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Target question: Is x an even integer?If x,y and z are integers and xy+z is an odd number, is x an even integer?
1) xy + xz is an even integer.
2) y + xz is an odd integer.
Given: xy+z is an odd number
Statement 1: xy+xz is an even integer.
Notice that statement 1 has an xy term, and the given information also has an xy term. We can use this to our advantage.
We know the property: Even - Odd = Odd
So, we can conclude that (xy + xz) - (xy + z) is odd
Simplify to get: xz - z is odd
Factor: z(x - 1) is odd
IMPORTANT: if the product of two integers is odd, then both of those integers must be odd as well.
So, z must be odd
And (x-1) must be odd, which means x must be even
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: y + xz is an odd integer.
There are several conflicting sets of values that meet this condition. Here are two:
Case a: x = 0, y = 1 and z = 1, in which case x is even
Case b: x = 1, y = 2 and z = 1, in which case x is odd
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
