Last visit was: 09 Oct 2024, 22:00 It is currently 09 Oct 2024, 22:00
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
SORT BY:
Date
Tags:
Difficulty: 655-705 Level,   Algebra,                                          
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 96014
Own Kudos [?]: 666805 [158]
Given Kudos: 87567
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 96014
Own Kudos [?]: 666805 [37]
Given Kudos: 87567
Send PM
General Discussion
Joined: 04 Jan 2014
Posts: 378
Own Kudos [?]: 186 [1]
Given Kudos: 15
GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
GMAT 3: 680 Q48 V35
Send PM
User avatar
Joined: 13 Jun 2013
Posts: 223
Own Kudos [?]: 1081 [2]
Given Kudos: 14
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
2
Kudos
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
GMAT Club Legend
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4897
Own Kudos [?]: 7976 [3]
Given Kudos: 221
Location: India
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
3
Kudos
Bunuel
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:
1. Please provide your solutions to the questions;
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.

Hence answer is B
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21831
Own Kudos [?]: 11921 [1]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
1
Kudos
Expert Reply
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
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.

Answer (C).

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
avatar
Joined: 31 Aug 2014
Posts: 3
Own Kudos [?]: [0]
Given Kudos: 61
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
Bunuel
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.
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21831
Own Kudos [?]: 11921 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
Expert Reply
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
Joined: 20 Mar 2014
Posts: 2350
Own Kudos [?]: 3676 [2]
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
2
Bookmarks
rahulhkdwivedi
Bunuel
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.

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.
Joined: 26 Jan 2016
Posts: 100
Own Kudos [?]: 153 [0]
Given Kudos: 61
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
I got to one set of values of x and y in B, but then I rejected this option on the basis that nowhere it is Given that X and y are integers. What about real nos.

Please help.
Bunuel ScottTargetTestPrep

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 96014
Own Kudos [?]: 666805 [0]
Given Kudos: 87567
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
Expert Reply
kitipriyanka
I got to one set of values of x and y in B, but then I rejected this option on the basis that nowhere it is Given that X and y are integers. What about real nos.

Please help.
Bunuel ScottTargetTestPrep

Posted from my mobile device


As show above, xy = -6 and xy^2 = 18 has only one real solution: x = 2 and y = -3. If you check above, you'll see that while solving, we nowhere assumed that x and y are integers. We just got that they are after we solved.
avatar
Joined: 29 Oct 2018
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 25
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
Why couldn't we solve it by plugging in the (xy=-6) in xy(x+y) first? So it would look like this:
-6(x+y)
-6x-6y
(and then plug in our first statement)
-6(y+5) - 6y
-6y -30 - 6y
-12y -30
-12y=30
y=-30/12 and so forth
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6059
Own Kudos [?]: 14277 [2]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
1
Kudos
1
Bookmarks
Expert Reply
Bunuel
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

Hi NandishSS

I totally advocate the use of smart numbers for solving such problems.

The generalization of any method (ALgebraic or number plugging) is difficult as it works based on your first instinct.

P.S. When I solved this problem for teh first time, then I used numbers instead of algebraic approach

However, a good suggestion will be to simplify the expressions algebraically if it seems possible. When stcuk in solving/inferring it further then start using numbers

My flow of thought is as follows:

Given: If xy = - 6 Some possible values of (x,y) are (2, -3) (-2, 3) (3, -2) (-3, 2) but the values ,may be Non-integers too

Question: xy(x + y) = ? so we need only (x+y) as we know the value of x*y

Statement 1: \(x - y = 5\)

(2, -3) and (3, -2) satisfy but the value of x+y may be +1 or -1 hence

NOT SUFFICIENT

Statement 2: \(xy^2 = 18\)

i.e. Y must be negative and x must be positive
Also, \(18 = 2*3^2\) therefore (x, y) = (2, -3)
i.e. x+y = -1

SUFFICIENT

Answer: Option B
Joined: 06 Jan 2015
Posts: 724
Own Kudos [?]: 1617 [0]
Given Kudos: 579
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE:Information Technology (Computer Software)
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
GMATinsight Why you didn't choose (6,1)?

What are the smart numbers?

There might be many possibilities as well.
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6059
Own Kudos [?]: 14277 [0]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
Expert Reply
NandishSS
GMATinsight Why you didn't choose (6,1)?

What are the smart numbers?

There might be many possibilities as well.

NandishSS

Yes, it was possible but I had to stop somewhere realizing infinite possibilities in non-integer solutions. So after thinking a few possibilities I looked at statements and found my answer rather than summarising all possible solutions beforehand.
Joined: 09 Jan 2020
Posts: 945
Own Kudos [?]: 241 [0]
Given Kudos: 432
Location: United States
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
Bleepblop
Why couldn't we solve it by plugging in the (xy=-6) in xy(x+y) first? So it would look like this:
-6(x+y)
-6x-6y
(and then plug in our first statement)
-6(y+5) - 6y
-6y -30 - 6y
-12y -30
-12y=30
y=-30/12 and so forth

This is what I did too. Is this approach correct?
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19584
Own Kudos [?]: 23478 [0]
Given Kudos: 287
Location: United States (CA)
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
Expert Reply
Bunuel
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) \(xy^2 = 18\)


Solution:

We need to determine the value of xy(x + y) given that xy = -6.


Statement One Alone:

We can re-express x - y = 5 as x = y + 5 and substitute it into the equation provided in the question stem:

xy = -6

(y + 5)(y) = -6

y^2 + 5y + 6 = 0

(y + 3)(y + 2) = 0

y = -3 or y = -2

If y = -3, then x = -6/y = 2. In this case, x + y = -1 and xy(x + y) = (-6)(-1) = 6. However, if y = -2, then x = -6/y = 3. In this case, x + y = 1 and xy(x + y) = (-6)(1) = -6. Since there are two possible values for xy(x + y), statement one is not sufficient.

Statement Two Alone:

We can re-express xy^2 = 18 as (xy)(y) = 18. Since we are given that xy = -6, we have:

(xy)(y) = 18

-6y = 18

y = 18/-6

y = -3

Thus, the value of x can be determined:

xy^2 = 18

x(9) = 18

x = 2

We know the values of both x and y, so the value of xy(x + y) can be determined. Statement two is sufficient.

Answer: B
Joined: 23 May 2020
Posts: 88
Own Kudos [?]: 10 [0]
Given Kudos: 1529
Send PM
If xy = - 6, what is the value of xy(x+y)? [#permalink]
ScottTargetTestPrep

For statement 1 the quadratic route is good, however, can we use the following logic?
(1) x−y=5

(x - y)^2 = 25

x^2 - 2xy + y^2 = 25
x^2 + 12 + y^2 = 25
x^2 + y^2 = 13 Since the question stem does not mention that x and y are integers, there are many possible values for x and y. Therefore, not sufficient.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 35182
Own Kudos [?]: 891 [0]
Given Kudos: 0
Send PM
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
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.
GMAT Club Bot
Re: If xy = - 6, what is the value of xy(x+y)? [#permalink]
Moderator:
Math Expert
96014 posts