Equation

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salma: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sat Nov 03, 2007 5:54 pm

by salma » Thu Jan 24, 2008 3:27 am

Hi,
Can you plz help me with this question:
Is X+Y>0
1)X^2 - Y^2>1
2)X/Y +1>0

The actual answer is that the 2 statements together are not sufficient!!!!
My answer was B: from statement 2 we can get X/Y > -1, then X>-Y, then X+Y>0. Why is it wrong???

Thanks

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Source: Beat The GMAT — Data Sufficiency | Thu Jan 24, 2008 3:27 am

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: Equation

by Stuart@KaplanGMAT » Thu Jan 24, 2008 7:57 am

salma wrote:Hi,
Can you plz help me with this question:
Is X+Y>0
1)X^2 - Y^2>1
2)X/Y +1>0

The actual answer is that the 2 statements together are not sufficient!!!!
My answer was B: from statement 2 we can get X/Y > -1, then X>-Y, then X+Y>0. Why is it wrong???

Thanks

If we don't know the sign of a variable, we have to be very careful about manipulating inequalities.

Your first step was fine:

x/y + 1 > 0 ===> x/y > -1

However, to do the next step what you're actually doing is multiplying both sides by "y". If y is negative, that will flip the inequality.

So, if y is positive, we get:

x > -y
x + y > 0

However, if y is negative, we get:

x < -y
x + y < 0

Therefore, statement (2) is insufficient.

Statement (1) can be simplified as:

(x+y)(x-y) > 1

so, both terms could be + or both could be -. Also insufficient.

Even after combining, x+y could be greater or less than 0, so not enough information: choose (E).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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blue_lotus: Senior | Next Rank: 100 Posts; Posts: 50; Joined: Tue Jan 08, 2008 9:22 am; Thanked: 7 times

by blue_lotus » Thu Jan 24, 2008 8:04 am

I would say the correct answer would be E.
Both the statement is insufficent to conclude a finite answer.

And for your clarification when you had X/Y >-1, you cant multiply Y on
Both sides as we don’t know whether Y is +ve or -ve.
For +ve Y, X>-Y and for -ve Y, X <-Y [property of inequalities]

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Prasanna: Master | Next Rank: 500 Posts; Posts: 418; Joined: Mon Feb 26, 2007 6:41 pm; Thanked: 24 times

by Prasanna » Thu Jan 24, 2008 3:34 pm

Moved to DS section

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