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Are x and y both positive?

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Are x and y both positive? [#permalink] New post 02 Oct 2006, 20:25
1
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

51% (02:23) correct 49% (01:08) wrong based on 77 sessions
Are x and y both positive?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: are-x-and-y-both-positive-1-2x-2x-1-2-x-y-63377.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 26 Jun 2014, 00:06, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Are x and y both positive? [#permalink] New post 02 Oct 2006, 21:42
answer C.

1) x-y=1/2>0. not enough.
2) x/y>1. not enough.

from 2), x and y are either both negative or both negative. but with 1), both negative case doesn't stand. so they can only be positive.
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Re: Are x and y both positive? [#permalink] New post 03 Oct 2006, 13:22
(E) Neither. (-1.5, -2), and (2, 1.5) will satisfy both statements.
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Re: Are x and y both positive? [#permalink] New post 03 Oct 2006, 16:10
I think E too.
x=1, y=0.5
x=0.3, y=-0.2 both satify (i) and (ii)
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Re: Are x and y both positive? [#permalink] New post 03 Oct 2006, 18:00
How can your examples satisfy both statements?
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Re: Are x and y both positive? [#permalink] New post 03 Oct 2006, 19:15
My bad. you are right. I think in my head I had converted the equation to x>y.
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Re: Are x and y both positive? [#permalink] New post 03 Oct 2006, 19:17
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Are x and y both positive?
1) 2x-2y = 1
2) x/y >1

Statement 1 can have two possibilities. x=-1.5 and y= -1 OR x=1 and y=1.5. When plugged into Statement 1 they both yield 1. So x and y could be both positive or negative. Not sufficient.

2) x & y can be both either positive or negative. -4/-2=2 >1 and 3/1 =3 >1. Not sufficient

Together these are not sufficient either.....so my answer is E
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Re: Are x and y both positive? [#permalink] New post 03 Oct 2006, 19:26
Raghavender wrote:
Are x and y both positive?
1) 2x-2y = 1
2) x/y >1


Good Question !!
Answer B

Stmt 1 x-y= 1/2 Insuff

Stmt 2 x/y > 1
From this stmt we know x > y and since x > y , x and y could only be both +ve .
It cannot be both -ve because x/y > 1 would not hold true.

-1 > -2 but -1/-2 < 1 .
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Re: Are x and y both positive? [#permalink] New post 03 Oct 2006, 20:17
ivymba - for second statement x/y>1 couldn't you have both x and y be negative.

e.g. if x= -4 and y = -2 then x/y would be -4/-2 = 2 (which is >1)?

Thanks
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Re: Are x and y both positive? [#permalink] New post 03 Oct 2006, 20:23
Matrix02 wrote:
ivymba - for second statement x/y>1 couldn't you have both x and y be negative.

e.g. if x= -4 and y = -2 then x/y would be -4/-2 = 2 (which is >1)?

Thanks


Yes, you are right matrix. What was I thinking ?
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Re: Are x and y both positive? [#permalink] New post 04 Oct 2006, 04:45
Please post the Answer and Explanation. Thanks
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Re: Are x and y both positive? [#permalink] New post 04 Oct 2006, 06:40
Raghavender wrote:
Are x and y both positive?
1) 2x-2y = 1
2) x/y >1


Statement 1 reduces to x=y: Insuff

Statement 2 simplifies to x>y: Insuff

Together, still no solution.

(E)
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Re: Are x and y both positive? [#permalink] New post 04 Oct 2006, 07:20
Are x and y both positive?
1) 2x-2y = 1
2) x/y >1

1) INsufficient

2) x & y either both +ve or both -ve. We also extracted x>y

Combining:
we have already established that they are either both negative or both positive

both negative:
We know x - y = 1/2 and x>y
they both can not be negative because that wont satisfy the equation above.

They both positive. OA is C.
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Re: Are x and y both positive? [#permalink] New post 04 Oct 2006, 07:27
Raghavender - what is the OA and where did you get this question from?(If it is from OG11 could you please provide the page number).
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Re: Are x and y both positive? [#permalink] New post 04 Oct 2006, 07:32
[quote="asaf"]Are x and y both positive?

both negative:
We know x - y = 1/2 and x>y
they both can not be negative because that wont satisfy the equation above.


Good point asaf...but using this reasoning then A could be the answer no?


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

2x-2y=1

x-y=1/2

x must be greater than y and both must be positive in order to equal 1/2. Sufficient right?
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Re: Are x and y both positive? [#permalink] New post 04 Oct 2006, 08:04
I) x - y = 1/2

x = 1.5 and y = 1 or x = -0.5 and y = -1 INSUFF

II) x/y > 1

both -ve or both +ve and x > y, x = 1.5 and y = 1 or x = -0.5 and y = -1 INSUFF

using both:

x > y
both -ve or both +ve
x - y = 1/2

still could be x = 1.5 and y = 1 or x = -0.5 and y = -1, therefore both INSUFF - (E)
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Re: Are x and y both positive? [#permalink] New post 04 Oct 2006, 11:43
Are x and y both positive?
1) 2x-2y = 1
2) x/y >1

1. x-y=1/2 x could be negative and Y could be negative?

EX x= -1 y=-3/2 or
Both x and y could be positive.
EX x = 2 y= 3/2
Insufficient

2. x > Y Insufficient Both could be negative or positive
Combine 1 and 2 both X and Y not sufficient

ex: x =-1/4 & y=-3/4 supports 1 and 2 too. They both could be negative or positive

So E is the answer.
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Re: Are x and y both positive? [#permalink] New post 04 Oct 2006, 16:52
OA is already posted, and you still say E is hte answer.
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Re: Are x and y both positive? [#permalink] New post 04 Oct 2006, 20:13
baski6 wrote:
Are x and y both positive?
1) 2x-2y = 1
2) x/y >1

1. x-y=1/2 x could be negative and Y could be negative?

EX x= -1 y=-3/2 or
Both x and y could be positive.
EX x = 2 y= 3/2
Insufficient

2. x > Y Insufficient Both could be negative or positive
Combine 1 and 2 both X and Y not sufficient

ex: x =-1/4 & y=-3/4 supports 1 and 2 too. They both could be negative or positive

So E is the answer.

-(1/4) * -(4/3) is not > 1. Does not satisfy statement 2.

Both conditions satisfied only if both X and Y are positive.

If it's any consolation, I was composing a message to the contrary before I realized the mistake we've made. :roll: :wink:
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Re: Are x and y both positive? [#permalink] New post 05 Oct 2006, 20:48
I got the q wrong on GmatPrep

The OA is C

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Re: Are x and y both positive?   [#permalink] 05 Oct 2006, 20:48
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