunuel wrote:
Is \(X*Y*Z\) an even integer?
(1) \(X*Y\) is an even integer.
(2) \(Y*Z\) is an even integer.
It's not sufficient to find whether or not one out of X,Y, or Z is an even integer to confirm that X*Y*Z is an even integer since we don't know whether or not all three numbers are integers. We either need to know that all three numbers are integers and that one of them is even or not, or we need exact values of all three numbers.
(1) Let's assume that X*Y=4 and Z=1.2, so X*Y*Z=4.8, which is not an even integer.
However, if X*Y=4, and Z is any integer, X*Y*Z is also an even integer.
So, we don't get a unique nature of X*Y*Z from this statement.
Thus, insufficient.
(2) Similar working as for (1) applies here.
Thus, insufficient.
From (1) and (2) together, we do not get the required information.
Thus, insufficient.
Therefore, the answer is option E.