For xy to be even, y has to be either 0, 2, 4, 6 or 8 (basically y has to be even)
1) Given x is even doesn't help us draw any conclusions for value of y.
For eg: x=2. y=3 results in 23 which is odd
Or x=2 and y=4 results in 24 which is even
So, this statement is insufficient
2) GCF of x and y is 1 goes to show either of the following 3 cases: 1) One of the two x & y is odd and other is even, 2) x and y are distinct prime numbers, 3) at least one of the numbers x and y is 1.
Going by any of the cases we can prove that we cannot draw any conclusive inferences for value of y.
Hence, this statement is insufficientCombining 1 & 2, clearly x is even. Let's try putting this constraint on three cases we have mentioned in statement 2
Case 1: x is even. So, clearly y is odd.
Thus, xy is oddCase 2: x is even and prime so x=2. So, clearly y is any other prime number other than 2. All prime numbers except 2 are odd.
Hence xy is oddCase 3: x is even so x cannot be 1. Hence, y=1.
Hence xy is oddThis shows that answer is C
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