BTGModeratorVI wrote: ↑Sat Jun 27, 2020 6:47 am
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
