GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Jun 2018, 17:23

### 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 > 0, does (x - 1)(y - 1) = 1?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46284
If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

10 Feb 2014, 00:30
2
9
00:00

Difficulty:

25% (medium)

Question Stats:

70% (01:18) correct 30% (01:23) wrong based on 671 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

If xy > 0, does (x - 1)(y - 1) = 1?

(1) x + y = xy
(2) x = y

Data Sufficiency
Question: 83
Category: Algebra First- and second-degree equations
Page: 158
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 46284
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

10 Feb 2014, 00:30
2
4
SOLUTION

If xy > 0, does (x - 1)(y - 1) = 1?

$$xy>0$$ means that either both $$x$$ and $$y$$ are positive or both are negative (so neither of unknowns equals to zero: $$x\neq{0}$$ and $$y\neq{0}$$).

Question: is $$(x-1)(y-1)=1$$? --> is $$xy-x-y+1=1$$? is $$x+y=xy$$?

(1) x + y = xy --> directly gives YES answer to the question. Sufficient.

(2) x = y --> question becomes: is $$x+x=x^2$$? --> is $$x(x-2)=0$$? --> is $$x=0$$ or $$x=2$$? --> as given that $$x\neq{0}$$, then the question becomes is $$x=2$$? We don't know that, hence this statement is not sufficient.

_________________
Director
Joined: 25 Apr 2012
Posts: 702
Location: India
GPA: 3.21
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

10 Feb 2014, 11:00
1
Bunuel wrote:

If xy > 0, does (x - 1)(y - 1) = 1?

(1) x + y = xy
(2) x = y

]

Sol: given xy> 0 means booths x and y are of same sign.let us solve the given expression we get xy -(x+y) +1

St1: x+y=xy so putting these values in the exp we get xy-xy+1 or1 so st 1 is sufficient

St2 let's put these value in the statement so we get (y-1)^2 or y^2+2y-1=0

So if y=-2 then yes expression equals 1 but if y=2 then no

So st1 is sufficient therefore ans A

600 level is okay
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Intern
Joined: 30 Jan 2014
Posts: 18
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

10 Feb 2014, 16:49
1
If xy > 0, does (x - 1)(y - 1) = 1?

(1) x + y = xy
(2) x = y

xy>0 means that X=0 or y=0

The question ask us if $$(x - 1)(y - 1) = 1$$
Lets fix it up: $$xy-x-y-1=1$$ or $$xy=x+y$$

St(1) is exacty it. Sufficient
St tells us that x=y. Not helping us much.

ans is A
_________________

Please +1 KUDO if my post helps. Thank you.

Math Expert
Joined: 02 Sep 2009
Posts: 46284
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

17 Feb 2014, 01:34
SOLUTION

If xy > 0, does (x - 1)(y - 1) = 1?

$$xy>0$$ means that either both $$x$$ and $$y$$ are positive or both are negative (so neither of unknowns equals to zero: $$x\neq{0}$$ and $$y\neq{0}$$).

Question: is $$(x-1)(y-1)=1$$? --> is $$xy-x-y+1=1$$? is $$x+y=xy$$?

(1) x + y = xy --> directly gives YES answer to the question. Sufficient.

(2) x = y --> question becomes: is $$x+x=x^2$$? --> is $$x(x-2)=0$$? --> is $$x=0$$ or $$x=2$$? --> as given that $$x\neq{0}$$, then the question becomes is $$x=2$$? We don't know that, hence this statement is not sufficient.

_________________
Manager
Status: suffer now and live forever as a champion!!!
Joined: 01 Sep 2013
Posts: 133
Location: India
GPA: 3.5
WE: Information Technology (Computer Software)
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

14 Jan 2015, 05:13
stm11: x+y=xy;
substitute x and y as 2 & 2 ; then the equation satisfies the stmt1 ------>>>2+2=2*2;
and also the main equation -------->>> (2-1)*(2-1) = 1;
Hence Sufficient;

Stmt2: there are many values that satisfy the equation X=Y , but do not satisfy the equation (x - 1)(y - 1) = 1.
Hence Insufficient.
Intern
Joined: 19 May 2015
Posts: 4
Schools: AGSM '18
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

15 Jun 2015, 04:02
Statement one is easy enough

However statement two results in
(X)(x-2)=0 so x=0 or x=2. However x cannot be zero due to the xy>0 statement. Why is statement two not sufficient then ?

Posted from GMAT ToolKit
Math Expert
Joined: 02 Sep 2009
Posts: 46284
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

15 Jun 2015, 04:06
Neethling wrote:
Statement one is easy enough

However statement two results in
(X)(x-2)=0 so x=0 or x=2. However x cannot be zero due to the xy>0 statement. Why is statement two not sufficient then ?

Posted from GMAT ToolKit

How did you get x(x - 2) = 0?

Also, notice that (x - 1)(y - 1) = 1 is not given, it's what we need to find out.
_________________
Intern
Joined: 19 May 2015
Posts: 4
Schools: AGSM '18
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

15 Jun 2015, 04:15
Yes so you got x^2=2x -> (x)(x-2) = 0 so now we need to prove this to prove the question. So when x=2 or when x=0 then (x-1)(y-1)=1 ... However we have two results and it is on this ground that it is eliminated as not sufficient. I am asking whether the statement xy>0 does not eliminate x=0 as a possible answe leaving only x=2 and this making statement two sufficient ?

