Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 20 Jul 2019, 17:32 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If xy = - 6, what is the value of xy(x+y)?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56304
If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

3
1
37 00:00

Difficulty:   85% (hard)

Question Stats: 55% (02:02) correct 45% (02:10) wrong based on 959 sessions

### HideShow timer Statistics The Official Guide For GMAT® Quantitative Review, 2ND Edition

If xy = - 6, what is the value of xy(x + y)?

(1) $$x - y = 5$$

(2) $$xy^2 = 18$$

Data Sufficiency
Question: 100
Category: Algebra First- and second-degree equations
Page: 160
Difficulty: 650

_________________

Originally posted by Bunuel on 18 Feb 2014, 03:52.
Last edited by Bunuel on 06 Feb 2019, 05:21, edited 2 times in total.
Updated.
Math Expert V
Joined: 02 Sep 2009
Posts: 56304
Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

5
10
SOLUTION

If xy = - 6, what is the value of xy(x+y)?

(1) x - y = 5 --> $$x=y+5$$ --> $$xy=(y+5)y=-6$$ --> $$y^2+5y+6=0$$ --> $$y=-3$$ or $$y=-2$$. If $$y=-3$$ then $$x=y+5=2$$ so $$xy(x+y)=-6(x+y)=6$$. But if $$y=-2$$ then $$x=y+5=3$$ so $$xy(x+y)=-6(x+y)=-6$$. Two different answers, hence not sufficient.

(2) xy^2 = 18 --> $$xy*y=-6*y=18$$ --> $$y=-3$$ --> $$x=2$$ --> $$xy(x+y)=-6(x+y)=6$$. Sufficient.

_________________
##### General Discussion
Manager  Joined: 04 Jan 2014
Posts: 116
GMAT 1: 660 Q48 V32 GMAT 2: 630 Q48 V28 GMAT 3: 680 Q48 V35 Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

Basically we need to find the value for (x+y).

St1: x-y = 5

From stem, y = -6/x. Plugging this in statement 1, we will have x + 6/x = 5. Upon solving, we get x = 2 or 3. This means, y = -3 or -2. (x+y) = -1 or 1. Two different answers. Not sufficient.

St2: xy^2 = 18

This can be written as (xy)*y or -6y. This gives y = -3. We have no information about x. Not sufficient.

St1 + St2: We get x = 2 and y = -3. (x+y) = -1. Hence xy(x+y) = (-6)(-1) = 6. Sufficient.

Senior Manager  Joined: 13 Jun 2013
Posts: 271
Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

1
known xy=-6, unknown xy(x+y)

statement 1) x-y=5; we know that xy=-6, we can substitute x=-(6/y) in the given equation, which becomes
-(6/y)-y=5; y^2+5y+6=0; (y+3)(y+2)=0; hence y=-3 or y=-2,
when y=-3, x=2. thus x+y=-1 and xy(x+y)=-(6)(-1)=6
when x=-2, y=3 thus x+y=1 and xy(x+y)= (-6)(1)= -6 hence 1 is not sufficient

statement 2) xy^2=18; can be written as xy(y)=18,
-6y=18;
y=-3; also we know from the question statement that xy=-6; thus x=2 hence x+y=2-3=-1, hence xy(x+y) = -6(-1)= 6

hence sufficient. Therefore answer should be B
Manager  Status: Please do not forget to give kudos if you like my post
Joined: 19 Sep 2008
Posts: 89
Location: United States (CA)
Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

1
st1: x-y=5 we know that xy=-6 i.e. x=-6/y this give us 2 solution so not sufficient.
st2: xy2=18 i.e. -6y=18 give us y and we can find x. sufficient.

_________________

Director  G
Affiliations: CrackVerbal
Joined: 03 Oct 2013
Posts: 564
Location: India
GMAT 1: 780 Q51 V46 Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

1
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If xy = - 6, what is the value of xy(x+y)?

(1) x - y = 5
(2) xy^2 = 18

Data Sufficiency
Question: 100
Category: Algebra First- and second-degree equations
Page: 160
Difficulty: 650

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!

