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

It is currently 20 Jun 2018, 21:53

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 18 Apr 2015
Posts: 24
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 18 May 2015, 03:49
Bunnel,

Option B turns out to be x=0 or x=2.X cannot be equal to zero but we can use x=2 right.In that case we will get (x-1)(y-1)=1
Expert Post
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1522
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 18 May 2015, 04:29
kirtivardhan wrote:
Bunnel,

Option B turns out to be x=0 or x=2.X cannot be equal to zero but we can use x=2 right.In that case we will get (x-1)(y-1)=1


Dear kirtivardhan

Your question tells me that you analyzed St. 2 in one of the following two ways. I'll list them both here and discuss the error in them.

Way 1- You did your analysis of St. 2 as follows:

"Put x = y in x + y = xy
=> \(2x = x^2\)
Upon solving, x = 0 or x = 2"


The error a student who analyses St. 2 in this way does is that he is not considering the equation x = y alone (which is the only piece of info that St. 2 gives) but instead has mistakenly carried over information from St. 1 (x + y = xy) into his analysis of St. 2.

Way 2- You did your analysis of St. 2 as follows:

"Given that x = y
We need to find if \((x-1)^2 = 1\)?
That is, if \((x-1)^2 - 1 = 0\) or (x-1-1)(x-1+1) = 0
That is, x(x-2) = 0
That is, x = 0 or x = 2

We're given that xy > 0. This means, x cannot be EQUAL TO zero. So, x = 2"


The error a student who analyses St. 2 in this way does is that he has used the equation \((x-1)^2 = 1\) as a FACT, not as something to be verified

____________


The correct analysis of St. 2 would be as under:

From the question statement, we know that x and y have same sign and both are not equal to zero

From St. 2, x = y

Using this, we've to determine if (x-1)(y-1) = 1? That is, if \((x-1)^2 = 1\)? That is, if x(x-2) = 0

That is, we need to determine if x = 0 or x = 2.

We know that x cannot be equal to 0

So, we need to determine if x = 2. If x = 2, the equation in the question will hold true. For other values of x, the equation in the question will not hold true.

Since we don't know if x = 2 or not, St. 2 is insufficient to arrive at a unique answer for the given question.


Hope this discussion helped! :)

Regards, Japinder
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Intern
Intern
avatar
Joined: 18 Apr 2015
Posts: 24
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 18 May 2015, 04:39
Thanks Japinder,

You mean to say that we plugged option b in the question asked and we got x=0 and x=2.If x would have been mentioned to be 2 somehow then option b would have been suff.

I am making sense?

In short ,what we are trying to do is we are plugging an option in to the question asked and checking whether the result is there in the fact

Regards
Expert Post
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1522
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 18 May 2015, 05:05
kirtivardhan wrote:
Thanks Japinder,

You mean to say that we plugged option b in the question asked and we got x=0 and x=2.If x would have been mentioned to be 2 somehow then option b would have been suff.

I am making sense?

In short ,what we are trying to do is we are plugging an option in to the question asked and checking whether the result is there in the fact

Regards


Dear kirtivardhan

Yes, you're absolutely right in your first statement. If we were given, either in the question statement or in St. 2 itself that x = 2, then Option B would have been sufficient.

To answer your last statement, let me reiterate what we are trying to do here in Analysis of St. 2:

1. Info given in Question statement: xy > 0. This is a FACT

2. Info given in St. 2: x = y. This is also a FACT

Using these 2 facts, we need to confirm if (x-1)(y-1) = 1? This is the QUESTION.

By using Facts 1 and 2 to simplify the question, we saw that the answer to this question is YES, if x = 2 and NO, if x has some other value.

Hope this clarification helped! :)

Japinder
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Manager
User avatar
Joined: 18 Aug 2014
Posts: 124
Location: Hong Kong
Schools: Mannheim
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 19 May 2015, 03:57
Bunuel wrote:
guytree wrote:
I am bit sceptic to post this. But I wanted to check if this approach is right.

From the question we know that X and Y both are greater than 0.

In the statement 2 we could use simple plug-ins. If x=y=2 then (x-1)(y-1)=1. However, if x=y=3 then (x-1)(y-1) is not equal to 1.

I would greatly appreciate if you let me understand any loopholes in this approach.

Cheers


If \(xy>0\) does \((x-1)(y-1)=1\)?
(1) \(x + y = xy\)
(2) \(x=y\)

\(xy>0\) 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 us the answer YES. 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.

Answer: A.



