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

 It is currently 19 Nov 2018, 05:40

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
• ### The winning strategy for 700+ on the GMAT

November 20, 2018

November 20, 2018

06:00 PM EST

07:00 PM EST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# What is the value of (x + y)^2?

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

### Hide Tags

Manager
Status: Bell the GMAT!!!
Affiliations: Aidha
Joined: 16 Aug 2011
Posts: 143
Location: Singapore
Concentration: Finance, General Management
GMAT 1: 680 Q46 V37
GMAT 2: 620 Q49 V27
GMAT 3: 700 Q49 V36
WE: Other (Other)
What is the value of (x + y)^2?  [#permalink]

### Show Tags

04 Oct 2011, 06:37
1
5
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:22) correct 35% (01:39) wrong based on 212 sessions

### HideShow timer Statistics

What is the value of (x + y)^2?

(1) x^2 − xy = 28 and 3xy + y^2 = 72.

(2) (x + y)^4 = 10,000

_________________

If my post did a dance in your mind, send me the steps through kudos :)

My MBA journey at http://mbadilemma.wordpress.com/

Intern
Status: Need to read faster and get less distracted by the ticking clock!
Affiliations: Golden Key
Joined: 19 Nov 2010
Posts: 15
Location: Toronto, ON
Schools: INSEAD, ISB, NUS
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

04 Oct 2011, 08:59
How can you solve with A? I was inclining more towards E.
Manager
Joined: 20 Aug 2011
Posts: 128
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

04 Oct 2011, 09:12
hashjax wrote:
How can you solve with A? I was inclining more towards E.

Add equations in 1

x^2 − xy = 28 & 3xy + y^2 = 72.

x^2+2xy+y^2=100
(x+y)^2=100

Sufficient

Makes sense?

kaliaabhishek wrote:
D

Statement 2 gives us two values. Hence insufficient
_________________

Hit kudos if my post helps you.
You may send me a PM if you have any doubts about my solution or GMAT problems in general.

SVP
Joined: 14 Apr 2009
Posts: 2273
Location: New York, NY
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

04 Oct 2011, 13:55
Quote:
Statement 2 gives us two values. Hence insufficient

Actually statement 2 gives only 1 value.

(x + y)^2 = 100

it cannot = -100
because the left side is a square - which means the right side must be a positive number and cannot be negative.

If the square weren't there - then you can say there are 2 possible values: +100 and -100. But since the question asks for what (x+y)^2 is - we know that it must be the positive version.

Therefore, either (1) or (2) would work. Answer would be (D).
Intern
Joined: 03 Oct 2011
Posts: 2
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

04 Oct 2011, 16:15
Let x+y = -10, then (x+y)^4 = 10000. So A it is.

Cheers,

AJ

Posted from my mobile device
Manager
Joined: 20 Aug 2011
Posts: 128
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

04 Oct 2011, 17:43
gmatpill wrote:
Quote:
Statement 2 gives us two values. Hence insufficient

Actually statement 2 gives only 1 value.

(x + y)^2 = 100

it cannot = -100
because the left side is a square - which means the right side must be a positive number and cannot be negative.

If the square weren't there - then you can say there are 2 possible values: +100 and -100. But since the question asks for what (x+y)^2 is - we know that it must be the positive version.

Therefore, either (1) or (2) would work. Answer would be (D).

Yes, you're right. I missed it. Sorry all.

It is indeed.
Moral of the story- Read the question properly
_________________

Hit kudos if my post helps you.
You may send me a PM if you have any doubts about my solution or GMAT problems in general.

Manager
Status: Next engagement on Nov-19-2011
Joined: 12 Jan 2011
Posts: 60
Location: New Delhi, India
Schools: IIM, ISB, & XLRI
WE 1: B.Tech (Information Technology)
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

15 Oct 2011, 09:45
"D"

1. X^2 - XY = 28
Y^2 + 3XY = 72
________________
X^2 + Y^2 + 2XY = 100

=> (X + Y)^2 = 100
SUFFICIENT.

2. (X + Y)^4 = 10,000
=> ((X+Y)^2)^2 = ((10)^2)^2
=> (X+Y)^2 = 100
SUFFICIENT
_________________

GMAT is an addiction and I am darn addicted

Preparation for final battel:
GMAT PREP-1 750 Q50 V41 - Oct 16 2011
GMAT PREP-2 710 Q50 V36 - Oct 22 2011 ==> Scored 50 in Quant second time in a row
MGMAT---- -1 560 Q28 V39 - Oct 29 2011 ==> Left Quant half done and continued with Verbal. Happy to see Q39

My ongoing plan: http://gmatclub.com/forum/550-to-630-need-more-to-achieve-my-dream-121613.html#p989311

Appreciate by kudos !!

Manager
Joined: 06 Feb 2011
Posts: 61
WE: Information Technology (Computer Software)
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

03 Nov 2011, 06:41
(1) Add both the eq.
(2) (x + y)^4 = 10,000 means (x + y)^2 can be 100 or -100, but (x + y)^2 being a square we can have only 100.
Hence Ans = D
Math Expert
Joined: 02 Sep 2009
Posts: 50670
What is the value of (x + y)^2?  [#permalink]

### Show Tags

17 Jul 2016, 07:30
What is the value of (x + y)^2?

(1) x^2 − xy = 28 and 3xy + y^2 = 72.

Sum the equations: x^2 + 2xy + y^2 = 100 --> (x + y)^2 = 100. Sufficient.

(2) (x + y)^4 = 10,000 --> take the square root: (x + y)^2 = 100. Sufficient. Notice that (x + y)^2 cannot be -100 because the square of a number cannot be negative.

_________________
Intern
Joined: 13 Jun 2016
Posts: 19
What is the value of (x + y)^2?  [#permalink]

### Show Tags

03 Sep 2016, 03:16
Bunuel , a basic question if you don't mind clarifying;

For (x + y)^4 , you can simply take the square root .... but hypothetically if (x + y)^2 = 10,000 you can't simply take the square root? you'll have to FOIL it out?

For example, I've seen some Qs where if (x + y)^2 = 100 .... (x + y) does not equal +- 10, it's x^2 + 2xy + y^2 = 100

But (x + y)^4, you're able to simply take the square root?

Just really confused about this concept. Appreciate all the help. thank you
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3615
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

03 Sep 2016, 04:26
xnthic wrote:
Bunuel , a basic question if you don't mind clarifying;

For (x + y)^4 , you can simply take the square root .... but hypothetically if (x + y)^2 = 10,000 you can't simply take the square root? you'll have to FOIL it out?

For example, I've seen some Qs where if (x + y)^2 = 100 .... (x + y) does not equal +- 10, it's x^2 + 2xy + y^2 = 100

But (x + y)^4, you're able to simply take the square root?

Just really confused about this concept. Appreciate all the help. thank you

See, I have $$(x + y)^4 = 10000$$

Now, if take the fourth root of the above equation, we will get (x+y) = 10 or (x+y) = - 10

So, we have two values for (x+y).

But NOTICE, the question stem asks the value of $$(x + y)^2$$, so whichever value of (x+y) when squared will always give 100.

Hence, we have a single value of (x+y) => The statement is sufficient.

Even if we had $$(x + y)^2 = 10000$$, we would have got the value of (x+y) either equal to 100 and -100. But remember question is NOT asking you the value of (x+y), it is asking the value of $$(x+y)^2$$

I hope its clear now.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.

Intern
Joined: 13 Jun 2016
Posts: 19
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

03 Sep 2016, 23:26
Thanks for clarifying ! I definitely get the answer and logic.

However, related to this about a basic math concept. My question is simply: in other math situations, is it allowed to simply take square root (x + y)^2 which gives +-10 OR is that not allowed and you'd have to foil out the algebraic expression?

Thanks for the help !

Posted from my mobile device
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3615
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

03 Sep 2016, 23:35
1
xnthic wrote:
Thanks for clarifying ! I definitely get the answer and logic.

However, related to this about a basic math concept. My question is simply: in other math situations, is it allowed to simply take square root (x + y)^2 which gives +-10 OR is that not allowed and you'd have to foil out the algebraic expression?

Thanks for the help !

Posted from my mobile device

Yes, it is allowed to take the square root on both the sides of the equation. But make sure both signs(+ and -) are considered.

Go through the below link to get more clarity on this concept.

_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.

Intern
Status: Working
Affiliations: IITK, KOEL
Joined: 30 Nov 2014
Posts: 6
Location: India
Concentration: International Business, Real Estate
Schools: ISB '19, NUS '18
GPA: 2.8
WE: Design (Manufacturing)
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

03 Nov 2016, 09:57
D
Both options are individually sufficient
1) adding both equations,
(x+y)^2=100
Sufficient
2) (x+y)^2 =100
[*can't be the negative solution as it is a square]
Sufficient

Sent from my HTC One E9PLUS dual sim using GMAT Club Forum mobile app
Current Student
Joined: 26 Jan 2016
Posts: 105
Location: United States
GPA: 3.37
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

03 Nov 2016, 11:33
What is the value of (x + y)^2?

(1) x^2 − xy = 28 and 3xy + y^2 = 72.

(2) (x + y)^4 = 10,000

(1) x^2 − xy = 28 and 3xy + y^2 = 72.

I first factored out (x+y)²=x²_2xy+y²

x²-xy=28
x²=28+xy

3xy + y² = 72.

y²=72-3xy

if we substitute the values back into the equation we get

28+xy+2xy+72-3xy

From here the variables cancel out and we get =100

(2) (x + y)^4 = 10,000
Take the square root of both sides
(x+y)²=100

D
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1370
Location: India
Re: What is the value of (x + y)^2?  [#permalink]

### Show Tags

25 Dec 2017, 22:20
GMATmission wrote:
What is the value of (x + y)^2?

(1) x^2 − xy = 28 and 3xy + y^2 = 72.

(2) (x + y)^4 = 10,000

We need to find (x + y)^2. And (x + y)^2 = x^2 + y^2 + 2xy

(1) We are given two equations:
x^2 − xy = 28 and 3xy + y^2 = 72. If we add these two equations, we get: x^2 - xy + 3xy + y^2 = 28+72 OR x^2 + y^2 + 2xy = 100. This is sufficient.

(2) (x + y)^4 = 10,000 Or ((x + y)^2)^2 = (100)^2
This gives us (x + y)^2 = 100
This is also sufficient. (We should note that though 10000 is also the square of -100, we cannot write -100 on RHS as LHS is (x + y)^2, and square of anything cannot be negative)

Re: What is the value of (x + y)^2? &nbs [#permalink] 25 Dec 2017, 22:20
Display posts from previous: Sort by

# What is the value of (x + y)^2?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 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®.