BTGModeratorVI wrote: ↑

Thu Aug 27, 2020 12:18 pm

If x, y, and z are positive integers, is x+y divisible by 2?

1) x+z is divisible by 2
2) y+z is divisible by 2

Answer: C
Source: Math Revolution

Target question: Is x+y divisible by 2?

Statement 1: x+z is divisible by 2
No information about y.
Statement 1 is NOT SUFFICIENT

Statement 2: y+z is divisible by 2
No information about x.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1: If x+z is divisible by 2, then we can say that x+z = 2k for some integer k
Statement 2: If y+z is divisible by 2, then we can say that y+z = 2j for some integer j

Now take the two red equations add ADD them to get: x + y + 2z = 2k + 2j
Subtract 2z from both sides to get: x + y = 2k + 2j - 2z
Factor right side: x + y = 2(k + j - z)
This tells us that x+y is DEFINITELY divisible by 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent