NEW HERE? LEARN MORE
closeclose
Last visit was: 28 Apr 2024, 16:36 It is currently 28 Apr 2024, 16:36
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Is xy positive? (1) (x-y)^2 = 8 (2) (x+y)^2 = 10

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92977
Own Kudos [?]: 619713 [4]
Given Kudos: 81613
Send PM
CAT Tests Forum Quiz Mode
Is xy positive? (1) (x-y)^2 = 8 (2) (x+y)^2 = 10 [#permalink] New post   26 May 2019, 04:22
4
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

71% (01:54) correct 29% (02:12) wrong based on 136 sessions
Hide Show timer Statistics
Is xy positive?

(1) (x-y)^2 = 8
(2) (x+y)^2 = 10
ShowHide Answer
Official Answer
C
User avatar
L
AkshdeepS
VP
VP
Joined: 13 Apr 2013
Status:It's near - I can see.
Posts: 1479
Own Kudos [?]: 1603 [2]
Given Kudos: 1002
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE:Engineering (Real Estate)
Send PM
Reviews Badge
Is xy positive? (1) (x-y)^2 = 8 (2) (x+y)^2 = 10 [#permalink] New post   Updated on: 26 May 2019, 10:01
2
Kudos
Bunuel wrote:
Is xy positive?

(1) (x-y)^2 = 8
(2) (x+y)^2 = 10


Question : Is xy > 0?

Is x & y > 0 Or Is x & y < 0 ?

St 1 : \(x - y = \sqrt{8}\)

x - y = 2.8 approx

If 2.8 - 0 = 2.8 , then xy = 0 --- Not positive

If 5.6 - 2.8 = 2.8, then xy > 0 ---- Positive

Not sufficient

St 2 :

The same way statement 2 can be checked and the answer would be ---- Not sufficient

From 1 and 2 we get,

x^2 + y^2 - 2xy = 8 ------------ (I)

x^2 + y^2 + 2xy = 10 ------------ (II)

Multiplying (II) with -1 and then add I & II,

-4xy = -2

xy = 2/4 = 1/2

Hence SUFFICIENT, IMO (C) ------ xy > 0

Originally posted by AkshdeepS on 26 May 2019, 05:04.
Last edited by AkshdeepS on 26 May 2019, 10:01, edited 3 times in total.
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8022
Own Kudos [?]: 4101 [1]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User
Is xy positive? (1) (x-y)^2 = 8 (2) (x+y)^2 = 10 [#permalink] New post   26 May 2019, 10:13
1
Kudos
Bunuel wrote:
Is xy positive?

(1) (x-y)^2 = 8
(2) (x+y)^2 = 10


#1
(x-y)=√8; 2√2
so
x=6√2 and y=4√2
or x=√2 and y=-√2
insufficient
#2
x+y=√10
x=2√10 & y = -√10
or x=0 & y=√10
insufficient
from 1 & 1
open brackets
we get
x^2+y^2-2xy=8
and x^2+y^2+2xy=10
subtract
-4xy=(-)2
xy=1/2
IMO C
User avatar
B
a1997g
Intern
Intern
Joined: 09 Dec 2018
Posts: 13
Own Kudos [?]: 25 [1]
Given Kudos: 22
Location: India
Concentration: Strategy, Marketing
GPA: 2.77
WE:Accounting (Accounting)
Send PM
Re: Is xy positive? (1) (x-y)^2 = 8 (2) (x+y)^2 = 10 [#permalink] New post   26 May 2019, 14:44
1
Kudos
Bunuel wrote:
Is xy positive?

(1) (x-y)^2 = 8
(2) (x+y)^2 = 10




Statement 1 : x - y = underoot 8 . This value could either be positive OR negative . Therefore , this statement is insufficient.

Statement 2 : x + y = underoot 10. This value could either be positive OR negative . Therefore , this statement is insufficient.

Combined , Now either we can solve the entire thing or you can see that since we have 2 variables and 2 equations in which x square and y square can be eliminated ,they can be solved for the value of xy. Hence ANSWER : C
User avatar
G
m1033512
Senior Manager
Senior Manager
Joined: 25 Feb 2019
Posts: 279
Own Kudos [?]: 217 [0]
Given Kudos: 32
Send PM
Reviews Badge
Re: Is xy positive? (1) (x-y)^2 = 8 (2) (x+y)^2 = 10 [#permalink] New post   26 May 2019, 05:44
statement 1 alone mot sufficient


staement 2 alone also not sufficient



now adding 1 and 2 we get ,

2 (x^2+y^2 )= 18
x^2+y^2 = 9

putting this in 1 , we get

2xy = 1 xy= 1/2 >0


so IMO C

Posted from my mobile device
User avatar
P
LeoN88
BSchool Moderator
Joined: 08 Dec 2013
Posts: 686
Own Kudos [?]: 516 [0]
Given Kudos: 227
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '23
GMAT 1: 630 Q47 V30
WE:Operations (Non-Profit and Government)
Send PM
Reviews Badge
Re: Is xy positive? (1) (x-y)^2 = 8 (2) (x+y)^2 = 10 [#permalink] New post   26 May 2019, 06:31
Bunuel wrote:
Is xy positive?

(1) (x-y)^2 = 8
(2) (x+y)^2 = 10


From both statement 1 & 2 independently we can't deduce the sign of x and y.

Let's take 1+2 together.

(x-y)^2 - (x+y)^2 = 64-100=-36
(2x)(-2y) = -36
xy= 9. C
User avatar
B
MonishBhawale
Intern
Intern
Joined: 15 Jun 2021
Posts: 27
Own Kudos [?]: 4 [0]
Given Kudos: 259
Send PM
CAT Tests
Re: Is xy positive? (1) (x-y)^2 = 8 (2) (x+y)^2 = 10 [#permalink] New post   18 Sep 2023, 21:20
Bunuel wrote:
Is xy positive?

(1) (x-y)^2 = 8
(2) (x+y)^2 = 10


st 1 (x2-2xy+y2) = 8
XY can be positive or negative

st 2 x2+2xy+y2 = 10
XY can be positive or negative
subtract 1 and 2
-4xy = -2
xy = 1/2
ans C
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11183
Own Kudos [?]: 32023 [0]
Given Kudos: 291
Send PM
Reviews Badge
Re: Is xy positive? (1) (x-y)^2 = 8 (2) (x+y)^2 = 10 [#permalink] New post   18 Sep 2023, 23:09
Expert Reply
Is xy positive?

Basically, the question is whether x and y have same sign.

(1) (x-y)^2 = 8
As we have square, we cannot say anything about sign.
\(x=\sqrt{2},y=-\sqrt{2}\) will satisfy equation and xy<0
\(x=3\sqrt{2},y=\sqrt{2}\) will satisfy equation and xy>0
Insufficient

(2) (x+y)^2 = 10
As we have square, we cannot say anything about sign.
\(x=\sqrt{10},y=-2\sqrt{10}\) will satisfy equation and xy<0
\(x=\sqrt{10}/2,y=\sqrt{10}/2\) will satisfy equation and xy>0
Insufficient


Combined
\((x-y)^2=8……x^2+y^2-2xy=8\)…(1)
\((x+y)^2=8……x^2+y^2+2xy=10\)..(2)
Subtract (1) from (2) => \(4xy=2…..xy=\frac{1}{2}\)
Sufficient


C
GMAT Club Bot
gmatclubot
Re: Is xy positive? (1) (x-y)^2 = 8 (2) (x+y)^2 = 10 [#permalink]
18 Sep 2023, 23:09
Moderator:
Bunuel
Math Expert
92977 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions