If 3x + 2y = -2z, what is x?

Expert replies

Previous Topic Next Topic

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Sep 06, 2018 3:13 am

Timer

00:00

Answers

Stats

Difficulty—

If 3x + 2y = -2z, what is x?

(1) x - y - z = 10

(2) x + y + z = -2

OA D

Source: Veritas Prep

Like this post

Source: Beat The GMAT — Data Sufficiency | Thu Sep 06, 2018 3:13 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Sep 06, 2018 4:38 am

BTGmoderatorDC wrote:If 3x + 2y = -2z, what is x?

(1) x - y - z = 10

(2) x + y + z = -2

\[? = x\]
\[3x + 2y = - 2z\,\,\,\, \Rightarrow \,\,\,\,3x = - 2\left( {y + z} \right)\,\,\,\,\,\,\left( * \right)\]
\[\left( 1 \right)\,\,\,\,x - \left( {y + z} \right) = 10\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,2} \,\,\,\,\,\,2x - 2\left( {y + z} \right) = 20\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,2x + 3x = 20\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x\,\,\,{\text{unique}}\]
\[\left( 2 \right)\,\,\,x + \left( {y + z} \right) = - 2\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,2} \,\,\,\,\,\,2x + 2\left( {y + z} \right) = - 4\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,2x - 3x = - 4\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,x\,\,\,{\text{unique}}\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Like this post

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 » Thu Sep 06, 2018 5:15 am

BTGmoderatorDC wrote:If 3x + 2y = -2z, what is x?

(1) x - y - z = 10

(2) x + y + z = -2

Prompt: 3x + 2y + 2z = 0

Statement 1:
Multiplying by 2, we get:
2x - 2y - 2z = 20
Adding together 3x+2y+2z=0 and 2x-2y-2z=20, we get:
(3x+2y+2z) + (2x-2y-2z) = 0 + 20
5x=20
x=4.
SUFFICIENT.

Statement 2:
Multiplying by 2, we get:
2x + 2y + 2z = -4
Subtracting 2x+2y+2z = -4 from 3x+2y+2z=0, we get:
(3x+2y+2z) - (2x+2y+2z) = 0 - (-4)
x=4.
SUFFICIENT.

The correct answer is D.

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

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Sep 06, 2018 5:21 am

BTGmoderatorDC wrote:If 3x + 2y = -2z, what is x?

(1) x - y - z = 10
(2) x + y + z = -2

Target question: What is the value of x?

Given: 3x + 2y = -2z
Notice that the two statements have the variables all on the left side of the equation. So, let's rearrange our given equation to look the same.
Take: 3x + 2y = -2z
Add 2z to both sides to get: 3x + 2y + 2z = 0

Statement 1: x - y - z = 10
Take this equation and multiply both sides by 2 to get the EQUIVALENT equation 2x - 2y - 2z = 20
So, we have:
2x - 2y - 2z = 20
3x + 2y + 2z = 0

Add the equations to get: 5x = 20
Solve: x = 4
So, the answer to the target question is x = 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x + y + z = -2
Take this equation and multiply both sides by 2 to get the EQUIVALENT equation 2x + 2y + 2z = -4
So, we have:
2x + 2y + 2z = -4
3x + 2y + 2z = 0

Subtract the bottom equation from the top equation to get:
-x = -4
Solve: x = 4
So, the answer to the target question is x = 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 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