must be true qs

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DevB: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Sun Apr 06, 2014 10:50 amFollowed by: 1 member; Thanked: 1 times

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.

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Source: Beat The GMAT — Problem Solving | Sat Jul 26, 2014 12:16 pm

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 » 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.

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

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

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perwinsharma: 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/

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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 » 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

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