All answers are satisfying.. which is correct?

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 58
Joined: Tue May 23, 2006 3:35 pm
Location: Seoul, Korea
Thanked: 2 times
Q:

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

1. x=0 & z = 0
2. x=1 & y=1
3. y=1 & z=0
4. x=1 OR y=0
5. x=1 OR z=0

I find all of the above to be true. Unfortunately I did not note down the answer choices given.. can anybody help solving this problem?

thanks,
Nikhil

Senior | Next Rank: 100 Posts
Posts: 34
Joined: Sun Sep 03, 2006 6:00 am

by gamemaster » Thu Nov 16, 2006 6:36 am
note that they say MUST true, not possibly true

and because we get:

xy + z = xy + xz

xz = z

only 5. must be true

Senior | Next Rank: 100 Posts
Posts: 62
Joined: Wed Oct 18, 2006 1:49 pm
Thanked: 1 times

by gmat_enthus » Mon Nov 20, 2006 7:09 am
Agree , only 5 satisfies.

Moderator
Posts: 772
Joined: Wed Aug 30, 2017 6:29 pm
Followed by:6 members

by BTGmoderatorRO » Sun Sep 03, 2017 6:39 am
To solve this question, we will collect the like terms
xy+z = x(y+z)
xy + z = xy + xz
xy - xy +z - xz = 0
z - xz = 0
z(1-x)= 0
from here, we can conclude that z=0 and (1-x)=0
1-x=0
x=1

Hence, x=1 or z=0 which is option 5

GMAT/MBA Expert

User avatar
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

by Brent@GMATPrepNow » Sun Sep 03, 2017 6:46 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
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
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

by [email protected] » Sun Sep 03, 2017 11:47 am
Hi All,

Notice how the answer choices to this question each involve two values and either an "and" or "or" qualifier. We can use those values against the prompt to determine what MUST be true.

To start, many of the answer choices include X=1, so let's see what happens when that 'condition' is met...

IF... X=1

XY + Z = X(Y+Z)
1(Y) + Z = 1(Y+Z)
Y + Z = Y + Z

X=1 certainly appears to be enough, on its own, to make the equation 'balance out' - so we wouldn't necessarily need any other restrictions on the values of Y or Z. There might be some other condition though that would also make the equation balance out, so we should take a good look at Answers D and E.

IF... Y=0

XY + Z = X(Y+Z)
X(0) + Z = X(0+Z)
X + Z = XZ

That isn't necessarily true (in fact, it's almost never true), so we can eliminate Answer D

IF... Z=0

XY + Z = X(Y+Z)
X(Y) + 0 = X(Y+0)
XY = XY

This is also balanced out, so this is another option.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7222
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members
kulksnikhil wrote:
Wed Nov 15, 2006 6:39 pm
Q:

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

1. x=0 & z = 0
2. x=1 & y=1
3. y=1 & z=0
4. x=1 OR y=0
5. x=1 OR z=0

I find all of the above to be true. Unfortunately I did not note down the answer choices given.. can anybody help solving this problem?

thanks,
Nikhil
Simplifying, we have:

xy + z = xy + xz

z = xz

xz - z = 0

z(x - 1) = 0

z = 0 or x = 1

Answer: 5

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage