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

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Manager
Joined: 14 Oct 2008
Posts: 160
Are x and y both positive ? 1. 2x-2y = 1 2. (x / y) > 1 [#permalink]

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10 Dec 2008, 12:43
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Are x and y both positive ?

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

Thanks.

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Senior Manager
Joined: 30 Nov 2008
Posts: 482
Schools: Fuqua

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10 Dec 2008, 13:34
I would go with E. here is my explanation.

Clue 1 - 2x-2y = 1 ==> 2(x-y) = 1 => x - y = 1/2. Ex - x = 1/4, y = -1/4 one is positive and another another is negative. x = 3/4, y = 1/4 = both are positive, x = -1/4 and y = -3/4, one is negative and another is positive. Cannot say whether x and y are positive.

Clue 2 - x / y > 1 ==> x > y - Cannot say whether x and y are positive.

Even if you combine both the clues, also you cannot say that x and y are positive.
SVP
Joined: 29 Aug 2007
Posts: 2452

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10 Dec 2008, 14:32
gameCode wrote:
Are x and y both positive ?

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

Thanks.

1: 2x-2y = 1
x = y + 1/2
x and y each could be -ve or +ve.......nsf..

2: x/y > 1
x and y could be -ve or +ve but lxl > lyl...........nsf.

1&2: since x = y + 1/2, x and y cannot be -ve because if they are then lxl < lyl, which is wrong.

So C.
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Senior Manager
Joined: 30 Nov 2008
Posts: 482
Schools: Fuqua

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10 Dec 2008, 15:09
GMAT Tiger,

mrsmarthi wrote:
1&2: since x = y + 1/2, x and y cannot be -ve because if they are then lxl < lyl, which is wrong.

what if x = -1/4 and y = -3/4 here both x and y are negative and x = y + 1/2.
Manager
Joined: 23 Nov 2008
Posts: 78

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10 Dec 2008, 15:36
I guess another way of looking at this is:

x-y=1/2 or, x=1/2+y
so, if x is positive, 1/2+y>0 => y>-1/2

The second statement does not help with the above.
So it cannot be concluded that both y and x are positive.

E
Intern
Joined: 26 Sep 2008
Posts: 19

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10 Dec 2008, 18:24
I'll go with C.
from 1 we have : x= y + 1/2 insuf
from 2 : x/y > 1 insuf
1&2:
x/y= (y+1/2)/y = (1+ 1/2y) > 1 then 1/2y > 0 or y must be greater than 0.
So we can see that both x and y are greater than 0.
Senior Manager
Joined: 21 Apr 2008
Posts: 265
Location: Motortown

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10 Dec 2008, 19:07
C

stmt1: x- y = 1/2

x = 3/2, y = 1
x = -1/2, y = -1 - In Suff

stmt2: x/y>1 - In Suff
x and y have to have same sign and x>y

Together: Suff
SVP
Joined: 29 Aug 2007
Posts: 2452

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10 Dec 2008, 19:54
mrsmarthi wrote:
GMAT Tiger,

mrsmarthi wrote:
1&2: since x = y + 1/2, x and y cannot be -ve because if they are then lxl < lyl, which is wrong.

what if x = -1/4 and y = -3/4 here both x and y are negative and x = y + 1/2.

Thats about st. 1 but you missed st. 2, which is x/y > 1.
if x = -1/4 and y = -3/4, x/y = 1/3 which is not > 1.

therefore, x = -1/4 and y = -3/4 do not fit to the statements 1 and 2.
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Director
Joined: 14 Aug 2007
Posts: 702

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10 Dec 2008, 20:00
1
KUDOS
gameCode wrote:
Are x and y both positive ?

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

Thanks.

1) can be simplified to x-y = 1/2 => x = y + 1/2.
This is equation of line which passes through 1st , 2nd as well as 3rd quadrant. so x and y both may not be positive. insuff

2) this represents area around the line x=y (as shown in attached fig). which passes through 1st and 3rd quadrant.
so again x and y can both be positive or both be negative.insuff.

together,
(y+1/2)/y > 1
1 + 1/2y > 1
1/2y > 0
i.e y > 0, from 2 it implies that if y>0, x must also be >0

Suff.

C
Attachment:

inequal2.JPG [ 13.85 KiB | Viewed 734 times ]

Last edited by alpha_plus_gamma on 10 Dec 2008, 20:39, edited 2 times in total.
attached diagram
Manager
Joined: 14 Oct 2008
Posts: 160

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11 Dec 2008, 02:30
Thanks everyone, the answer is C.
Current Student
Joined: 28 Dec 2004
Posts: 3309
Location: New York City
Schools: Wharton'11 HBS'12

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11 Dec 2008, 09:11
i get C..

here is my method any comments?

1)2(x-y)=1 so x=1/2 +y

insuff

2) x/y > 1
insuff both can be negative or postive ..insuff

so 1)+2)

(1/2 +y)/y > 1 which means 1/2Y +1> 1 means that Y has to be postive, also means that x is also positive..

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Re: DS- Gmatprep   [#permalink] 11 Dec 2008, 09:11
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