Question Bank- Equations "Catching Z"

[guest mk]

I understand most of the explanation, bust I having trouble with a particular part. The answer for statement 2 I understand, but not statement 1. Here it is:

Since the question asks for the value of the positive integer z, it is a good idea to isolate z in the given equation. Rearranging (2xy + z = 9) yields (z = 9 - 2xy), so one rephrase of this question is "what is the value of xy?

(1) SUFFICIENT: This statement can be manipulated by factoring the variable z.

z(xy - z) = 0

This equation indicates that either z or the expression (xy - z) must equal zero. Given that z is a positive integer, it follows that

xy - z = 0
xy = z

Note that this partially answers both the original question and the rephrased question; we know that z = 9 - 2xy, and that z = xy. By substituting z for xy in the original equation, we can solve for z:

2xy + z = 9
2z + z = 9
3z = 9
z = 3



My question is if you factoe into z(xy-z) = 0 does not z=0 and xy-z=0 as factors? What happened to the factored z, there is no mention of what happened to it.

[guest mk]

If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz - z2 = 0

(2) x + y - 3z = -5

Since the question asks for the value of the positive integer z, it is a good idea to isolate z in the given equation. Rearranging (2xy + z = 9) yields (z = 9 - 2xy), so one rephrase of this question is "what is the value of xy?

(1) SUFFICIENT: This statement can be manipulated by factoring the variable z.

z(xy - z) = 0

This equation indicates that either z or the expression (xy - z) must equal zero. Given that z is a positive integer, it follows that

xy - z = 0
xy = z

Note that this partially answers both the original question and the rephrased question; we know that z = 9 - 2xy, and that z = xy. By substituting z for xy in the original equation, we can solve for z:

2xy + z = 9
2z + z = 9
3z = 9
z = 3

(2) INSUFFICIENT: This equation cannot be manipulated or combined with the original equation to solve for any of the variables.

The correct answer is A.

[StaceyKoprince]

The explanation for statement 1 includes these words:

"This equation indicates that either z or the expression (xy - z) must equal zero. Given that z is a positive integer, it follows that

xy - z = 0 "

The explanation first indicates that one of the two must equal zero, but then references the fact that the question itself tells us that z is a positive integer. If z is a positive integer, it cannot equal zero. Therefore, the other bit (xy-z) must equal zero. If the question hadn't told us z was positive, then, yes, we would have had to test both possibiltiies.