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

Expert replies

BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Tue Dec 05, 2017 11:35 am

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.

Like this post

Source: Beat The GMAT — Problem Solving | Tue Dec 05, 2017 11:35 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

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!

Save $100 on any VP online course!

Like this post

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

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.
I am available if you'd like any follow up.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8139; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review