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# Are x and y both positive?

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Senior Manager
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Are x and y both positive? [#permalink]

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29 Jan 2009, 06:21
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Question Stats:

52% (02:22) correct 48% (01:21) wrong based on 110 sessions

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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
[Reveal] Spoiler: OA
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Re: Are x and y both positive? [#permalink]

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29 Jan 2009, 07:48
study wrote:
Are x and y both positive?

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

1) 2x - 2y = 1

Alone not sufficient

2) x/y > 1
alone not suffcieint
both can be +ve or both can be -ve

combined

2x - 2y = 1

x=2 y=3/2 both +ve
x= -3/2 y= -2 both -ve

not suffcieint

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

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29 Jan 2009, 08:53
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x2suresh wrote:
study wrote:
Are x and y both positive?

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

1) 2x - 2y = 1

Alone not sufficient

2) x/y > 1
alone not suffcieint
both can be +ve or both can be -ve

combined

2x - 2y = 1

x=2 y=3/2 both +ve
x= -3/2 y= -2 both -ve
not suffcieint

E

lxl cannot be < lyl.

in that case E may me changed into C.
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Re: Are x and y both positive? [#permalink]

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29 Jan 2009, 10:12
study wrote:
I too chose E.

x2suresh/gmat tiger, can you please xplain why C?

Thanks.

both x and y can't be -ve

when they both negative.. |x|>|y| (because x/y>1)
in this case stat1 fails 2x-2y=1 --> this is not possible at all
2x-2y ---> always negative.. (when both x and y are -ve)
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Re: Are x and y both positive? [#permalink]

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29 Jan 2009, 10:37
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study wrote:
Are x and y both positive?

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

1. x-y= 1/2
2. (x-y)y>0

C: 1/2*y>0 => y>0
x-y>0 => x>0

C.... http://www.snarkyarchies.com
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Re: Are x and y both positive? [#permalink]

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30 Jan 2009, 01:32
Similar approach in a different flavor.

From stmt1: x - y > 1/2 > 0
Hence, x > y.

Not sufficient as both x and y can be positive or negative.

From stmt2: x/y > 1
Hence, either x > y > 0 or x < y < 0
Hence, insufficient.

Combining stmt1 and stmt2:
x > y > 0. Hence, sufficient.
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Re: Are x and y both positive? [#permalink]

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19 Jun 2010, 05:21
DavidArchuleta wrote:
study wrote:
Are x and y both positive?

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

1. x-y= 1/2
2. (x-y)y>0

C: 1/2*y>0 => y>0
x-y>0 => x>0

C.... http://www.snarkyarchies.com

I don't agree with this solution with reference to statement 2, One cannot conveniently multiply both sides of the equation with y assuming y is positive. If y is negative, the inequality sign changes.
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Re: Are x and y both positive? [#permalink]

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19 Jun 2010, 05:39
Expert's post
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study wrote:
DavidArchuleta wrote:
study wrote:
Are x and y both positive?

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

1. x-y= 1/2
2. (x-y)y>0

C: 1/2*y>0 => y>0
x-y>0 => x>0

C.... http://www.snarkyarchies.com

I don't agree with this solution with reference to statement 2, One cannot conveniently multiply both sides of the equation with y assuming y is positive. If y is negative, the inequality sign changes.

There is no multiplication by $$y$$: it should be $$\frac{x}{y}>1$$ --> $$\frac{x}{y}-1>0$$ --> $$\frac{x-y}{y}>0$$ --> as $$x-y=\frac{1}{2}$$ --> $$\frac{1}{2y}>0$$ --> $$y>0$$ --> as $$\frac{x}{y}>1$$, they both have the same sign, thus $$x>0$$.

Complete solution:

Are x and y both positive?

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

(1) 2x-2y=1. Well this one is clearly insufficient. You can do it with number plugging OR consider the following: x and y both positive means that point (x,y) is in the I quadrant. 2x-2y=1 --> y=x-1/2, we know it's an equation of a line and basically question asks whether this line (all (x,y) points of this line) is only in I quadrant. It's just not possible. Not sufficient.

(2) x/y>1 --> x and y have the same sign. But we don't know whether they are both positive or both negative. Not sufficient.

(1)+(2) Again it can be done with different approaches. You should just find the one which is the less time-consuming and comfortable for you personally.

One of the approaches:
$$2x-2y=1$$ --> $$x=y+\frac{1}{2}$$
$$\frac{x}{y}>1$$ --> $$\frac{x-y}{y}>0$$ --> substitute x --> $$\frac{1}{y}>0$$ --> $$y$$ is positive, and as $$x=y+\frac{1}{2}$$, $$x$$ is positive too. Sufficient.

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

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23 Apr 2015, 00:39
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Re: Are x and y both positive? [#permalink]

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23 Apr 2015, 03:12
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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Re: Are x and y both positive?   [#permalink] 23 Apr 2015, 03:12
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