If xy = - 6, what is the value of xy(x+y)?

(1) x - y = 5
(2) xy^2 = 18

the question asks what is the value of -6(x+y)?

Statement I is insufficient:

xy = -6
x = y + 5
-6 = y^2 + 5y
y^2 + 5y + 6 = 0
y = -3, y = -2
y = -3, x = 2, x + y = -1
y = -2, x = 3, x + y = 1
Since we have two different answers hence statement I is insufficient

Statement II
x(y)(y) = 18
-6(y) = 18
y = -3 and since xy = -6, x = 2.

_________________
- CrackVerbal Prep Team

Register for the Free GMAT Kickstarter Course : http://bit.ly/2DDHKHq

Register for our Personal Tutoring Course : https://www.crackverbal.com/gmat/personal-tutoring/

Join the free 4 part GMAT video training series : http://bit.ly/2DGm8tR
Manager  Status: Applied
Joined: 02 May 2014
Posts: 125
Location: India
Concentration: Operations, General Management
GMAT 1: 690 Q47 V38 GPA: 3.35
WE: Information Technology (Computer Software)
Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

Solving A we get 2 values of x and y hence not sure which one is the value.
Solving B we get one set of values for x and y hence definite answer so B.
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14597
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

1
Hi All,

There's a subtle, but important lesson in how this question is designed: you MUST make sure that you finish the work and answer the question that is asked.....

Donnie84 wrote:
Basically we need to find the value for (x+y).

St2: xy^2 = 18

This can be written as (xy)*y or -6y. This gives y = -3. We have no information about x. Not sufficient.

This poster correctly figured out the value of Y from Fact 2, but then stopped working....by plugging the value of Y back into either the starting equation or the one in Fact 2, we have the value of X.....AND we can answer the question.
Fact 2 is SUFFICIENT.

It's important to remember that DS questions have NO "safety net" - the moment you make a little mistake, you're probably going to get the question wrong and you won't even realize it. It's important to make sure that you have PROOF of what you believe. In this case, if we really had no idea about the value of X, then we should be able to quickly come up with 2 different possibilities that fit the given restrictions and PROVE that the answer to the question changes. When Quant scores take a significant drop, it's almost always due to some type of little mistakes. Practice putting ALL of the work that yo do on the pad and you'll be far more likely to remove those silly mistakes from your approaches.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin Follow
Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ Intern  Joined: 31 Aug 2014 Posts: 3 Re: If xy = - 6, what is the value of xy(x+y)? [#permalink] ### Show Tags Bunuel wrote: SOLUTION If xy = - 6, what is the value of xy(x+y)? (1) x - y = 5 --> $$x=y+5$$ --> $$xy=(y+5)y=-6$$ --> $$y^2+5y+6=0$$ --> $$y=-3$$ or $$y=-2$$. If $$y=-3$$ then $$x=y+5=2$$ so $$xy(x+y)=-6(x+y)=6$$. But if $$y=-2$$ then $$x=y+5=3$$ so $$xy(x+y)=-6(x+y)=-6$$. Two different answers, hence not sufficient. (2) xy^2 = 18 --> $$xy*y=-6*y=18$$ --> $$y=-3$$ --> $$x=2$$ --> $$xy(x+y)=-6(x+y)=6$$. Sufficient. Answer: B. In the Option 1 , cant we write X - Y =5 as (X - Y)^2 = 25 ?? as in this way we can get answer by A also. EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14597 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If xy = - 6, what is the value of xy(x+y)? [#permalink] ### Show Tags Hi rahulhkdwivedi, While you could square both sides of that equation, you haven't shown any of the steps that you would do next... so how do you know that it's sufficient? I suggest that you attempt what you've suggested, and then answer try to answer the GIVEN question: What is the value of XY(X+Y)? You should be able to prove that it's insufficient. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Follow Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
CEO  S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

1
rahulhkdwivedi wrote:
Bunuel wrote:
SOLUTION

If xy = - 6, what is the value of xy(x+y)?

(1) x - y = 5 --> $$x=y+5$$ --> $$xy=(y+5)y=-6$$ --> $$y^2+5y+6=0$$ --> $$y=-3$$ or $$y=-2$$. If $$y=-3$$ then $$x=y+5=2$$ so $$xy(x+y)=-6(x+y)=6$$. But if $$y=-2$$ then $$x=y+5=3$$ so $$xy(x+y)=-6(x+y)=-6$$. Two different answers, hence not sufficient.

(2) xy^2 = 18 --> $$xy*y=-6*y=18$$ --> $$y=-3$$ --> $$x=2$$ --> $$xy(x+y)=-6(x+y)=6$$. Sufficient.

In the Option 1 , cant we write X - Y =5 as (X - Y)^2 = 25 ?? as in this way we can get answer by A also.

I agree with EMPOWERgmatRichC. Additionally, if you do square the expression to get $$(x-y)^2=25$$ --->$$x^2+y^2-2xy=25$$, you still wont get any answers for $$xy(x+y)$$ or $$x^2y+xy^2$$

Also, when you square any expression you end up increasing the number of solutions by a factor of 2. For example, you are given x-y=5 but when you square the expression,

$$(x-y)^2=25$$ ---> this is quadratic equation, you end up getting, $$x-y=\pm 5$$, thus giving you an additional equation in $$x-y=-5$$

Do not square or cube any given expression unless absolutely needed to. Even when you do make sure to check whether all solutions given by the squared or the cubed equations satisfy the given requirements.

Hope this helps.
Board of Directors P
Joined: 17 Jul 2014
Posts: 2539
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

I was actually thinking about A as well to square (x-y).
x-y)^2=25 or x^2+y^2-2xy=25
x^2+y^2+12=25
x^2+y^2=13

now, (x+y)^2=x^2+y^2+2xy.
13-12=1.
from this:
x+y=1
or x+y=-1.

since 2 outcomes are possible, A is not correct.

I answered B, because I solved the way it was explained above, yet this method bothers me as well..
_________________
Intern  B
Joined: 14 Dec 2015
Posts: 46
Concentration: Entrepreneurship, General Management
WE: Information Technology (Computer Software)
Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

I got ditched! help pls.

If xy = - 6, what is the value of xy(x+y)?

(1) x - y = 5
$$(x-y)^2$$ = $$(x+y)^2$$ - 4xy --> 25 = $$(x+y)^2$$ + 24 --> $$(x+y)^2$$ = 1 --> $$(x+y)$$=1 ( Possible to find xy(x+y) )

(2) $$xy^2$$ = 18
(xy)(y)=18 - the same method everyone did above. ( Possible to find xy(x+y) )

I selected D

okk.. I know it isn't D
After my analysis, I reckon the mistake I committed was deducing $$(x+y)^2$$ =1 --> $$(x+y)$$= 1 ; probably this must've been (+1) or (- 1).
Somebody, please confirm is this where I got it wrong _________________
"Fight the HARDEST battle that anyone can ever imagine"
CEO  S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

snorkeler wrote:

okk.. I know it isn't D
After my analysis, I reckon the mistake I committed was deducing $$(x+y)^2$$ =1 --> $$(x+y)$$= 1 ; probably this must've been (+1) or (- 1).
Somebody, please confirm is this where I got it wrong Yes. The catch with S1 was that you will end up getting x= $$\pm$$ 1, giving you 2 different values for xy(x+y) ---> Not sufficient.

FYI, when you have a quadratic equation , you must have 2 solutions (as per the definition). Even if you dont know this, you can also realize that there are 2 values that will give you a value =1 when squared ---> when a (any variable)= $$\pm$$ 1

Hope this helps.
Non-Human User Joined: 09 Sep 2013
Posts: 11718
Re: If xy = - 6, what is the value of xy(x+y)?  [#permalink]

### Show Tags

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.
_________________ Re: If xy = - 6, what is the value of xy(x+y)?   [#permalink] 24 Sep 2018, 20:20
Display posts from previous: Sort by

# If xy = - 6, what is the value of xy(x+y)?  