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

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SVP
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Are x and y both positive? 1. 2x-2y = 1 2. x/y >1 [#permalink]  07 Sep 2006, 01:59
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Are x and y both positive?

1. 2x-2y = 1
2. x/y >1
Current Student
Joined: 29 Jan 2005
Posts: 5240
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C is the TRAP answer for the rushed, paniky test taker.

It's (E)

Gonna prove it now...

Statement 1: 2x-2y=1 ---> x-y=1/2 ---> x=y+1/2

If x>0 then y>-1/2 <or> if x<0 then y<-1/2 INSUFF

Statement 2: x/y>1 ---> x>y ---> x-y>0

If x>0 then y>0 <or> if x<0 then y<0 INSUFF

Together, if x>0 then y can be > 0 or -1/2 <or> if x<0 y can be <0 or -1/2 INSUFF

Bring it on yezz..

Last edited by GMATT73 on 07 Sep 2006, 05:33, edited 1 time in total.
Current Student
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haas_mba07 wrote:
I am with you until the S1 & S2 insufficient parts.

For S1 & S2,
if x>0, then y > {0, -1/2},

Wouldn't that violate x/y > 1?

If x = 1, y = 1/2 x/y = -2 ?

GMATT73 wrote:
Together, if x>0 then y can be > 0 or -1/2 <or> if x<0 y can be <0 or -1/2 INSUFF

Double checked my math Haas. The two statements combined leave a void between 0 and -1/2. This is why I am standing by (E)
VP
Joined: 02 Jun 2006
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Can you imply
x>y, when x/y > 1, though we don't know signs of x and y?

If x = -5, y = -1,
x/y > 1, but x < y.

What you need to say is |x| > |y|...?

GMATT73 wrote:
Statement 2: x/y>1 ---> x>y ---> x-y>0

S1 & S2:
Together, if x>0 then y can be > 0 or -1/2 <or> if x<0 y can be <0 or -1/2 INSUFF
VP
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I will go with C.

Here are my reasons:

We all agree that x and y can be either both positive or both negative. If we substitute both negative numbers in 2x-2y=1, then those same values dont hold good in case of x/y>1. If we substitute both positive numbers in 2x-2y=1, then those same values hold good in case of x/y>1. So I say that x and y are positive values.

Do correct me if I am wrong.
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VP
Joined: 02 Jun 2006
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I second that... C for me too.
Both x and y have to be both +ve or -ve.
Plugging in for S1 & S2 satisfies only one condition.

Good questions yezz... keep them coming.

ak_idc wrote:
I will go with C.

Here are my reasons:

We all agree that x and y can be either both positive or both negative. If we substitute both negative numbers in 2x-2y=1, then those same values dont hold good in case of x/y>1. If we substitute both positive numbers in 2x-2y=1, then those same values hold good in case of x/y>1. So I say that x and y are positive values.

Do correct me if I am wrong.
Current Student
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haas_mba07 wrote:
I second that... C for me too.
Both x and y have to be both +ve or -ve.
Plugging in for S1 & S2 satisfies only one condition.

Good questions yezz... keep them coming.

ak_idc wrote:
I will go with C.

Here are my reasons:

We all agree that x and y can be either both positive or both negative. If we substitute both negative numbers in 2x-2y=1, then those same values dont hold good in case of x/y>1. If we substitute both positive numbers in 2x-2y=1, then those same values hold good in case of x/y>1. So I say that x and y are positive values.

Do correct me if I am wrong.

Hey guys, can't both x and y be negative too? Now what's the answer???
VP
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If we take both negative, then we can't satisfy the second condition. That means effectively we are not using the information in second condition. If we take both positive, we are fullfiling the second condition and also we can solve the problem. Hence, I say C..
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CEO
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C

St1: x-y = 1/2 : Clearly INSUFF

St2: x/y > 1: Clearly INSUFF

Together:
From St2 we can say that either both x and y are +ve or both are -ve.

If both +ve then x>y and st1 will also be satisfied.
If both -ve then y>x then lets take out the -ve sign of both x and y. Then st1 becomes x-y = -1/2 and st2 becomes x>y and its impossible.
So both x and y are +ve.
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Intern
Joined: 06 Jan 2006
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I go with E

from 1) x-y=1/2

insuff cause 3.5-3=0.5 (-->x,y positive) and -3+3.5=0.5 (-->x,y negative)

from 2) x>y

insuff

but in both exemples above x>y while x,y either positive or negative

thus 1) + 2) insuff.
SVP
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Are x and y both positive?

