sukhman wrote:If c and d are integers, is C even?
1) c(d+1) is even
2) (c+2)(d+4) is even

Perhaps I can help.

Target question: Is C even?

Statement 1: c(d+1) is even
Let's test all 4 cases
case a: c is even and d is even: In this case c(d+1) is EVEN
case b: c is even and d is odd: In this case c(d+1) is EVEN
case c: c is odd and d is even: In this case c(d+1) is ODD
case d: c is odd and d is odd : In this case c(d+1) is EVEN
So, cases a, b and d are all possible.
Cases a and b say that C is even
Case d says that C is odd
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: If anyone is interested, we have a free video on testing possible cases for these question types: https://www.gmatprepnow.com/module/gmat- ... ies?id=839

Statement 2: (c+2)(d+4) is even
Let's test all 4 cases
case a: c is even and d is even: In this case (c+2)(d+4) is EVEN
case b: c is even and d is odd: In this case (c+2)(d+4) is EVEN
case c: c is odd and d is even: In this case (c+2)(d+4) is EVEN
case d: c is odd and d is odd : In this case (c+2)(d+4) is ODD
So, cases a, b and c are all possible.
Cases a and b say that C is even
Case c says that C is odd
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that cases a, b and d are all possible.
Statement 2 tells us that cases a, b and c are all possible.
Combined, we know that either case a or case b is possible.
In BOTH of these cases, C is EVEN.
So, C must be EVEN
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent