Please help ..

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NehaBhandari: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Mon Nov 17, 2008 12:08 pm; Thanked: 1 times

by NehaBhandari » Sat Dec 13, 2008 2:42 pm

Is x+y>0

1)x(x+y)>0
2)y(x+y)>0

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Source: Beat The GMAT — Data Sufficiency | Sat Dec 13, 2008 2:42 pm

dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Sat Dec 13, 2008 3:06 pm

Is x+y>0

So is x > -y

1)x(x+y)>0

x^2 + xy > 0
X^2 > -xy
x > -y

SUFF

2)y(x+y)>0

yx + y^2 >0
yx > -y^2
x > -y

SUFF

I choose D.

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NehaBhandari: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Mon Nov 17, 2008 12:08 pm; Thanked: 1 times

by NehaBhandari » Sat Dec 13, 2008 3:16 pm

if u take x=-5 and y=-1 then it satisfies both eqns x+y<0
x=5 y=1 x+y>0

I think its E..
I dont have the OA myself..

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nitintahiliani: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Mon Nov 12, 2007 4:51 pm

by nitintahiliani » Sat Dec 13, 2008 3:48 pm

Thanks Dmateer ,
But i see a flaw in this logic . You cannot cancel x from both sides without having an impact on sign of the equation. It would depend from equation to equation , but doing this
[ X^2 > -xy
x > -y
] and maintaining the sign i.e > may not be correct. Actually i feel the answer should be E .
1)x(x+y)>0
Either [ x is > 0 and (x+y) > 0] OR [x < 0 and (x +y) < 0].
if we consider from this the result could be anything.
Insufficient.
2. y(x+y) > 0
Either [ y is > 0 and (x+y) > 0] OR [y < 0 and (x +y) < 0].
Insufficient.

COMBINED
x(x+y) + y(x+y) > 0 i.e (x+y)(x+y) > 0 which again is inconclusive cause (x+y) can be positive or negative.

Any comments pls.

I choose E.

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Dec 13, 2008 3:54 pm

x^2 + xy > 0
X^2 > -xy
x > -y

Dmateer,

I dont think we can divide by x since we dont know the sign of x.If x is negative then the inequality reverses.

Stmt I

x(x+y)>0
x^2+xy>0

x=1 y=1
x+y>0 and x(x+y)>0
yes

x=-2 y=-1

x(x+y) > 0
x+y < 0

INSUFF

Stm II
Similar to above

INSUFF

Stmt I and II together

x(x+y)>0
y(x+y)>0

Add inequalities facing same direction:

x^2+xy+y^2+xy>0

(x+y)^2>0

|x+y|>0

x>-y or

-x-y>0

-x> y

Divide by -1 inequality reverse

x <-y

Dont know for sure anyhting about the signs of x and y still or their magnitudes(values)

Choose E)

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dmateer25: Community Manager; Posts: 1049; Joined: Sun Apr 06, 2008 5:15 pmFollowed by: 27 members; Location: Pittsburgh, PA; Thanked: 113 times; GMAT Score:710

by dmateer25 » Sat Dec 13, 2008 4:17 pm

Thanks for correcting me!

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Dec 13, 2008 4:19 pm

Thanks for correcting me!

No probs! Keep up the good work (I have seen some excellent solutions from u for various other problems)

Good luck!

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: Please help ..

by Stuart@KaplanGMAT » Sat Dec 13, 2008 5:12 pm

NehaBhandari wrote:Is x+y>0

1)x(x+y)>0
2)y(x+y)>0

Let's use number properties.

When the product of two terms is positive, then both are positive or both are negative. Accordingly:

(1) either x and (x+y) are both positive or both negative... insufficient.

(2) either y and (x+y) are both positive or both negative.. insufficient.

Together: x and y could both be positive or both be negative.. insufficient.

Choose (E).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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ronniecoleman: Legendary Member; Posts: 546; Joined: Sun Nov 16, 2008 11:00 pm; Location: New Delhi , India; Thanked: 13 times

by ronniecoleman » Sun Dec 14, 2008 4:56 am

IMO E

Admission champion, Hauz khaz
011-27565856

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pbanavara: Master | Next Rank: 500 Posts; Posts: 279; Joined: Wed Sep 24, 2008 8:26 am; Location: Portland, OR; Thanked: 6 times

by pbanavara » Sun Dec 14, 2008 3:17 pm

dmateer25 wrote:Is x+y>0

So is x > -y

1)x(x+y)>0

x^2 + xy > 0
X^2 > -xy
x > -y

SUFF

2)y(x+y)>0

yx + y^2 >0
yx > -y^2
x > -y

SUFF

I choose D.

This is exactly how GMAT tricks us. By solving the equatins like this, we tend to forget that x^2 could also be -x * -x. Thanks for posting this dmateer

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