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Practice Exam 1 - GMAT Prep - Algebra

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by lucas211 » Thu May 26, 2016 6:36 am
Hello BTG

Would like to know if my approach to the following question is correct:

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1) we multiply out the right side to get the equation: xy+z = xy + xz
2) we subtract xy from both sides to get z = xz
3) from here we see, that z = xz, either x have to be one or z have to be "0".

Is this the correct approach?

Thanks in advance :-)
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by Brent@GMATPrepNow » Thu May 26, 2016 6:49 am
If xy+z = x(y+z) which of the following must be true?

A. x = 0 and Z = 0
B. x = 1 and y = 1
B. y = 1 and z = 0
D. x = 1 or y = 0
E. x = 1 or Z = 0
The key word here is must.
So, for example, consider answer choice A. While it's possible that x = 0 and z = 0, it need not be the case.
For example, x=1, y=1 and z=1 is a solution to the equation. So, this eliminates A.

The solution . . .
Given: xy+z = x(y+z)
Expand: xy+z = xy + xz
Subtract xy from both sides: z = xz
Rearrange: xz - z = 0
Factor: z(x-1) = 0

This tells us that z = 0 or x = 1
Answer: E

Cheers,
Brent
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by [email protected] » Thu May 26, 2016 9:15 am
Hi lucas211,

There's a discussion of this question here:

https://www.beatthegmat.com/must-be-true-qs-t278003.html

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by Matt@VeritasPrep » Thu May 26, 2016 2:28 pm
Your approach is dead on! Great job.
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by danielle07 » Sun Sep 03, 2017 1:38 pm
Hi, How did you come up for the word "must"? Thanks
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by ceilidh.erickson » Mon Sep 04, 2017 8:19 am
danielle07 wrote:Hi, How did you come up for the word "must"? Thanks
It's written in the question: "which of the following MUST be true?" With such a question, we can eliminate any answer that does not HAVE to be true.
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by Admin1 » Mon Sep 04, 2017 10:13 am
xy + z = x (y + z)
xy + z = xy + xz (Distributive property)
xy + z - xy = xy + xz - xy (Subtracting xy on both sides)
z = xz (Simplify)
z - xz = xz - xz (Subtracting xz on both sides)
z - xz = 0 (Simplify)
z (1 - x) = 0 (Factor out z)
Either z = 0 or
1 - x = 0 => x = 1
Therefore, x = 1 or z = 0.
Option E must be correct.
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Re: Practice Exam 1 - GMAT Prep - Algebra

by Scott@TargetTestPrep » Sat Feb 08, 2020 12:41 pm
lucas211 wrote: ↑
Thu May 26, 2016 6:36 am
 Hello BTG

Would like to know if my approach to the following question is correct:

Image


1) we multiply out the right side to get the equation: xy+z = xy + xz
2) we subtract xy from both sides to get z = xz
3) from here we see, that z = xz, either x have to be one or z have to be "0".

Is this the correct approach?

Thanks in advance :-)
Simplifying, we have:

xy + z = xy + xz

z = xz

xz - z = 0

z(x - 1) = 0

z = 0 or x = 1

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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