BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Is x sq + y sq < 6?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Newbie | Next Rank: 10 Posts
Posts: 5
Joined: Sun May 16, 2010 2:39 am
Location: Bangalore
GMAT Score:580

Is x sq + y sq < 6?

by angxif » Fri May 21, 2010 10:55 am
Is x^2+ y^2> 6?
(1) (x+y)^2>6
(2) xy=2

I think the answer is B.
1) (x+y)^2- x^2+y^2+2xy 2xy could be negative or positive hence insuff
2)for xy to be 2 it can either be -1x-2 or -2x-1 or 2x1 or 1x2.
In all the above cases x^2+y^2will be less than 6 so B is suff.

OA[spoiler]E

Help!
Top
Source: — Data Sufficiency |
Junior | Next Rank: 30 Posts
Posts: 16
Joined: Tue Apr 06, 2010 12:19 pm
Location: US
Thanked: 1 times

by kel2010 » Fri May 21, 2010 11:53 am
STATEMENT I

(x+y)^2>6
take (i) x=1 and y=2
(ii) x2 and y=2
not sufficient

statement II
xy=2

take (i)x=1 and y=2
(ii) x=1/2 and y=4
so not sufficient

combining
take x=1/2 and y=4
(ii) x=-1 and y=-2
so not sufficient

hence ans is E.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 106
Joined: Mon Sep 28, 2009 9:29 am
Location: Boston, MA
Thanked: 26 times
Followed by:2 members
GMAT Score:700

by asamaverick » Fri May 21, 2010 12:01 pm
angxif wrote:Is x^2+ y^2> 6?
(1) (x+y)^2>6
(2) xy=2

I think the answer is B.
1) (x+y)^2- x^2+y^2+2xy 2xy could be negative or positive hence insuff
2)for xy to be 2 it can either be -1x-2 or -2x-1 or 2x1 or 1x2.
In all the above cases x^2+y^2will be less than 6 so B is suff.

OA[spoiler]E

Help!
Your reasoning in support of (2) is flawed. You have considered only integers. Take for example x=4 & y = ½. Here xy = 2 and x^2 + y^2 = 16.25 > 6.
Hence (2) alone is not sufficient.

When (1) & (2) are combined.
(x+y)^2 > 6 and xy = 2.
X^2 + y^2 = (x+y)^2 - 2xy = [>6] - 4.

The first part of this equation (even though > 6) is not sufficiently known. It could be 7 or even 12 giving two different values of x^2 + y^2. Hence E is the correct answer.
Top
Post new topic Post Reply
• Page 1 of 1