xy + z = x(y + z), which of the following must be true?

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cgc: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Tue Jan 12, 2010 10:37 am; Thanked: 1 times

by cgc » Wed Jan 20, 2010 10:59 am

xy + z = x(y + z), which of the following must be true?

a. x=0, z=0
b. x=1, y=1
c. y=1, z=0
d. x=1, y=0
e. x=1, z=0

why is the answer e not a?

please explain. thanks,

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Source: Beat The GMAT — Problem Solving | Wed Jan 20, 2010 10:59 am

aakar: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Sep 02, 2009 6:06 am; Thanked: 1 times

by aakar » Wed Jan 20, 2010 11:54 am

Personally I think simplifying the expression is the easiest way to solve this:

xy + z = xy + xz
cross out the xy and bring the z terms to one side:
z - xz = 0

z(1-x) = 0

z = 0 and 1-x = 0

1-x = 0 -> -x = -1 -> x = 1

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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 » Wed Jan 20, 2010 5:50 pm

cgc wrote:xy + z = x(y + z), which of the following must be true?

a. x=0, z=0
b. x=1, y=1
c. y=1, z=0
d. x=1, y=0
e. x=1, z=0

why is the answer e not a?

please explain. thanks,

I have a feeling that you took the values of x and z in answer choice A and plugged them into the equation.
This is an okay strategy, but you are really solving the question "Which of the following could be true?"
You'll see that, if you plug in the values from B, C and E, they will work as well.

To anwer the question, "Which of the following must be true?," follow the steps that aakar used.

Brent Hanneson - Creator of GMATPrepNow.com

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cgc: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Tue Jan 12, 2010 10:37 am; Thanked: 1 times

by cgc » Wed Jan 20, 2010 10:22 pm

So if i understand correctly, i solve the equation by expanding/factoring to get "zero" on one side. Same as solving a quadratic equation. Correct?

This is the way to determine what MUST be true for the remaining variables in an equation.

Thanks,

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Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members; Location: Toronto; Thanked: 539 times; GMAT Score:800

by Testluv » Wed Jan 20, 2010 11:35 pm

I discussed this question here, and gave some associated tips:

https://www.beatthegmat.com/gmat-prep-i- ... tml#211948

Note that you could have picked numbers, but you would have to check ALL answer choices, eliminating the impossible choices. This would leave you with A and E, at which point you would have to ask which must be true, which again, you can pick numbers to see.

But, definitely the best approach is algebraic here.

Kaplan Teacher in Toronto

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