Posted from GMAT ToolKit
Math Expert
Joined: 02 Sep 2009
Posts: 46284
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

15 Jun 2015, 04:20
Neethling wrote:
Yes so you got x^2=2x -> (x)(x-2) = 0 so now we need to prove this to prove the question. So when x=2 or when x=0 then (x-1)(y-1)=1 ... However we have two results and it is on this ground that it is eliminated as not sufficient. I am asking whether the statement xy>0 does not eliminate x=0 as a possible answe leaving only x=2 and this making statement two sufficient ?

Posted from GMAT ToolKit

(2) x = y --> question becomes: is $$x+x=x^2$$? --> is $$x(x-2)=0$$? --> is $$x=0$$ or $$x=2$$? --> as given that $$x\neq{0}$$, then the question becomes is $$x=2$$? We don't know that, hence this statement is not sufficient.
_________________
Intern
Joined: 19 May 2015
Posts: 4
Schools: AGSM '18
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

15 Jun 2015, 04:36
Ah! Yes that makes more sense than the explanations above. Thanks so much.

Posted from GMAT ToolKit
Math Expert
Joined: 02 Sep 2009
Posts: 46284
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

15 Jun 2015, 04:37
Neethling wrote:
Ah! Yes that makes more sense than the explanations above. Thanks so much.

Posted from GMAT ToolKit

That's the same exact solution as in the second post: if-xy-0-does-x-1-y-167337.html#p1330071
_________________
Intern
Joined: 19 May 2015
Posts: 4
Schools: AGSM '18
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

15 Jun 2015, 04:40
Indeed. Thanks again.

Posted from GMAT ToolKit
SVP
Joined: 06 Nov 2014
Posts: 1888
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

16 Jun 2015, 10:18
1
If xy > 0, does (x - 1)(y - 1) = 1?
One way to think of this is, are (x-1) and (y-1) reciprocals? If that is true,
y - 1 = 1/(x - 1)

(1) x + y = xy
x = xy - y => x = y (x - 1) => (x/(x-1)) = y
This can be plugged into the original equation:
( (x/(x-1) ) - 1 = (1/(x - 1) ) => multiply 1 by (x - 1) to get a common denominator => (x - (x - 1) )/ (x - 1) =(1/(x-1))
(x - x + 1)/(x - 1) = (1/(x-1))
1/(x-1) = 1/(x-1)
Sufficient.
(2) x = y
It's probably easier to try a number. For instance x = y = 8
y - 1 = 8-1 = 7
1/(x - 1) = 1/(8 - 1) = 1/7

But if x = y = 2
y - 1 = 2 - 1 = 1
1/(x - 1) = 1 (2-1) = 1
Not sufficient.
A
Intern
Joined: 21 Jul 2016
Posts: 6
Location: United Arab Emirates
GPA: 2.97
WE: Operations (Other)
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

13 Aug 2016, 04:08
Bunuel wrote:
SOLUTION

If xy > 0, does (x - 1)(y - 1) = 1?

$$xy>0$$ means that either both $$x$$ and $$y$$ are positive or both are negative (so neither of unknowns equals to zero: $$x\neq{0}$$ and $$y\neq{0}$$).

Question: is $$(x-1)(y-1)=1$$? --> is $$xy-x-y+1=1$$? is $$x+y=xy$$?

(1) x + y = xy --> directly gives YES answer to the question. Sufficient.

(2) x = y --> question becomes: is $$x+x=x^2$$? --> is $$x(x-2)=0$$? --> is $$x=0$$ or $$x=2$$? --> as given that $$x\neq{0}$$, then the question becomes is $$x=2$$? We don't know that, hence this statement is not sufficient.

hi Bunnel.
i don't understand why statement 2 is not sufficient. From x^2 = 2x we get x=2. Why are we considering x=0 or x=2?
On substituting x=2, it satisfies the question stem.
Math Expert
Joined: 02 Sep 2009
Posts: 46284
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

13 Aug 2016, 04:11
asmitap wrote:
Bunuel wrote:
SOLUTION

If xy > 0, does (x - 1)(y - 1) = 1?

$$xy>0$$ means that either both $$x$$ and $$y$$ are positive or both are negative (so neither of unknowns equals to zero: $$x\neq{0}$$ and $$y\neq{0}$$).

Question: is $$(x-1)(y-1)=1$$? --> is $$xy-x-y+1=1$$? is $$x+y=xy$$?

(1) x + y = xy --> directly gives YES answer to the question. Sufficient.

(2) x = y --> question becomes: is $$x+x=x^2$$? --> is $$x(x-2)=0$$? --> is $$x=0$$ or $$x=2$$? --> as given that $$x\neq{0}$$, then the question becomes is $$x=2$$? We don't know that, hence this statement is not sufficient.

hi Bunnel.
i don't understand why statement 2 is not sufficient. From x^2 = 2x we get x=2. Why are we considering x=0 or x=2?
On substituting x=2, it satisfies the question stem.

Two solutions satisfy x^2 = 2x, x=0 and x=2.
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2773
Location: United States (CA)
Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

### Show Tags

20 Feb 2018, 17:18
Bunuel wrote:

If xy > 0, does (x - 1)(y - 1) = 1?

(1) x + y = xy
(2) x = y

We can re-express the question as:

Does xy - x - y + 1 = 1 ?

Does xy = x + y ?

Statement One Alone:

x + y = xy

We see that statement one answers the question.

Statement Two Alone:

x = y

Knowing that x = y, is not sufficient to answer the question. If x = y = 2, then (2 - 1)(2 - 1) = 1; however, if x = y = 1, then (1 - 1)(1 - 1) does not does equal 1.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If xy > 0, does (x - 1)(y - 1) = 1?   [#permalink] 20 Feb 2018, 17:18
Display posts from previous: Sort by

# If xy > 0, does (x - 1)(y - 1) = 1?

 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®.