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# Are x and y both positive? 1) 2x -2y = 1 2) x/y > 1 I

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Senior Manager
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Are x and y both positive? 1) 2x -2y = 1 2) x/y > 1 I [#permalink]

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22 Oct 2006, 22:10
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Are x and y both positive?

1) 2x -2y = 1
2) x/y > 1

I actually don't agree with the GMATPREP answer. But again maybe I didn't interpret the words right. Using 2 numbers of hte same sign, either positive at same time or both negative at same time and I was able to get the same answer. Anyways I'd like to see how you guys interpret it.
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22 Oct 2006, 22:16
I first thought E, but on second thoughts..I think C.

1. x-y = 1/2
so x = 1; y = 1/2 or
x = -2 y = -2 1/2 INSUFF

2. x > y INSUFF

Combined: if both are negative then the value of y has to be greater than x which means x/y cannot be > 1. So x and y have to be positive
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22 Oct 2006, 22:45
gk3.14 wrote:
I first thought E, but on second thoughts..I think C.

1. x-y = 1/2
so x = 1; y = 1/2 or
x = -2 y = -2 1/2 INSUFF

2. x > y INSUFF

Combined: if both are negative then the value of y has to be greater than x which means x/y cannot be > 1. So x and y have to be positive

Ok here are the values I used:)

1) x-y = 1/2

So taking x=1 and y=1/2 satisfies
another set of values that satisfies 1) x= -1/2, y = -1

Since both 1 and 2 are insufficient. Combining the 2, I can still use the same values I used for 1)

Do you see what I am saying? This problem is killing me
Senior Manager
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22 Oct 2006, 22:56
I see it.. that is exactly the same conculsion i first came to as well..
However for 2 put -1/2/-1 = 1/2 which is not greater than 1..

The inequality is x/y > 1 ; for negative numbers x/y < 1. When substituting for negatives in inequalities the sign has to be changed.. A given inequality is not true for both positive and negative numbers.

Hope that helps
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23 Oct 2006, 11:22
Are x and y both positive?

1) 2x -2y = 1
2) x/y > 1

from one x-y =1/2 ........insuff

/X/>/Y/ , X , Y POSITIVE
OR
/Y/>/X/ , X ,Y -VE
OR

X A PSOITIVE FRACTION , Y IS A NEGATIVE FRACYION AND THEIR ABSOLUTE VALUES SUMS UP TO 1/2

from two

x/y > 1 thus either both negative or both positive and /x/>/y/

insuff

both together suff

Manager
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23 Oct 2006, 12:29

1) 2x-2y= 1 => x-y=1/2

1-(1/2) = 1/2 Yes
0-(-1/2) = 1/2 No

Insufficient

2) x/y > 1 => x>y

Insufficient

Together Sufficient.
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23 Oct 2006, 13:41
I got trapped on this one too. One of my biggest problems is that when I solve these problems slowly I get them right, but when I'm moving quickly I miss little things.
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23 Oct 2006, 15:35
(C) as well

From 1)
2x -2y = 1
<=> y = x -1/2 : represents the equation of line.
o if x < 0, then y < 0 also
o if x > 0, then y <0 or y > 0.

INSUFF

From 2)
x/y > 1 means that x and y are either both positive or both negative.

INSUFF

(1) & (2):
Since 2x -2y = 1 <=> x = 1/2 + y, then
x/y > 1
<=> (1/2 + y)/y > 1
<=> 1/(2*y) + 1 > 1
<=> 1/(2*y) > 0
<=> y > 0

As y = x - 1/2,

x - 1/2 > 0
<=> x > 1/2 > 0

SUFF.
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23 Oct 2006, 17:09
You guys are awesome! Thanks for such detailed explanations

Yes the OA is C and I think I am ok now
23 Oct 2006, 17:09
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