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

From one x-y = 1/2 this could be possible in three ways

1) x,y could be positive

2) x +ve and y -ve both fractions with absolute value less than 1/2

3) x,y are both -ve and y<x

thus insuff

from two

x/y > 1 they could be both positive x>y

or both -ve and y>x

thus not suff

both together

x/y >1 could be expressed as x-y/y>0 ie (1/2)/y>0

thus y is +ve AND SINCE X/Y> 1 thus x is positive and answer is C

OA is C

Last edited by yezz on 07 Sep 2006, 23:36, edited 2 times in total.
Intern
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Insider wrote:
I go with E

from 1) x-y=1/2

insuff cause 3.5-3=0.5 (-->x,y positive) and -3+3.5=0.5 (-->x,y negative)

from 2) x>y

insuff

but in both exemples above x>y while x,y either positive or negative

thus 1) + 2) insuff.

Insider, if x=-3 and y=-3.5, the first statement is fulfilled, but the second isn't: (-3/-3.5)<1.
Director
Joined: 28 Dec 2005
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The trick here is that

x/y > 1 does not simply mean that x > y.....MEMORIZE THIS.

it means :

1. x and y have the same sign
2. if x,y are +ve then x > y.
3. if x,y are -ve then x < y

Excellent problem...I was stumped for a bit.
GMAT Instructor
Joined: 04 Jul 2006
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Re: A v.good iniquality DS(Dahiya post) [#permalink]  11 Sep 2006, 01:57
yezz wrote:
Are x and y both positive?

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

(1) y=x+1/2 NOT SUFF

(2) x and y have the same sign and x is further from 0 than is y (i.e |x|>|y|) NOT SUFF

Together, if x>y from (1) and |x|>|y| from (2), it follows than x>0 and thus (from (2)) y>0 SUFF

C
Senior Manager
Joined: 15 Aug 2004
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Futuristic wrote:
2. if x,y are +ve then x > y.

Doesn't you second choice mean that the answer should be B...

It cannot be one +ve and one -ve or vice versa...
I cannot be both -ve, so only both +ve is left...
Director
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I wud go with B on this one

the Q is is x & y both +ve

from II we see x / y > 1 or x > y

for x/y > +1 either both have to be -ve or both + ve

if we take both -ve then we cannot get x / y > 1 it will be always be < 1

eg: - 10 / -15 as -10 > -15 = .667 for this value to be > 1 and both x and y to be -ve then x < y eg : -10 / -5 = 2

so we are left with if x/y > 1 then both x and y are positive
Senior Manager
Joined: 07 Jul 2005
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(C).
As explained by Dahiya.

Combining both,
I says that x > y, and II says that either {x, y} are +ve or -ve
If {x, y} are -ve, then we cannot have x >y and x/y >1
Hence both x, y have to be +ve.
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Re: A v.good iniquality DS(Dahiya post) [#permalink]  13 Oct 2006, 07:01
yezz wrote:
Are x and y both positive?

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

Sorry to drag this thread out of its grave. I thought it's a good chance to advocate my way of solving thing algebrally.

Here's what I'd do for 1 and 2 combined:

1=> 2x=1+2y, or x=(1+2y)/2
2=> x/y>1 meaning (1+2y)/2y>1
rephrase: 1/2y+1>1 => 1/2y>0
Therefore y>0
x=(1+2y)/2>0

Solving in this fashion sometimes can help to avoid the sign confusions that may accompany inequalities.
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Manager
Joined: 08 Jul 2006
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Picked C too. (Developing a new strategy for approaching tricky DS problems)

Making Statement 1 true by quickly picking numbers.
We can have 2(3) - 2(5/2) = 1 OR 2(-3) - 2(-7/2) = 1
x and y can be either both positive or both negative. INSUFF

From Statement 2, we only know x>y. INSUFF

Together,
If X>Y, then, in order for 2x - 2y = 1, both a and y must be positive.

C should suffice.
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Re: A v.good iniquality DS(Dahiya post) [#permalink]  14 Oct 2006, 22:28
HongHu wrote:
yezz wrote:
Are x and y both positive?

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

Sorry to drag this thread out of its grave. I thought it's a good chance to advocate my way of solving thing algebrally.

Here's what I'd do for 1 and 2 combined:

1=> 2x=1+2y, or x=(1+2y)/2
2=> x/y>1 meaning (1+2y)/2y>1
rephrase: 1/2y+1>1 => 1/2y>0
Therefore y>0
x=(1+2y)/2>0

Solving in this fashion sometimes can help to avoid the sign confusions that may accompany inequalities.

Excellent approach Honghu . it makes it much simpler and saves time.
Re: A v.good iniquality DS(Dahiya post)   [#permalink] 14 Oct 2006, 22:28
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