Author 
Message 
Harish Dorai

Post subject: Are x and y both positive? 1) 2x  2y = 1, 2) x/y > 1 Posted: Tue Jul 31, 2007 11:21 am 


Data sufficiency question:
Are x and y both positive?
1) 2x  2y = 1
2) x/y > 1
I thought the answer choice is (E), but it is not correct as per GMATPrep software.
My reasoning was as follows:
Statement (1) can be simplified as
x  y = 1/2. This is NOT SUFFICIENT.
Statement (2) can be rewritten as x > y. This is NOT SUFFICIENT
Combining the above 2 statements and taking an example as shown below.
x = 3/2 and y = 2. In this case x > y as per the second statement and x  y = 1/2 as per the second statement. Similarly I could also have an example that satisfies x and y as positive. So I went ahead with answer choice (E).
However what I failed to realize in the above example was that it actually doesn't satisfy the original condition x/y > 1. Because 3/2 divided by 2 will give 3/4 which is less than 1.
So is it correct to rewrite the inequality x/y > 1 to x > y?





GMAT 2007

Post subject: Posted: Tue Jul 31, 2007 1:19 pm 


Harish another approach: 
I agree (1) or (2) are INSUFFICIENT. but consider both of them together
(1) 2x2y = 1
(2) x/y >1
Rephrasing (1)
xy = 1/2
x = y + 1/2
Now substituting value of x in (2)
(y+1/2)/y >1
Solving:
1+ 1/2y > 1
so, 1/2y > 0 it means y >0 since x = y+1/2 s0 X >0 as well.
Hope it helps
GMAT 2007





GMAT 2007

Post subject: Posted: Tue Jul 31, 2007 1:20 pm 


So, the answer should be (C). Am I correct?
GMAT 2007





a7lee

Post subject: Posted: Tue Jul 31, 2007 1:55 pm 


The answer is C.
For A) 2x  2y = 1 > x  y = 1/2. You can have 0  (1/2) = No or You can have +1  (+1/2) = Yes. So A is insufficient.
For B) x/y > 1 > Either X and Y are both + or X and Y are both negative. So B is insufficent. NOTE: x > y.
For A+B.
Have x and y be positive and make it work with equation A. So +1  (+1/2) = 1/2 Yes.
.... be negative and make it work with equation B. So 1  (y) = 1/2. y = (3/2) which is > x. So you will see that two negatives cannot work because it violtates the rule that x/y > 1. So for A+B the answer is yes.





Harish Dorai

Post subject: Posted: Tue Jul 31, 2007 2:13 pm 


Thanks for the explanation. (C) is the right answer.





givemeanid

Post subject: Posted: Tue Jul 31, 2007 2:16 pm 


Quote: Statement (2) can be rewritten as x > y.
You CANNOT do this. You do not know at this point whether y > 0 or y < 0.





GMAT 2007

Post subject: Posted: Tue Jul 31, 2007 2:43 pm 


givemeanid,
In my approach, with help of (1) & (2) , I have calculated y. Instead of substituting values, the calculation makes it clear that y >0 and so x>0. Hence both are +ve. I feel it was the better approach rather than picking numbers. It helped to stayaway from intricacies of possibility of ve values.
GMAT 2007





givemeanid

Post subject: Posted: Tue Jul 31, 2007 5:01 pm 


GMAT 2007, your solution is good. I also tend to do the same before using numbers for inequalities!





dbernst

Post subject: Posted: Thu Aug 02, 2007 11:31 am 


ManhattanGMAT Staff 

Posts: 302

Good discussion all. Now that's teamwork!





unique

Post subject: Posted: Fri Aug 10, 2007 2:09 pm 


I did it this way 
1. 2(xy) =1
xy = 1/2 clearly insufficient
2. x/y > 1
x>y when y > 0
x<y when y< 0
insufficient
TOGETHER xy =1/2 means x>y
From 2 x>y when y>0 so x>0 answer C





Guest

Post subject: Posted: Fri Jun 13, 2008 12:13 am 


GMAT 2007 wrote: so, 1/2y > 0 it means y >0
Im sure this is pretty remedial for you guys, but can someone really quickly explain how from 1/2y > 0 = y>0 ??
Thanks!





rfernandez

Post subject: Posted: Fri Jun 13, 2008 4:26 am 


ManhattanGMAT Staff 

Posts: 384

Quote: Im sure this is pretty remedial for you guys, but can someone really quickly explain how from 1/2y > 0 = y>0 ??
Multiply both sides of the inequality by 2. 2 * 1/2y yields y; 2 * 0 yields 0.





albert.chi

Post subject: Re: Are x and y both positive? 1) 2x  2y = 1, 2) x/y > 1 Posted: Wed Aug 05, 2009 1:33 am 


Course Students 

Posts: 6

Can someone help me understand how my 'intuition' is incorrect?
To me:
Statement 1) says that the difference between X and Y is .5, no matter where on the number line they are. Both cases work: <0Y(1)X(1.5)> or <Y(2)X(1.5)0>
Statement 2) says that X is greater than Y and that they have the same sign (negative or positive)
 Now taking these together without plugging them into each other like the solution above, isn't all the information I have just saying that:
X is to the right of Y on the number line, they are spaced .5 apart, and they both have the same sign? (Therefore E)
Can someone please help me find the missing piece in my logic to understand why it's C?
Thanks





albert.chi

Post subject: Re: Are x and y both positive? 1) 2x  2y = 1, 2) x/y > 1 Posted: Sun Aug 09, 2009 7:27 am 


Course Students 

Posts: 6

Hi, can someone please answer my question in case it was missed?
Thanks!





Ben Ku

Post subject: Re: Are x and y both positive? 1) 2x  2y = 1, 2) x/y > 1 Posted: Tue Aug 18, 2009 11:35 pm 


ManhattanGMAT Staff 

Posts: 818

Quote: Statement 2) says that X is greater than Y and that they have the same sign (negative or positive)
This quote is incorrect. X > Y only if both are positive. For example if x = 3 and y =2, then x/y = 3/2. However, if both x and y are negative, then x < y. For example, if x = 3 and y = 2, then x / y = 3/2. Here, x < y. So (2) basically states that x > y > 0 or x < y < 0. (1) states that x > y, so then they must both be positive. Hope that makes sense.
_________________ Ben Ku Instructor ManhattanGMAT





