BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

OG question

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Fri Dec 14, 2007 7:58 am
Thanked: 1 times

OG question

by Riggz » Mon Apr 07, 2008 6:55 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


any explanation for this one?
Top
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 34
Joined: Wed Feb 20, 2008 7:15 pm
Thanked: 6 times
Followed by:1 members

by mmukher » Mon Apr 07, 2008 7:21 pm
Given that XY + Z = X(Y + Z)

xy + z = xy + xz
xy + z - xy - xz = 0
z - xz = 0
z(x-z) = 0

z=0 OR x = z
Top
Junior | Next Rank: 30 Posts
Posts: 25
Joined: Mon Mar 31, 2008 6:09 pm

by GMAT_crusher » Mon Apr 07, 2008 8:30 pm
xy + z = xy +xz
i.e zx = z
i.e x = 1 for sure.
y does not matter.
so ..

x = 1; z =0 fits the most ... did I get that right ???

oa??
Top
Junior | Next Rank: 30 Posts
Posts: 24
Joined: Mon Mar 31, 2008 4:11 am

by mandy12 » Mon Apr 07, 2008 11:25 pm
x = 1 or z = 0
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 400
Joined: Mon Dec 10, 2007 1:35 pm
Location: London, UK
Thanked: 19 times
GMAT Score:680

by II » Thu Apr 10, 2008 12:35 pm
xy+z = x(y+z)
xy+z = xy+xz
z = xz ---> subtract xy from both sides
z - xz = 0 ---> move terms to one side
z(1-x) = 0 ---> factor left hand side of equation
So z = 0 or (1-x) = 0, which means x = 1.

So z=0, x=1.
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Thu Apr 10, 2008 1:21 pm
mmukher wrote:Given that XY + Z = X(Y + Z)

xy + z = xy + xz
xy + z - xy - xz = 0
z - xz = 0
z(x-z) = 0

z=0 OR x = z
All good until:

z - xz = 0

if you factor out z, you get:

z(1-x) = 0

So, z=0 or x=1: choose (5).
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Senior | Next Rank: 100 Posts
Posts: 32
Joined: Sat Apr 12, 2008 6:23 pm
Thanked: 1 times

by richardwang6430 » Sat Apr 12, 2008 6:49 pm
xy + z= x(y+z)
xy + z = xy + xz
z = xz
so, z=0 or x=1
Top
Senior | Next Rank: 100 Posts
Posts: 93
Joined: Thu Apr 10, 2008 1:42 pm
Location: Chicago
Thanked: 20 times

Re: OG question

by Musiq » Sat Apr 12, 2008 8:57 pm
Riggz 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


any explanation for this one?
This is a great question to work on with the options as help.

XY + Z = XY + XZ.

Therefore, Z = XZ.

At this point eliminate, every option that has Y in it (That eliminates B / C and E).

Since the 2 remaining options have Z= 0, we know this must be true,so elminate Z from both sides of the equation to get X= 1.

You can do this since you have accounted for the Z=0 possibility.
For love, not money.
Top
Post new topic Post Reply
• Page 1 of 1