What is the value of x - y ?

[BTGModeratorVI]

What is the value of x - y ?

(1) 3x - z = 42 and y - z = 5.

(2) x^2 - xy - xz + yz = 84 and x - z = 12.

Source: Kaplan
Answer: B

[Brent@GMATPrepNow]

What is the value of x - y ?

(1) 3x - z = 42 and y - z = 5.

(2) x^2 - xy - xz + yz = 84 and x - z = 12.

Source: Kaplan
Answer: B

Target question: What is the value of x - y ?

Statement 1: 3x - z = 42 and y - z = 5.
Take:
3x - z = 42
y - z = 5.

Subtract the bottom equation from top equation to get: 3x - y = 37
This doesn't really help us much since we want to know the value of x - y (not 3x - y)
This suggests to me that statement 1 is not sufficient but let's be certain of this by testing some values.
There are several values of x, y and z that satisfy statement 1. Here are two:
Case a: x = 14, y = 5 and z = 0. In this case, the answer to the target question is x - y = 14 - 5 = 9
Case b: x = 15, y = 8 and z = 3. In this case, the answer to the target question is x - y = 15 - 8 = 7
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x² - xy - xz + yz = 84 and x - z = 12
We can factor the first equation in parts
Take: x² - xy - xz + yz = 84
Factor as follows: x(x - y) - z(x - y) = 84
Simplify to get: (x - z)(x - y) = 84

Since we also know that x - z = 12, we get: (12)(x - y) = 84
Divide both sides by 12 to get: x - y = 7
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent