It is currently 20 Nov 2017, 23:42

### 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

# m04 #24

Author Message
Intern
Joined: 22 Sep 2008
Posts: 11

Kudos [?]: 1 [0], given: 0

### Show Tags

09 Oct 2008, 15:47
Is $$x = 0$$ ?

1. $$xy = x$$
2. $$x + y = y$$

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions

Please explain why statement 1 is insufficient.
_________________

It's not the IMO, it's the OA!!

Kudos [?]: 1 [0], given: 0

VP
Joined: 30 Jun 2008
Posts: 1031

Kudos [?]: 729 [1], given: 1

### Show Tags

09 Oct 2008, 19:26
1
KUDOS
gmat4life wrote:
Is x=0?

1. xy=x

2. x+y=y

Please explain why statement 1 is insufficient.

Now xy=x means xy-x=0 or x(1-y)=0
For the equation x(1-y)=0 to hold good, either x has to be 0 or y has to be 1. It can very well be that x=0 and y=1 at the same time. We are not sure. So since it is not clear if x=0 or not, this statement is not sufficient.

Now in statement 2. x+y=y clearly shows x=0.

So it must be B

HTH
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Kudos [?]: 729 [1], given: 1

Manager
Joined: 04 Oct 2010
Posts: 60

Kudos [?]: 37 [1], given: 17

GMAT 1: 720 Q48 V41

### Show Tags

17 Oct 2010, 00:07
1
KUDOS
for statement 1 :
x*y=x
if x=0 and y=1 then 0*1=0 ; satisfies
if x=2 and y=1 then 2*1=2 ; satisfies

thus statement 1 is insufficient to say that x is 0

for statement 2:
x+y=y
if x=0 and y=any integer then 0+y = y ; satisfies
if x=2(or any int but not zero) and y=any int then x+y=y is not satisfying

thus statement 2 is sufficient to say that x=0

SO B

But what would be the answer if the second statement was : x + y = x ??
_________________

---
Jimmy

Lifes battles dont always go,
To the stronger or faster man;
But sooner or later the man who wins,
Is the man who THINKS HE CAN .

KUDOS me if you feel my contribution has helped you.

Kudos [?]: 37 [1], given: 17

Math Expert
Joined: 02 Sep 2009
Posts: 42275

Kudos [?]: 132869 [1], given: 12389

### Show Tags

20 Oct 2010, 05:16
1
KUDOS
Expert's post
sivai87 wrote:
@ GMAT BULL

Is X = 0?

1) X * Y = X

2) X + Y = X

The statements 1 and 2 are contradicting to each other..
Option 1 says that, X * Y = X which tends to give Y = 1,

But option 2 gives, X + Y = X, and So Y = 0.

Not so. First of all statement (2) is $$x+y=y$$ and not $$x+y=x$$.

Next, (1) $$xy=x$$ --> $$x(y-1)=0$$ --> either $$x=0$$ (and $$y$$ can take any value) OR $$y=1$$ (and $$x$$ can take any value). So we can not say that $$y=1$$ from this statement.

If the question were:

Is $$x = 0$$?

(1) $$xy = x$$
(2) $$x+y=x$$ (Note that this statement is changed)

Then the answer would be C:

(1) $$xy=x$$ --> $$x(y-1)=0$$ --> either $$x=0$$ (and $$y$$ can take any value) OR $$y=1$$ (and $$x$$ can take any value). Not sufficient.
(2) $$x+y=x$$ --> $$y=0$$. Not sufficient to answer whether $$x=0$$.

(1)+(2) As from (2) $$y=0\neq{1}$$ then according to (1) $$x=0$$. Sufficient.

So for this revised question answer would be C.

Hope it helps.
_________________

Kudos [?]: 132869 [1], given: 12389

CIO
Joined: 02 Oct 2007
Posts: 1216

Kudos [?]: 987 [0], given: 334

### Show Tags

22 Oct 2008, 07:04
Thanks for a good explanation!
+1
amitdgr wrote:
gmat4life wrote:
Is x=0?

1. xy=x

2. x+y=y

Please explain why statement 1 is insufficient.

Now xy=x means xy-x=0 or x(1-y)=0
For the equation x(1-y)=0 to hold good, either x has to be 0 or y has to be 1. It can very well be that x=0 and y=1 at the same time. We are not sure. So since it is not clear if x=0 or not, this statement is not sufficient.

Now in statement 2. x+y=y clearly shows x=0.

So it must be B

HTH

_________________

Welcome to GMAT Club!

Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 987 [0], given: 334

Intern
Affiliations: SPE
Joined: 02 Sep 2010
Posts: 8

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

Location: Copenhagen
Schools: Columbia, MIT, Harvard, LBS

### Show Tags

15 Oct 2010, 06:02
This question goes to show that when you have been looking at 700 level questions too long, you try and pick holes in something as simple as x = y - y ....

on the other hand, its good to finally get a question right!

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

Intern
Joined: 10 Oct 2010
Posts: 7

Kudos [?]: [0], given: 1

### Show Tags

15 Oct 2010, 09:36
For the first option, lets assume Y = 1. So whatever the value of x, the product of XY is always X.

X * 1 = X (For any values of X). So, option 1 is ruled out..

Kudos [?]: [0], given: 1

Director
Joined: 21 Dec 2009
Posts: 582

Kudos [?]: 841 [0], given: 20

Concentration: Entrepreneurship, Finance

### Show Tags

18 Oct 2010, 05:48
Hi Jimmy86;
if (2) where: x + y = x
--> y = 0 [no information about x after subtracting x from both sides]

combining (1) & (2) [x*y=x; x+y=x]:
x(0) = x
for all values of x, x*0 is always a zero.
So, we can say x (the result of the multiplication) is a zero.
IMO C
_________________

KUDOS me if you feel my contribution has helped you.

Kudos [?]: 841 [0], given: 20

Intern
Joined: 10 Oct 2010
Posts: 7

Kudos [?]: [0], given: 1

### Show Tags

18 Oct 2010, 06:20
If X+Y=X, then I go for E..

we have options,

x * y = x and

x + y = x.

Combining 1 and 2,

(x + y) * y = x,

xy + y^2 = x

y (x + y) = x and so, x will be zero only if Y is also 0 or else the condition is not satisfied. So, IMO its E.

jimmy86 wrote:
for statement 1 :
x*y=x
if x=0 and y=1 then 0*1=0 ; satisfies
if x=2 and y=1 then 2*1=2 ; satisfies

thus statement 1 is insufficient to say that x is 0

for statement 2:
x+y=y
if x=0 and y=any integer then 0+y = y ; satisfies
if x=2(or any int but not zero) and y=any int then x+y=y is not satisfying

thus statement 2 is sufficient to say that x=0

SO B

But what would be the answer if the second statement was : x + y = x ??

Kudos [?]: [0], given: 1

Manager
Joined: 04 Oct 2010
Posts: 60

Kudos [?]: 37 [0], given: 17

GMAT 1: 720 Q48 V41

### Show Tags

18 Oct 2010, 07:06
[quote="sivai87"]If X+Y=X, then I go for E..

we have options,

x * y = x and

x + y = x.

Combining 1 and 2,

(x + y) * y = x,

xy + y^2 = x

y (x + y) = x and so, x will be zero only if Y is also 0 or else the condition is not satisfied. So, IMO its E.

I agree... its E.

in case statement 2 : x+y = x
x=-1 , y=0 gives -1+0 = -1 ; satisfies
x=0 , y= 0 gives 0+0 = 0 ; satisfies
we see x is not necessarily 0. Insufficient

And combining
y(x+y)=x
if x=0 ; y=0 then 0*(0+0)=0 ; satisfies
if x=1/2 ; y=1/2 then 1/2*(1/2+1/2)=1/2 ; satisfies
So x is not necessarily 0.Insufficient

Thus IMO its E

But what if the question states that x is an integer.
Then i suppose the only value that of x that satisfies y(x+y)=x is x=0. and answer would be C(not sure, feel i am missing something)
_________________

---
Jimmy

Lifes battles dont always go,
To the stronger or faster man;
But sooner or later the man who wins,
Is the man who THINKS HE CAN .

KUDOS me if you feel my contribution has helped you.

Kudos [?]: 37 [0], given: 17

Intern
Status: Current Student
Joined: 16 May 2010
Posts: 44

Kudos [?]: 11 [0], given: 4

Schools: Darden '13

### Show Tags

18 Oct 2010, 08:05
Supasubi wrote:
This question goes to show that when you have been looking at 700 level questions too long, you try and pick holes in something as simple as x = y - y ....

on the other hand, its good to finally get a question right!

Haha yes! I definitely know what you mean. You're so traumatized from every question trying to trick you, that you're reluctant to believe that the answer could be sufficient with something as easy as X=Y-Y. I stared at it for a good 30 seconds trying to pick it apart too. That's hilarious.

Kudos [?]: 11 [0], given: 4

Director
Joined: 21 Dec 2009
Posts: 582

Kudos [?]: 841 [0], given: 20

Concentration: Entrepreneurship, Finance

### Show Tags

18 Oct 2010, 09:30
(2) if y = x - x, then, it is sufficient to say y = "0".

plug in y (0) into (1) [x*y = x]
or x = x*y
x = x*0
RHS = x*0 = 0
for any value of a number, 0 times that number = 0
So, RHS is always "0"
LHS = x
LHS = RHS
--> x = RHS
x = 0
Sufficient

So, C IMO....except am doing something stupid somewhere.
_________________

KUDOS me if you feel my contribution has helped you.

Kudos [?]: 841 [0], given: 20

Intern
Joined: 10 Oct 2010
Posts: 7

Kudos [?]: [0], given: 1

### Show Tags

18 Oct 2010, 10:48
@Gmatbull..

Buddy, I dont think u went wrong... I believe I am somewhere wrong..

The first mistake i made was, in substitution...
I shud have substituted as (x+y) * y = (x+y)... instead of (X+Y)*Y= X..

But even after this I am getting (X+Y)*Y=(X+Y) ---> Y=1.. and this will finally yield that Both option are not suffiient...
And I am not sure how to proceed further...

Can anyone help me pls...

gmatbull wrote:
(2) if y = x - x, then, it is sufficient to say y = "0".

plug in y (0) into (1) [x*y = x]
or x = x*y
x = x*0
RHS = x*0 = 0
for any value of a number, 0 times that number = 0
So, RHS is always "0"
LHS = x
LHS = RHS
--> x = RHS
x = 0
Sufficient

So, C IMO....except am doing something stupid somewhere.

Kudos [?]: [0], given: 1

Director
Joined: 21 Dec 2009
Posts: 582

Kudos [?]: 841 [0], given: 20

Concentration: Entrepreneurship, Finance

### Show Tags

18 Oct 2010, 12:19
sivai87 wrote:
@Gmatbull..
The first mistake i made was, in substitution...
I shud have substituted as (x+y) * y = (x+y)... instead of (X+Y)*Y= X..

But even after this I am getting (X+Y)*Y=(X+Y) ---> Y=1.. and this will finally yield that Both option are not suffiient...
And I am not sure how to proceed further...

I think you seem to make the expression difficult to yourself.
First, realize that (2) has simplified the job:
from x+y = x, you know y = 0.
(x+y) * y = (x+y) ==> (x+y)0 = x+0
0 = x +0
0 = x
you still arrive at C.
_________________

KUDOS me if you feel my contribution has helped you.

Kudos [?]: 841 [0], given: 20

Intern
Joined: 10 Oct 2010
Posts: 7

Kudos [?]: [0], given: 1

### Show Tags

20 Oct 2010, 04:54
@ GMAT BULL

Is X = 0?

1) X * Y = X

2) X + Y = X

The statements 1 and 2 are contradicting to each other..
Option 1 says that, X * Y = X which tends to give Y = 1,

But option 2 gives, X + Y = X, and So Y = 0.

gmatbull wrote:
sivai87 wrote:
@Gmatbull..
The first mistake i made was, in substitution...
I shud have substituted as (x+y) * y = (x+y)... instead of (X+Y)*Y= X..

But even after this I am getting (X+Y)*Y=(X+Y) ---> Y=1.. and this will finally yield that Both option are not suffiient...
And I am not sure how to proceed further...

I think you seem to make the expression difficult to yourself.
First, realize that (2) has simplified the job:
from x+y = x, you know y = 0.
(x+y) * y = (x+y) ==> (x+y)0 = x+0
0 = x +0
0 = x
you still arrive at C.

Kudos [?]: [0], given: 1

Manager
Joined: 10 Jan 2011
Posts: 232

Kudos [?]: 81 [0], given: 25

Location: India
GMAT Date: 07-16-2012
GPA: 3.4
WE: Consulting (Consulting)

### Show Tags

19 Oct 2011, 09:14
statement 1 XY=X means y=1 but X can take any value not sufficient
statement 2 x + y = Y means X = y-y or X=0 sufficient
_________________

-------Analyze why option A in SC wrong-------

Kudos [?]: 81 [0], given: 25

Intern
Joined: 17 Aug 2011
Posts: 2

Kudos [?]: 7 [0], given: 1

### Show Tags

19 Oct 2011, 12:51
Bunuel wrote:
sivai87 wrote:
@ GMAT BULL

Is X = 0?

1) X * Y = X

2) X + Y = X

The statements 1 and 2 are contradicting to each other..
Option 1 says that, X * Y = X which tends to give Y = 1,

But option 2 gives, X + Y = X, and So Y = 0.

Not so. First of all statement (2) is $$x+y=y$$ and not $$x+y=x$$.

Next, (1) $$xy=x$$ --> $$x(y-1)=0$$ --> either $$x=0$$ (and $$y$$ can take any value) OR $$y=1$$ (and $$x$$ can take any value). So we can not say that $$y=1$$ from this statement.

If the question were:

Is $$x = 0$$?

(1) $$xy = x$$
(2) $$x+y=x$$ (Note that this statement is changed)

Then the answer would be C:

(1) $$xy=x$$ --> $$x(y-1)=0$$ --> either $$x=0$$ (and $$y$$ can take any value) OR $$y=1$$ (and $$x$$ can take any value). Not sufficient.
(2) $$x+y=x$$ --> $$y=0$$. Not sufficient to answer whether $$x=0$$.

(1)+(2) As from (2) $$y=0\neq{1}$$ then according to (1) $$x=0$$. Sufficient.

So for this revised question answer would be C.

Hope it helps.

I seem to recall that you can't add/subtract variables from both sides of the equation unless you know the sign of the variables. But the question doesn't tell you the sign of x or y so I don't think the problem can be approached this way. I think the only way to answer the question is to plug in numbers for x and y then check to see if the equation holds.

Kudos [?]: 7 [0], given: 1

Manager
Joined: 20 Nov 2010
Posts: 214

Kudos [?]: 42 [0], given: 38

### Show Tags

19 Oct 2011, 13:32
St 1:
xy = x. Either x=0 and y can take any value OR x can be any value and y=1. So insufficient.

St2
x+y = Y => X=0, Y can be anything. Hence Sufficient.

OA is B.
_________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MGMAT 6 650 (51,31) on 31/8/11
MGMAT 1 670 (48,33) on 04/9/11
MGMAT 2 670 (47,34) on 07/9/11
MGMAT 3 680 (47,35) on 18/9/11
GMAT Prep1 680 ( 50, 31) on 10/11/11

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned

Kudos [?]: 42 [0], given: 38

Manager
Joined: 16 Sep 2010
Posts: 219

Kudos [?]: 136 [0], given: 2

Location: United States
Concentration: Finance, Real Estate
GMAT 1: 740 Q48 V42

### Show Tags

20 Nov 2011, 07:44
B.

1 tells us that y=1 and 2 tells us that x=0.

Kudos [?]: 136 [0], given: 2

Manager
Joined: 06 May 2012
Posts: 75

Kudos [?]: 52 [0], given: 16

### Show Tags

07 Oct 2012, 12:47
Quote:
Is $$x = 0$$ ?

1. $$xy = x$$
2. $$x + y = y$$

For Option1, which of the below method need to be followed?

Method1 ---- $$xy = x$$ ----> $$xy-x = 0$$ ----> $$x(y-1) = 0$$ ----> $$x = 0, y = 1$$ ---- I thought this method is always true in determining a value
Method2 ---- $$xy = x$$ - Substitute values $$x=0$$ & $$y$$can be any value? or $$x$$ can be any value and $$y=1?$$

Kudos [?]: 52 [0], given: 16

Re: m04 #24   [#permalink] 07 Oct 2012, 12:47

Go to page    1   2    Next  [ 25 posts ]

Display posts from previous: Sort by

# m04 #24

Moderator: Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.