Hi Bunuel,

I cannot find any values that represent xy = x+y
Can you provide some explanation?
Expert Post
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1522
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 19 May 2015, 04:12
LaxAvenger wrote:
Bunuel wrote:
If \(xy>0\) does \((x-1)(y-1)=1\)?
(1) \(x + y = xy\)
(2) \(x=y\)

\(xy>0\) 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 us the answer YES. 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.

Answer: A.



Hi Bunuel,

I cannot find any values that represent xy = x+y
Can you provide some explanation?


LaxAvenger
xy = x+y

So, xy - x = y
=> x(y-1) = y
=> \(x = \frac{y}{(y-1)}\)

From this equation, you can find a number of (x,y) pairs.

Example, when y = 2, x = 2
When y = 3, x = 3/2 etc.

Please note that you're not told that x and y are integers. So, you should not assume it.

Hope this helped! :)

Japinder
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Senior Manager
Senior Manager
User avatar
S
Joined: 08 Dec 2015
Posts: 304
GMAT 1: 600 Q44 V27
Reviews Badge
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 26 Jun 2016, 05:28
Is it valid to solve 1) as: is xy-x-y+1=1 ? -> since xy=x+y we get: is x+y-x-y=0 ? same as is 0=0 ? answer: yes it is. sufficient.
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 398
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 19 Sep 2016, 07:17
A is correct. Here's why:

(1) x+y = xy --> Plug into main equation

xy-x-y+1 = 1
xy -x-y = 0
x+y-x-y = 0
0 = 0

SUFFICIENT

(2) x=y --> Rewrite as (y-1)^2 = 1 --> (y-1) = +/- 1

NOT SUFFICIENT
Manager
Manager
avatar
B
Joined: 26 Mar 2017
Posts: 145
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 21 May 2017, 05:17
jakolik wrote:
Hi,

The question is:
(x-1)(y-1)=1 or xy-y-x+1=1 or xy=y+x

Thus first statement is sufficient.
Second statement x=y
x^2=2x which is not sufficient to answer the question.

So the right answer should be A. Are you sure the OA is C?

regards,
Jack



hey just a question, why can we not divide both sides by x to get x=2

I know its wrong but could someone pls let me know why it is wrong ?
_________________

I hate long and complicated explanations!

Manager
Manager
avatar
B
Joined: 26 Mar 2017
Posts: 145
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 21 May 2017, 05:40
TehJay wrote:
zuperman wrote:
From Statement 2 you still get x^2-2x+1=1 or x*(x-2)=0. So x is either 0 or 2. Obviously x cannot be 0 hence x=2 and thence y=2. This is sufficient to find the value of (x-1)(y-1)=1.
Am I still missing something here?


You're misreading the question - they're ASKING you if (x-1)(y-1)=1, not TELLING you. You're assuming that's true and solving for x to fit the question. But by the criteria in statement 2, what if x=y=5? Then (x-1)(y-1) = (4)(4) = 16 =/= 1.



I made exactly the same mistake.

I assumed that (x-1)(y-1) = 1

and then x=y --> 2=2
_________________

I hate long and complicated explanations!

Expert Post
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1522
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 23 May 2017, 06:51
daviddaviddavid wrote:
jakolik wrote:
Hi,

The question is:
(x-1)(y-1)=1 or xy-y-x+1=1 or xy=y+x

Thus first statement is sufficient.
Second statement x=y
x^2=2x which is not sufficient to answer the question.

So the right answer should be A. Are you sure the OA is C?

regards,
Jack



hey just a question, why can we not divide both sides by x to get x=2

I know its wrong but could someone pls let me know why it is wrong ?



Hey,

If we do not whether the variable x is greater than zero or not, we cannot divide both sides by x and get x = 2.

    \(x^2 = 2x\)
    \(x^2 -2x = 0\)
    \(x(x-2) = 0\)
Therefore the value of x can be 0 or 2.

If you divide \(x^2 = 2x\) by \(x\) on both sides, you are assuming that x is not equal to 0 and thus this division would make sense: \(\frac{x^2}{x} = \frac{2x}{x}\) .

If \(x = 0\) then, \(\frac{x^2}{0} = \frac{2x}{0}\) is not valid as such. Hence, if one does not know whether x is 0 or non-zero, we take all the terms to the left-hand side of the equation and then solve for the value of x.

Thanks,
Saquib
Quant Expert
e-GMAT
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46215
Re: If xy > 0 does (x-1)(y-1)=1 ? [#permalink]

Show Tags

New post 12 Feb 2018, 08:25
Re: If xy > 0 does (x-1)(y-1)=1 ?   [#permalink] 12 Feb 2018, 08:25

Go to page   Previous    1   2   [ 32 posts ] 

Display posts from previous: Sort by

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.