It is currently 21 Nov 2017, 07:10

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If XY+Z=X(Y+Z), which of the following must be true ?

Author Message
TAGS:

### Hide Tags

Manager
Status: GMAT Preperation
Joined: 04 Feb 2010
Posts: 101

Kudos [?]: 190 [0], given: 15

Concentration: Social Entrepreneurship, Social Entrepreneurship
GPA: 3
WE: Consulting (Insurance)
If XY+Z=X(Y+Z), which of the following must be true ? [#permalink]

### Show Tags

26 Aug 2010, 00:20
7
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

68% (00:49) correct 32% (01:28) wrong based on 323 sessions

### HideShow timer Statistics

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
C) Y=1 AND Z=0
D) X=1 OR Y=0
E) X=1 OR Z=0
[Reveal] Spoiler: OA

Last edited by vanidhar on 26 Aug 2010, 00:26, edited 1 time in total.

Kudos [?]: 190 [0], given: 15

Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 680

Kudos [?]: 169 [0], given: 15

Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Re: confusing Question from GMAT Prep test [#permalink]

### Show Tags

26 Aug 2010, 00:23
You have got the options wrong. Z(X-1) = 0 means Z=0 or X=1.
_________________

Consider kudos, they are good for health

Kudos [?]: 169 [0], given: 15

Manager
Status: GMAT Preperation
Joined: 04 Feb 2010
Posts: 101

Kudos [?]: 190 [0], given: 15

Concentration: Social Entrepreneurship, Social Entrepreneurship
GPA: 3
WE: Consulting (Insurance)
Re: confusing Question from GMAT Prep test [#permalink]

### Show Tags

26 Aug 2010, 00:28
whats the method .. cause for me even x=0 and z=0 made sense when i put them into the eq

Kudos [?]: 190 [0], given: 15

Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 680

Kudos [?]: 169 [1], given: 15

Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Re: confusing Question from GMAT Prep test [#permalink]

### Show Tags

26 Aug 2010, 02:00
1
KUDOS
XY+Z = XY +ZX
Cancel XY
Z=ZX
Z(X-1)=0
so Z=0 or X=1
_________________

Consider kudos, they are good for health

Kudos [?]: 169 [1], given: 15

Math Expert
Joined: 02 Sep 2009
Posts: 42280

Kudos [?]: 132904 [2], given: 12391

Re: confusing Question from GMAT Prep test [#permalink]

### Show Tags

26 Aug 2010, 05:24
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
vanidhar wrote:
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
C) Y=1 AND Z=0
D) X=1 OR Y=0
E) X=1 OR Z=0

$$xy+z=x(y+z)$$ --> $$xy+z=xy+xz$$ --> $$xy$$ cancels out --> $$xz-z=0$$ --> $$z(x-1)=0$$ --> either $$z=0$$ (in this case $$x$$ can take ANY value) OR $$x=1$$ (in this case $$z$$ can take ANY value).

To elaborate more:
As the expression with $$y$$ cancels out, we can say that given expression $$xy+z=x(y+z)$$ does not depend on value of $$y$$. Which means that $$y$$ can take ANY value. So all answer choices which specify the exact value of $$y$$ are wrong.

Next: "AND" in answer choices means that BOTH values must be true, but "OR" in answer choices means that EITHER value must be true.

Hope it helps.
_________________

Kudos [?]: 132904 [2], given: 12391

Non-Human User
Joined: 09 Sep 2013
Posts: 15579

Kudos [?]: 283 [0], given: 0

Re: If XY+Z=X(Y+Z), which of the following must be true ? [#permalink]

### Show Tags

04 Feb 2014, 19:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 283 [0], given: 0

Intern
Joined: 17 Aug 2015
Posts: 7

Kudos [?]: 17 [1], given: 1

If XY+Z=X(Y+Z), which of the following must be true ? [#permalink]

### Show Tags

26 Sep 2015, 03:56
1
KUDOS
Simple and fast:

XY+Z=X(Y+Z)...... XY+Z=XY+XZ..... Z=XZ (we would eliminate all the answer options that regard Y)

Looking at the simplified equation, we come to a conclusion that Z is equal to ZX only when when X=1 or Z=0. You can also check the solution by testing each answer separately !

Hope it helps!

Kudos [?]: 17 [1], given: 1

Manager
Joined: 01 Dec 2016
Posts: 118

Kudos [?]: 13 [0], given: 32

Location: Cote d'Ivoire
Concentration: Finance, Entrepreneurship
WE: Investment Banking (Investment Banking)
Re: If XY+Z=X(Y+Z), which of the following must be true ? [#permalink]

### Show Tags

22 Mar 2017, 12:39
Really easy one.
it might be a sub 600 level question, or even sub 500 level.
_________________

What was previously considered impossible is now obvious reality.
In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them

Kudos [?]: 13 [0], given: 32

Re: If XY+Z=X(Y+Z), which of the following must be true ?   [#permalink] 22 Mar 2017, 12:39
Display posts from previous: Sort by