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If x-y+z=-1, -x+y+z=1, and x+y-z=-1, then x+y+z=?

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by GMATGuruNY » Tue Dec 05, 2017 12:01 pm
LUANDATO wrote:If x-y+z=-1, -x+y+z=1, and x+y-z=-1, then x+y+z=?

A. -2
B. -1
C. 0
D. 1
E. 2
Adding together the 3 equations, we get:

(x-y+z) + (-x+y+z) + (x+y-z) = (-1) + 1 + (-1)

(x-x+x) + (-y+y+y) + (z+z-z) = -1

x + y + z = -1.

The correct answer is B.
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by Matt@VeritasPrep » Tue Dec 05, 2017 6:14 pm
We could also invoke the Lazy Testwriter Principle: the answers are probably friendly and/or small numbers, so try those.

Let's start with
x-y+z=-1

This looks like -1 - 0 + 0, so let's say x = -1, y = 0, and z = 0. If we plug those into our other two equations:

-x + y + z =>

-(-1) + 0 + 0 => 1

and

x + y - z =>

-1 + 0 - 0 => -1

They both check out, so we're set!
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by EconomistGMATTutor » Wed Dec 06, 2017 12:45 pm
If x-y+z=-1, -x+y+z=1, and x+y-z=-1, then x+y+z=?

A. -2
B. -1
C. 0
D. 1
E. 2

The OA is B.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
Hi LUANDATO,
Let's take a look at your question.

$$x-y+z=-1 ... (i)$$
$$-x+y+z=1... (ii)$$
$$x+y-z=-1 ... (iii)$$

$$x+y+z=?$$

Adding equations (i), (ii) and (iii),
$$\left(x-y+z\right)+\left(-x+y+z\right)+\left(x+y-z\right)=-1+1-1$$
$$x-y+z-x+y+z+x+y-z=0-1$$
$$x-x+x-y+y+y+z+z-z=-1$$
$$x+y+z=-1$$

Therefore, Option B is correct.

Hope it helps.
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by Scott@TargetTestPrep » Fri Oct 11, 2019 2:43 pm
BTGmoderatorLU wrote:If x-y+z=-1, -x+y+z=1, and x+y-z=-1, then x+y+z=?

A. -2
B. -1
C. 0
D. 1
E. 2

The OA is B.
Adding the 3 equations together, we have:

x + y + z = -1 + 1 - 1

x + y + z = -1

Answer: B

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