Hello BTG
Would like to know if my approach to the following question is correct:
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
Practice Exam 1 - GMAT Prep - Algebra
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- 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
The key word here is must.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
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
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi lucas211,
There's a discussion of this question here:
https://www.beatthegmat.com/must-be-true-qs-t278003.html
GMAT assassins aren't born, they're made,
Rich
There's a discussion of this question here:
https://www.beatthegmat.com/must-be-true-qs-t278003.html
GMAT assassins aren't born, they're made,
Rich
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
-
- Senior | Next Rank: 100 Posts
- Posts: 40
- Joined: Wed Aug 30, 2017 6:48 pm
GMAT/MBA Expert
- ceilidh.erickson
- GMAT Instructor
- Posts: 2095
- Joined: Tue Dec 04, 2012 3:22 pm
- Thanked: 1443 times
- Followed by:247 members
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.danielle07 wrote:Hi, How did you come up for the word "must"? Thanks
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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.
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.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Simplifying, we have:lucas211 wrote: ↑Thu May 26, 2016 6:36 amHello BTG
Would like to know if my approach to the following question is correct:
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
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]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews