Fast way to do this?

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fangtray: Master | Next Rank: 500 Posts; Posts: 273; Joined: Thu Sep 08, 2011 6:50 amFollowed by: 3 members; Thanked: 5 times

by fangtray » Tue Apr 24, 2012 6:30 am

If x does not equal -y, is (x-y)/(x+y) > 1?

1. x > 0
2. y < 0

got the right answer here, but took me too long. i plugged in answers to get the right one. Wondering if there was a faster way to do this one. thanks.

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Source: Beat The GMAT — Data Sufficiency | Tue Apr 24, 2012 6:30 am

shantanu86: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Sun Mar 11, 2012 8:57 pmFollowed by: 1 member; Location: India; Thanked: 16 times

by shantanu86 » Tue Apr 24, 2012 6:46 am

fangtray wrote:If x does not equal -y, is (x-y)/(x+y) > 1?

1. x > 0
2. y < 0

got the right answer here, but took me too long. i plugged in answers to get the right one. Wondering if there was a faster way to do this one. thanks.

IMO the answer is E.. both together not sufficient.

Here is the explanation-
is (x-y)/(x+y)>1 ?
=> (x-y)/(x+y) - 1 > 0 ?
=> -2y/(x+y) > 0 ?
=> y/(x+y) < 0 ?

Now, if you analyze the last equation.. y & (x+y) must be of different signs.
[A] If x>0 it tells nothing abt signs of y and (x+y)
If y< 0 .. sign of (x+y) is still unknown
[B} & [A] together.. if y is -ve and x is +ve still for (x+y) to be positive |x| > |y|.. this info is not given

Hence both together not sufficient.

Hope it helps!!

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Apr 24, 2012 7:53 am

fangtray wrote:If x does not equal -y, is (x-y)/(x+y) > 1?

1. x > 0
2. y < 0

got the right answer here, but took me too long. i plugged in answers to get the right one. Wondering if there was a faster way to do this one. thanks.

This problem seems to be about POSITIVE VS. NEGATIVE.
Try numbers that are at varying DISTANCES FROM 0.

If x=2 and y=-1, then (x-y)/(x+y) = 3, which is greater than 1.
If x=1 and y=-2, then (x-y)/(x+y) = -3, which is not greater than 1.
Since each combination satisfies both statements, and in the first case (x-y)/(x+y)>1, and in the second case (x-y)/(x+y)<1, the two statements combined are INSUFFICIENT.

The correct answer is E.

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spartacus1412: Master | Next Rank: 500 Posts; Posts: 110; Joined: Wed Feb 22, 2012 11:28 pmFollowed by: 1 member; Location: India; Thanked: 13 times

by spartacus1412 » Wed Apr 25, 2012 2:35 am

E it is

Its do or die this time!
Practise, practise and practise.

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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

by Stuart@KaplanGMAT » Wed Apr 25, 2012 9:04 am

fangtray wrote:If x does not equal -y, is (x-y)/(x+y) > 1?

1. x > 0
2. y < 0

got the right answer here, but took me too long. i plugged in answers to get the right one. Wondering if there was a faster way to do this one. thanks.

You can use your knowledge of concepts to solve rather than plugging in numbers (although picking numbers is also a great way to go).

First, let's ask ourselves when we'll get a YES answer to the question.

First, we need the sign of the top and bottom to be the same (if the signs were different, the result would be negative, giving us an automatic "NO").

Second, we need the absolute value of the numerator to be greater than the absolute value of the denominator (otherwise we'll get a fraction, giving us an automatic "NO").

To the statements!

Each of (1) and (2) is clearly insufficient alone, since each only gives info about one of the two variables, so let's jump right to combination.

If x > 0 and y < 0, then x > 0 > y.

So, we know that:

x - y = (+) - (-) = +; and
x + y = (+) + (-) = it depends on which has a greater magnitude (if x=10 and y=-1, then it's positive; if x=1 and y=-10, then it's negative).

So, we could have:
+/+ which gives a potential YES answer; or
+/- which gives a definite NO answer.

Maybe YES, maybe NO - insufficient, choose E.

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