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Are x and y both positive? 1. 2x2y = 1 2. x/y >1 [#permalink]
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07 Sep 2006, 02:59
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Are x and y both positive?
1. 2x2y = 1
2. x/y >1



Current Student
Joined: 29 Jan 2005
Posts: 5218

C is the TRAP answer for the rushed, paniky test taker.
It's (E)
Gonna prove it now...
Statement 1: 2x2y=1 > xy=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 > xy>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
Answer is (E)
Bring it on yezz..
Last edited by GMATT73 on 07 Sep 2006, 06:33, edited 1 time in total.



Current Student
Joined: 29 Jan 2005
Posts: 5218

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
Posts: 1260

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 > xy>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
Joined: 21 Aug 2006
Posts: 1016

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 2x2y=1, then those same values dont hold good in case of x/y>1. If we substitute both positive numbers in 2x2y=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
Posts: 1260

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 2x2y=1, then those same values dont hold good in case of x/y>1. If we substitute both positive numbers in 2x2y=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
Joined: 29 Jan 2005
Posts: 5218

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 2x2y=1, then those same values dont hold good in case of x/y>1. If we substitute both positive numbers in 2x2y=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
Joined: 21 Aug 2006
Posts: 1016

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
Joined: 20 Nov 2005
Posts: 2894
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD  Class of 2008

C
St1: xy = 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 xy = 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
Posts: 13

I go with E
from 1) xy=1/2
insuff cause 3.53=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
Joined: 05 Jul 2006
Posts: 1747

Are x and y both positive?
1. 2x2y = 1
2. x/y >1
From one xy = 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 xy/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 08 Sep 2006, 00:36, edited 2 times in total.



Intern
Joined: 02 Aug 2006
Posts: 23
Location: NYC

Insider wrote: I go with E
from 1) xy=1/2
insuff cause 3.53=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
Posts: 752

The answer is C.
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
Posts: 1262
Location: Madrid

Re: A v.good iniquality DS(Dahiya post) [#permalink]
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11 Sep 2006, 02:57
yezz wrote: Are x and y both positive?
1. 2x2y = 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
Posts: 327

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
Joined: 07 Jun 2004
Posts: 612
Location: PA

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
Posts: 404
Location: Sunnyvale, CA

(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.



SVP
Joined: 03 Jan 2005
Posts: 2233

Re: A v.good iniquality DS(Dahiya post) [#permalink]
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13 Oct 2006, 08:01
yezz wrote: Are x and y both positive?
1. 2x2y = 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
Posts: 89

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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Joined: 11 Jul 2006
Posts: 380
Location: TX

Re: A v.good iniquality DS(Dahiya post) [#permalink]
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14 Oct 2006, 23:28
HongHu wrote: yezz wrote: Are x and y both positive?
1. 2x2y = 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)
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14 Oct 2006, 23:28






