must be true qs

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 43
Joined: Sun Apr 06, 2014 10:50 am
Thanked: 1 times
Followed by:1 members

must be true qs

by DevB » Sat Jul 26, 2014 12:16 pm
If xy + z = x(y + z), which of the following must be true:

1. x = 0 and z = 0
2. x = 1 and y = 1
3. y = 1 and z = 0
4. x = 1 or y = 0
5. x = 1 or z = 0

Qs is from GMAT Prep. Please help in answering.

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Jul 26, 2014 12:40 pm
DevB wrote:If xy + z = x(y + z), which of the following must be true:

1. x = 0 and z = 0
2. x = 1 and y = 1
3. y = 1 and z = 0
4. x = 1 or y = 0
5. x = 1 or z = 0

Qs is from GMAT Prep. Please help in answering.
xy + z = x(y +z)

xy + z = xy + xz

z = xz

z - xz = 0

z(1 - x) = 0.

For the resulting equation to be valid, either z=0 or x=1.

The correct answer is E.
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

User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Sat Jul 26, 2014 12:40 pm
DevB wrote:If xy + z = x(y + z), which of the following must be true:

1. x = 0 and z = 0
2. x = 1 and y = 1
3. y = 1 and z = 0
4. x = 1 or y = 0
5. x = 1 or z = 0

Qs is from GMAT Prep. Please help in answering.
Given, xy + z = x(y + z),
i.e. xy + z = xy + xz
i.e. z = xz
i.e. xz - z = 0
i.e. z(x - 1) = 0
i.e. either z = 0 or x = 1

Answer: Option E
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

User avatar
Junior | Next Rank: 30 Posts
Posts: 21
Joined: Mon Jun 22, 2009 9:43 pm
Location: India
Thanked: 3 times
GMAT Score:770

by perwinsharma » Sat Jul 26, 2014 10:29 pm
If xy + z = x(y + z), which of the following must be true:

1. x = 0 and z = 0
2. x = 1 and y = 1
3. y = 1 and z = 0
4. x = 1 or y = 0
5. x = 1 or z = 0
[/quote]

We open the brackets first as we can see that it will give us a similar term as on the left hand side
xy + z = xy + xz
=> z = xz
=> z - xz = 0
=> z(1 - x) = 0
=> either z = 0 or 1 - x = 0
=> either z = 0 or x = 1

The answer is (E).
Praveen Sharma
Wizius Careers
Gurgaon
India
https://www.facebook.com/wiziuscareergmat/

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sun Jul 27, 2014 7:40 am
IMPORTANT: Some students make the mistake taking the x- and y-values in the answer choices and PLUGGING them into the given equation.
Students who do this are actually solving the question "Which of the following could be true?"
So, for example, if we plug in x = 0 and z = 0 (from answer choice A), we see that these values work. We'll also see that the values from answer choices B, C and E work as well, so it's obvious that PLUGGING in the answer choices doesn't work.

To answer the question, "Which of the following must be true?," we must follow the steps that the posters used above.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image