Given: x = 2y
Target question: What is the value of xy?
Statement 1: x > y
There are several values of x and y that satisfy statement 1 (and the given equation, x = 2y). Here are two:
Case a: x = 2 and y = 1. In this case, the answer to the target question is xy = (2)(1) = 2
Case b: x = 6 and y = 3. In this case, the answer to the target question is xy = (6)(3) = 18
Since we can't answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3x - 2y = 14
When we combine this equation with the given equation, x = 2y, we see that we have a system of 2 different linear equations with 2 variables.
This means we COULD solve the system for x and y, which means we COULD determine the value of xy (although we would never waste valuable time on test day performing such calculations)
Since we COULD answer the target question with certainty, statement 2 is SUFFICIENT
Aside: if you want to solve the system of equations for "fun," you'll find that the solution is x = 7 and y = 3.5, which means xy = 24.5
Answer: B
Cheers,
Brent
