chendawg wrote:If x, y, and z are positive integers, is x - y odd ?

(1) x = z²
(2) y = (z - 1)²

Whether (x - y) is odd or even, depends upon both x and y.

Statement 1: Not sufficient as no information about y.

Statement 2: Not sufficient as no information about x.

1 & 2 Together: (x - y) = z² - (z - 1)² = z² - (z² -2z + 1) = (2z - 1) = Even - 1 = odd

Sufficient

The correct answer is C.

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