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Are x and y both positive? [#permalink ]
02 Oct 2006, 20:25

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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
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ARISE AWAKE AND REST NOT UNTIL THE GOAL IS ACHIEVED

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 ]
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 ]
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 ]
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 ]
03 Oct 2006, 18:00

How can your examples satisfy both statements?

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Re: Are x and y both positive? [#permalink ]
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 ]
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 ]
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 ]
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 ]
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 ]
04 Oct 2006, 04:45

Please post the Answer and Explanation. Thanks

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Re: Are x and y both positive? [#permalink ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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 ]
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.

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

I got the q wrong on GmatPrep The OA is C _________________

ARISE AWAKE AND REST NOT UNTIL THE GOAL IS ACHIEVED

Re: Are x and y both positive?
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05 Oct 2006, 20:48