If x, y, and z are positive integers, is x-y odd?
1) x = z²
2) y = (z-1)²
Here's an algebraic approach:
Target question: Is x-y odd?
Given: x, y, and z are positive integers
Statement 1: x = z²
There's no information about y, so there's no way to determine
whether or not x-y is odd.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y = (z-1)²
There's no information about x, so there's no way to determine
whether or not x-y is odd.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1: x = z²
Statement 2: y = (z-1)²
Subtract equations to get: x-y = z² - (z-1)²
Expand to get: x-y = z² - [z² - 2z + 1]
Simplify to get: x-y = 2z - 1
Since z is a positive integer, we know that 2z is EVEN, which means 2z-1 is ODD.
If 2z-1 is ODD, we can conclude that
x-y is definitely ODD
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
