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

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Senior Manager
Joined: 20 Feb 2007
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Are x and y both positive? (1) 2x - 2y = 1 (2) x/y > 1 [#permalink]  24 Mar 2007, 19:33
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Q: Are x and y both positive?

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

OA is C but I got E here.

Senior Manager
Joined: 20 Feb 2007
Posts: 257
Followers: 1

Kudos [?]: 14 [0], given: 0

Here how I did it:

Q: is x,y > 0?

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

Taking (1):
2x -2y = 1 => 2 (x - y) = 1 => x - y = 1/2

If x = 2, y = 3/2 => x,y > 0
but if x = -3/2, y = -2 => x,y < 0 INSUFF

Taking (2):
x/y > 1 => x > y INSUFF

Taking (1) and (2) together:

If x = 2, y = 3/2 => x,y > 0 (also here x > y or x/y = 4/3 or > 1)
but if x = -3/2, y = -2 => x,y < 0 (also here x > y as -3/2 > -2 but x/y is 3/4)
That's why I got E...

What am I doing wrong here???
Senior Manager
Joined: 20 Feb 2007
Posts: 257
Followers: 1

Kudos [?]: 14 [0], given: 0

I got it!

For +ve values, if x>y then x/y > 1
for -ve values, if x>y, then x/y < 1
Director
Joined: 14 Jan 2007
Posts: 779
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Kudos [?]: 76 [0], given: 0

Q: Are x and y both positive?

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

statement 1:
2x-2y = 1 =>x-y = 1/2 this deduces positive x and y or negative x and y. so INSUFF

statement 2:
x/y >1 => x and y both negative or both positive. So INSUFF.

Combining the two:
Take positive x and y . statement 2 is: x/y >1 means x>y
x-y = 1/2 is possible with only positive x and y.
Take negative x and y. statement 2 x/y >1 means x<y. statement 1 can't be achieved by negative x and y.

so x and y must be positive. Hence answer is 'C'
Manager
Joined: 29 Nov 2006
Posts: 56
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i don't understand why statement 1 can't be achieved by negative x and y.

eg
if x = -1/2, y= -1
(-1/2) - (-1) =1/2

edit:
nevermind x must be < y. since we distribute the negative sign
Manager
Joined: 02 Jan 2007
Posts: 208
Followers: 2

Kudos [?]: 5 [0], given: 0

I get E
Can somebody help

Firstly,
we can't say x > y, right?
becos if x = -8 & y = -4 then
x/y > 1 but x < y

Secondly,
I cant get C becos I am thinking if
x = -3.5 and y = -4 (assuming x>y- both are -ve)
then 2x-2y = 1
so both are negative?

if x = 4 & y = 3.5 then (assuming x>y- both are +ve)
(assuming x>y, both are -ve)
2x - 2y = 1
so both are positive?

so E?
Manager
Joined: 29 Nov 2006
Posts: 56
Followers: 1

Kudos [?]: 0 [0], given: 0

Q: Are x and y both positive?

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

(1) is insufficient

(2) x/y can be either both +ve or -ve.

case +ve:

x>y => 2(+1) -2 (+0.5) = 1

case -ve:
-x/-y >1, x<y> 2(-0.5) -2 (-1) =1. no case.

therefore both must be +ve
Manager
Joined: 28 Aug 2006
Posts: 160
Followers: 2

Kudos [?]: 13 [0], given: 0

Consider X=0.25 and Y=-0.25

(1) 2x-2y =1 TRUE
(2) x/y>1 => X>Y
=> 0.25>-0.25 TRUE

Answer is E, as we still cant be certain about sign of X and Y.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
Location: Singapore
Followers: 23

Kudos [?]: 194 [0], given: 0

St1
2x-2y = 1
x-y = 1/2

Can be anything. For instance 1-1/2 = 1/2 (then x and y are both positive), or
-1/4 - (-3/4) = 1/2 (then both x and y are negative).

Insufficient.

St2:
x > y. Can be any combination. Insuffcient.

Using both, then we know the second case (where x and y are negative) cannot exist.

So must be C
Director
Joined: 14 Jan 2007
Posts: 779
Followers: 2

Kudos [?]: 76 [0], given: 0

Think this way-
Statement 1 and 2 alone are insuff
Taken them together:

x- y = 1/2 . This means irrespective of signs of x and y, the statement 1 will always give x > y.

Statement 2 x/y > 1. From statement 1 we have derived that x > y. Statement 2 will only be true if x and y both positive.

Manager
Joined: 02 Jan 2007
Posts: 208
Followers: 2

Kudos [?]: 5 [0], given: 0

Thank you Gang
It's always nice to have a mystery solved
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