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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.
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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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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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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).
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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,
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