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# Positive / negative

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Intern
Joined: 21 Apr 2007
Posts: 8
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Kudos [?]: 2 [0], given: 0

Positive / negative [#permalink]  21 Apr 2007, 13:19

Are x and y both positive?

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

Naturally, I can eliminate both on their own, but testing to see if both or neither are sufficient is time consuming. Does anyone have any tips to get through this question quickly? I got it right after about 3 mins of work
Director
Joined: 26 Feb 2006
Posts: 907
Followers: 4

Kudos [?]: 46 [0], given: 0

Re: Positive / negative [#permalink]  21 Apr 2007, 16:25
afiggy1 wrote:

Are x and y both positive?

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

Naturally, I can eliminate both on their own, but testing to see if both or neither are sufficient is time consuming. Does anyone have any tips to get through this question quickly? I got it right after about 3 mins of work

from i, x = y + 0.5.
x and y could be anything -ve or +ve.

from ii, x-y>0.
x and y are either both -ve or both +ve.

from i and ii, should be E cuz they both can be -ve or +ve..
Senior Manager
Joined: 01 Jan 2007
Posts: 326
Followers: 1

Kudos [?]: 17 [0], given: 0

Re: Positive / negative [#permalink]  21 Apr 2007, 22:27
afiggy1 wrote:

Are x and y both positive?

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

Naturally, I can eliminate both on their own, but testing to see if both or neither are sufficient is time consuming. Does anyone have any tips to get through this question quickly? I got it right after about 3 mins of work

From 1-> x=(2y+1)/2 . form this statement we cannot say that x and y are both positive.

From 2 -> (x/y)>1. So the value of x is y+something. But still its insufficient.

From both the statements combine we have x=(2y+1)/2 and (x/y)>1.
Now x/y = [(2y+1)/2]/y = (2y+1)/2y = 1+1/2y.
This expression shows that when y is +ve then and only then is the value of x/y >1. So answere is C.

Javed.

Cheers!
Director
Joined: 14 Jan 2007
Posts: 781
Followers: 2

Kudos [?]: 65 [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: 28 Feb 2007
Posts: 198
Location: California
Followers: 2

Kudos [?]: 6 [0], given: 0

Re: Positive / negative [#permalink]  22 Apr 2007, 11:23
afiggy1 wrote:

Are x and y both positive?

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

Naturally, I can eliminate both on their own, but testing to see if both or neither are sufficient is time consuming. Does anyone have any tips to get through this question quickly? I got it right after about 3 mins of work :(

From (1) we have x = y + 1/2 . If y = 0, x is 1/2 and if y = -1/2, x is 0 so INSUFF

From (2) we have either both x and y are positive or both are negative. Hence INSUFF

Now (1) and (2) will both hold only when x and y are both postives.

Hence C
Re: Positive / negative   [#permalink] 22 Apr 2007, 11:23
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