Data Sufficiency

dddanny2006 wrote: If xy ≠ 0, is x > y?

(1)4x = 3y
(2)x = y + 1 or x = y

Let's answer the question step by step.

Target question: Is x > y?

Given: xy ≠ 0. In other words, x ≠ 0 and y ≠ 0

Statement 1: 4x = 3y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 3 and y = 4, in which case x < y
Case b: x = -3 and y = -4, in which case x > y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = y + 1 or x = y
Let's examine each possibility.
case a: if x = y + 1, then x is 1 greater than y, which means x is greater than y
case b: if x = y, then x is not greater than y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are two cases to consider:
case a: 4x = 3y and x = y + 1. If we solve this, we get x = -3 and y = -4, in which case x is greater than y
case b: 4x = 3y and x = y. If we solve this, we get x = 0 and y = 0. This solution does not satisfy the given condition that x and y ≠ 0. So, we can ELIMINATE CASE B as a possibility.
This leaves only case a as a possible scenario, in which case x is greater than y

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent