Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 04 Jul 2015, 00:45

### 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 June
Open Detailed Calendar

# Is xy < 1 ? (I) x + y = 1 (II) x^2 + y^2 = 1

Author Message
TAGS:
SVP
Joined: 24 Sep 2005
Posts: 1891
Followers: 12

Kudos [?]: 159 [0], given: 0

Is xy < 1 ? (I) x + y = 1 (II) x^2 + y^2 = 1 [#permalink]  12 Mar 2006, 09:28
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Is xy < 1 ?

(I) x + y = 1

(II) x^2 + y^2 = 1
SVP
Joined: 14 Dec 2004
Posts: 1706
Followers: 1

Kudos [?]: 58 [0], given: 0

Laxie buddy, I'm scared of your problems

I'm getting D on this!
SVP
Joined: 24 Sep 2005
Posts: 1891
Followers: 12

Kudos [?]: 159 [0], given: 0

vivek123 wrote:
Laxie buddy, I'm scared of your problems

I'm getting D on this!

hik, this is not my problem. I just picked it from somewhere
Btw, how is Tanvi, buddy?!!! ^.^ ....I'm looking forward to her new pix~
Manager
Joined: 20 Feb 2006
Posts: 213
Followers: 1

Kudos [?]: 5 [0], given: 0

I too am for D.
Statement 2 is definitely sufficient.
Statement 1 is also sufficient.
Manager
Joined: 20 Mar 2005
Posts: 201
Location: Colombia, South America
Followers: 1

Kudos [?]: 6 [0], given: 0

Re: DS inequality [#permalink]  12 Mar 2006, 14:23
laxieqv wrote:
Is xy < 1 ?

(I) x + y = 1

(II) x^2 + y^2 = 1

the thing with D is that x or y can be negative (not both) then xy would be negative

like any value on the second and third quadrant of a cartesian plane

that's why I wouldn't pick D, I go with A on this one
SVP
Joined: 24 Sep 2005
Posts: 1891
Followers: 12

Kudos [?]: 159 [0], given: 0

Can anyone give a numerical explanation?!
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
Location: Singapore
Followers: 23

Kudos [?]: 194 [0], given: 0

(1) Can be:
x = 1/2, y = 1/2 xy < 1
x = 2, y = -1 xy < 1

No other case will result in xy < 1 and still satisfy x+y=1 (at least I can't think of any right now)

Sufficient

(2) Can be x = 1, y = 0 xy < 1. Can be x = 1/sqrt(2), y = 1/sqrt(2)xy > 1. Insufficient.

I go with A
SVP
Joined: 14 Dec 2004
Posts: 1706
Followers: 1

Kudos [?]: 58 [0], given: 0

ywilfred wrote:
(1) Can be:
x = 1/2, y = 1/2 xy < 1
x = 2, y = -1 xy < 1

No other case will result in xy < 1 and still satisfy x+y=1 (at least I can't think of any right now)

Sufficient

(2) Can be x = 1, y = 0 xy < 1. Can be x = 1/sqrt(2), y = 1/sqrt(2)xy > 1. Insufficient.

I go with A

Wilfred,

If x = 1/sqrt(2), y = 1/sqrt(2)
then xy = [1/sqrt(2)] * [1/sqrt(2)] = 0.5 < 1.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
Location: Singapore
Followers: 23

Kudos [?]: 194 [0], given: 0

oops
Senior Manager
Joined: 22 Nov 2005
Posts: 478
Followers: 2

Kudos [?]: 3 [0], given: 0

laxieqv wrote:
vivek123 wrote:
Laxie buddy, I'm scared of your problems

I'm getting D on this!

hik, this is not my problem. I just picked it from somewhere
Btw, how is Tanvi, buddy?!!! ^.^ ....I'm looking forward to her new pix~

lexi what is the source. I also want to solve these problems...
SVP
Joined: 24 Sep 2005
Posts: 1891
Followers: 12

Kudos [?]: 159 [0], given: 0

Re: DS inequality [#permalink]  12 Mar 2006, 21:05
laxieqv wrote:
Is xy < 1 ?

(I) x + y = 1

(II) x^2 + y^2 = 1

(1) x+y= 1 --> x= 1-y
---> xy= (1-y)*y= y- y^2 = - ( y^2 -y + 1/4) +1/4 = - ( y-1/2)^2 + 1/4
Because - (y-1/2) ^2 <= 0 ---> - (y-1/2) ^2 +1/4 <= 1/4 < 1
---> suff

(2) x^2+y^2 - 2xy = (x-y)^2 >= 0 ---> x^2+y^2 >= 2xy ---> 2xy<=1 -----> xy<=1/2< 1
---> suff

OA is C.

Good job, buddies~
SVP
Joined: 14 Dec 2004
Posts: 1706
Followers: 1

Kudos [?]: 58 [0], given: 0

Re: DS inequality [#permalink]  12 Mar 2006, 21:35
laxieqv wrote:
laxieqv wrote:
Is xy < 1 ?

(I) x + y = 1

(II) x^2 + y^2 = 1

(1) x+y= 1 --> x= 1-y
---> xy= (1-y)*y= y- y^2 = - ( y^2 -y + 1/4) +1/4 = - ( y-1/2)^2 + 1/4
Because - (y-1/2) ^2 <= 0 ---> - (y-1/2) ^2 +1/4 <= 1/4 < 1
---> suff

(2) x^2+y^2 - 2xy = (x-y)^2 >= 0 ---> x^2+y^2 >= 2xy ---> 2xy<=1 -----> xy<=1/2< 1
---> suff

OA is C.
Good job, buddies~

You mean "D"?
SVP
Joined: 24 Sep 2005
Posts: 1891
Followers: 12

Kudos [?]: 159 [0], given: 0

Re: DS inequality [#permalink]  12 Mar 2006, 21:46
vivek123 wrote:
laxieqv wrote:
laxieqv wrote:
Is xy < 1 ?

(I) x + y = 1

(II) x^2 + y^2 = 1

(1) x+y= 1 --> x= 1-y
---> xy= (1-y)*y= y- y^2 = - ( y^2 -y + 1/4) +1/4 = - ( y-1/2)^2 + 1/4
Because - (y-1/2) ^2 <= 0 ---> - (y-1/2) ^2 +1/4 <= 1/4 < 1
---> suff

(2) x^2+y^2 - 2xy = (x-y)^2 >= 0 ---> x^2+y^2 >= 2xy ---> 2xy<=1 -----> xy<=1/2< 1
---> suff

OA is C.
Good job, buddies~

You mean "D"?

Ah,hik, this is the consequence of staying up late till 4 am

OA is D.
VP
Joined: 29 Dec 2005
Posts: 1348
Followers: 7

Kudos [?]: 37 [0], given: 0

Re: DS inequality [#permalink]  13 Mar 2006, 09:03
laxieqv wrote:
Is xy < 1 ?
(I) x + y = 1
(II) x^2 + y^2 = 1

good question and good discussions.
VP
Joined: 20 Sep 2005
Posts: 1021
Followers: 3

Kudos [?]: 27 [0], given: 0

Re: DS inequality [#permalink]  13 Mar 2006, 10:11
D it is. I freaked out for a moment when you posted the OA is C.

laxieqv wrote:
vivek123 wrote:
laxieqv wrote:
laxieqv wrote:
Is xy < 1 ?

(I) x + y = 1

(II) x^2 + y^2 = 1

(1) x+y= 1 --> x= 1-y
---> xy= (1-y)*y= y- y^2 = - ( y^2 -y + 1/4) +1/4 = - ( y-1/2)^2 + 1/4
Because - (y-1/2) ^2 <= 0 ---> - (y-1/2) ^2 +1/4 <= 1/4 < 1
---> suff

(2) x^2+y^2 - 2xy = (x-y)^2 >= 0 ---> x^2+y^2 >= 2xy ---> 2xy<=1 -----> xy<=1/2< 1
---> suff

OA is C.
Good job, buddies~

You mean "D"?

Ah,hik, this is the consequence of staying up late till 4 am

OA is D.
Manager
Joined: 20 Feb 2006
Posts: 213
Followers: 1

Kudos [?]: 5 [0], given: 0

Vivek and Laxie, did you give your GMAT already? Just curious on seeing the number of replies you both posted.
SVP
Joined: 14 Dec 2004
Posts: 1706
Followers: 1

Kudos [?]: 58 [0], given: 0

chuckle wrote:
Vivek and Laxie, did you give your GMAT already? Just curious on seeing the number of replies you both posted.

Me? Not yet! Need to face the ghost sometime!
Manager
Joined: 20 Feb 2006
Posts: 213
Followers: 1

Kudos [?]: 5 [0], given: 0

oh..ok.. you are very accurate. So, I thought you already took it.
Similar topics Replies Last post
Similar
Topics:
Is xy<1? (I) x + y = 1 (II) x^2 + y^2 = 1 4 11 Dec 2008, 14:44
0<X<Y What does (X+Y)^2/(X-Y)^2 = (1) X^2 +Y^2 = 3XY 9 13 May 2007, 15:50
If x = 3y, is x^2 > y^2? 1. y+x < x-y 2. x^2 = 9 y^2 4 14 Sep 2006, 05:41
What is the value of X^2 -Y^2? 1. x+y=2x 2. x+y=0 I 4 17 Jul 2006, 20:59
Is 1/x < 1/y for integers x,y ? (1) x^2 + y^2 = 25 (2) xy 7 04 Nov 2005, 18:05
Display posts from previous: Sort by