Data Sufficiency

Hi EricKryk,

This DS question is perfect for either TESTing Values or using Number Properties. I'll show you how knowing Number Properties can make this question a pretty easy pick-up.

We're told that X, Y and Z are POSITIVE INTEGERS. We're asked "is X - Y ODD?" This is a YES/NO question. Before we deal with the two Facts, here is something to keep in mind about odds and evens as they relate to this question:

Even - Even = Even (answer is NO)
Odd - Odd = Even (answer is NO)
Even - Odd = Odd (answer is YES)
Odd - Even = Odd (answer is YES)

Fact 1: X = Z^2

This tells us NOTHING about Y, so there's no way to answer the question. However, it does tell us this:

If Z = Odd, then X = Odd
If Z = Even, then X = Even

Fact 1 is INSUFFICIENT

Fact 2: Y = (Z-1)^2

This tells us NOTHING about X, so there's no way to answer the question. It does tell us this though:

If Z = Odd, then Y = Even
If Z = Even, then Y = Odd

Fact 2 is INSUFFICIENT

Combined, we have these two possibilities:

If Z = Odd, then X = Odd and Y = Even (the answer to the question is YES).
If Z = Even, then X = Even and Y = Odd (the answer to the question is YES).
The answer is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

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

1) x = z²
2) y = (z-1)²

Patrick's and Rich's solutions (testing cases) are great.
Here's a different (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