GMAT "Combos" Strategy is Confusing

[VadimC819]

GMAT says that the strategy for "Algebra Combos" is to solve for the "COMBINATION OF VARIABLES", not for "EACH INDIVIDUAL VARIABLE" and then finding a solution.

Assuming this is statement is true (solving for COMBINATION OF VARIABLES, not INDIVIDUAL), why is answer (E) here wrong and (C) correct? Shouldn't (E) be correct? If you solve for 1 and 2 individually, you can find the value of "x - y" but the combination of both variables is not possible? What am I misunderstanding?

Question:

"What is the value of x - y?"

1) z^2 + 4x + 4 = 0
2) y^2 -4y + 4 = 0

[esledge]

“Combos” can be used; please don’t take that to mean that they must be used on every algebra DS question. There are plenty of problems where the traditional “solve for each variable separately” approach is still ok, or maybe even the only possible way to answer.

Using your example, if it’s what I think it is: (Should it have an x instead of a z in stmt (1)?)

Question [Edited by esledge]

"What is the value of x - y?"

1) x^2 + 4x + 4 = 0
2) y^2 – 4y + 4 = 0

The combo concept doesn’t (easily) apply because the combo “x – y” is not embedded in either statement alone:
(1) solves with traditional factoring to give x = -2. Insufficient because you have x but still need y.
(2) solves with traditional factoring to give y = +2. Insufficient because you have y but still need x.

(C) is the answer, because with the statements together, you can just plug these x and y values in to answer that x – y = -2 – (2) = -4. There’s no need to do any more algebraic manipulations of the statements together.

The combo concept would only be beneficial on a problem like this one that I just wrote below, which is a variation on your example:

What is the value of x – y ?
(1) (x – y)^2 + 8(x – y) = -16
(2) x = y – 4

The answer on this variation is (D). Each statement can be manipulated to isolate x – y on one side of the equation and a single number of the other side of the equation. That’s the combo idea: solve for the x – y combo only when it’s easier or more direct than solving for x and y individually.