divisibility

Malolo355 wrote:"If x, y and z are positive integers, is the product xyz a multiple of 3?

1) The sum of x,y and z is a multiple of 3
2) x, y, and z are consecutive integers

Target question: Is the product xyz a multiple of 3?

Statement 1: (x + y + z) is a multiple of 3
There are several values of x, y and z that satisfy this condition. Here are two:
Case a: x = 3, y = 3 and z = 3 (the SUM is 9, which is a multiple of 3). In this case, the product xyz IS a multiple of 3
Case b: x = 2, y = 2 and z = 2 (the SUM is 6, which is a multiple of 3). In this case, the product xyz is NOT a multiple of 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x, y, and z are consecutive integers
There's a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2, ... ,2, and 1
So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1

Statement 2 tells us that we have 3 consecutive integers, so the product xyz MUST be divisible by 3.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent