is xy>0 ?
1. x-y>-2
2. x-2y<-6
power prep DS
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For xy> 0 when:Feruza Matyakubova wrote:is xy>0 ?
1. x-y>-2
2. x-2y<-6
1) x = positive, y = positive
2) x = negative, y = negative
Statement (1)
x-y>-2
x-y+2>0
we can make up multiple values of x and y and this statement is still true...INSUFFICIENT
Statement (2)
x-2y<-6
x-2y+6<0
same as above, we can have multiple values of x and y and statement is still true...INSUFFICIENT
St (1) and (2)
x-y+2>0
x-2y+6<0
-x+y-2<0
x-2y+6<0
-y+4<0
y>4
If y>4, then x>2 or x<2
INSUFFICIENT (E)
What's the OA?
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It is E.
While typing this reply I figured out B is wrong.
Here is what I did.
Stmt 2: x -2y < -6 is xy > 0 ?? Yes or no question.
let x = -11, y = -2
x -2y => -11 -2(-2) = -11 +4 => -7 which is < -6.
however x*y = -11 * -2 = +22 > 0 YES
Let x = 2, y = 11
x -2y => 2 -2(11) => 2 - 22 => -22 which is < -6.
However x*y = 2*11 = 22 > 0 YES.
Let x = -8, y = 1/2
x-2y = -9 which is < -6.
but xy = -8*1/2 = -4 > 0 ?? NO.
So N/S
combining does not give a unique answer.
so E
HT Helps
While typing this reply I figured out B is wrong.
Here is what I did.
Stmt 2: x -2y < -6 is xy > 0 ?? Yes or no question.
let x = -11, y = -2
x -2y => -11 -2(-2) = -11 +4 => -7 which is < -6.
however x*y = -11 * -2 = +22 > 0 YES
Let x = 2, y = 11
x -2y => 2 -2(11) => 2 - 22 => -22 which is < -6.
However x*y = 2*11 = 22 > 0 YES.
Let x = -8, y = 1/2
x-2y = -9 which is < -6.
but xy = -8*1/2 = -4 > 0 ?? NO.
So N/S
combining does not give a unique answer.
so E
HT Helps
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Should have solved it dligently instead of voting for an E)
y> 4 only possible wiht stmts I and II
1. x-y>-2
2. x-2y<-6
x-y>-2
x+2 > y
y < x+2
x has to be positive since anything negative would make y>4 false
xy>0
Hence C)
y> 4 only possible wiht stmts I and II
1. x-y>-2
2. x-2y<-6
x-y>-2
x+2 > y
y < x+2
x has to be positive since anything negative would make y>4 false
xy>0
Hence C)
- logitech
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x-y>-2Feruza Matyakubova wrote:is xy>0 ?
1. x-y>-2
2. x-2y<-6
-x+2y>6
+
----------------------
y>4
x>2
xy>0
C
LGTCH
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- ronniecoleman
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IMO C
This is can be solved through coordinate representation.
This is can be solved through coordinate representation.
Last edited by ronniecoleman on Mon Dec 15, 2008 12:34 am, edited 1 time in total.
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- logitech
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Dude if you have an IMO , keep it for yourself.ronniecoleman wrote:IMO E
If you have a solution, share so we all can learn.
Sorry for the tough love, I hate IMOs!
LGTCH
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love you logitechlogitech wrote:Dude if you have an IMO , keep it for yourself.ronniecoleman wrote:IMO E
If you have a solution, share so we all can learn.
Sorry for the tough love, I hate IMOs!
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OOps I too fell for the E trap. took a risky leap of guess and broke my nose .
Anyway here is how I solved it... similar to cramya..
from 1 and 2
x - y > -2
-x +2y > 6
Applying an important takeaway I learnt from this forum:
when two inequalities are in the same direction u can solve the inequalities as if they are simultanaeous equations.
Applying that we get y > 4.
Now plug in y > 4 in x -y > -2
we get x > 2.
So xy is greater than 8 and hence > 0
So C
Anyway here is how I solved it... similar to cramya..
from 1 and 2
x - y > -2
-x +2y > 6
Applying an important takeaway I learnt from this forum:
when two inequalities are in the same direction u can solve the inequalities as if they are simultanaeous equations.
Applying that we get y > 4.
Now plug in y > 4 in x -y > -2
we get x > 2.
So xy is greater than 8 and hence > 0
So C
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When two inequalities face the same direction we can add the inequalities together.Applying an important takeaway I learnt from this forum:
when two inequalities are in the same direction u can solve the inequalities as if they are simultanaeous equation
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Ah,
I forgot to go back and plug in the value to see if the statement y > 4 is still true.
Moral of story: For inequalities, go back and plug in your answer choices to validate if the statement is still true
I forgot to go back and plug in the value to see if the statement y > 4 is still true.
Moral of story: For inequalities, go back and plug in your answer choices to validate if the statement is still true
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OOps Oh yeah... thanks Cramya for the correction.cramya wrote:When two inequalities face the same direction we can add the inequalities together.Applying an important takeaway I learnt from this forum:
when two inequalities are in the same direction u can solve the inequalities as if they are simultanaeous equation
We cannot technically solve like simultaneous eqn coz if we multiply/divide by a -ve number the direction will change and then we cannot do anything with them!!!...
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I solved it in a rather informal way. Let´s see if my reasoning is OK:
The problem is asking as if it is possible to say that x and y are both positive or negative ( so as xy<0)
(1) Only relative info, impossible to tell about the main issue.
INSUFF
(2) The same, only relative info.
INSUFF
Now considering together (1) and (2).
From (1) we know the "distance" between x and y is 2, but we don´t know if both of them are in the same "side" of the number line (if both of them are negative or positive).
From (2) we get that, by susbstracting an addiotional "y" to x, we get a "lowe" number, so y is deffinetly negative. And we also get that the result is less than -6, so to go from -2 to -6, that additional "y" has to be greater than 4. With that info, if we look again in (1) if you substract a number bigger than 4 (y) from x it gives you a number bigger than -2, so X must be positive too.
Then (1) + (2) SUFF. Answer C
The problem is asking as if it is possible to say that x and y are both positive or negative ( so as xy<0)
(1) Only relative info, impossible to tell about the main issue.
INSUFF
(2) The same, only relative info.
INSUFF
Now considering together (1) and (2).
From (1) we know the "distance" between x and y is 2, but we don´t know if both of them are in the same "side" of the number line (if both of them are negative or positive).
From (2) we get that, by susbstracting an addiotional "y" to x, we get a "lowe" number, so y is deffinetly negative. And we also get that the result is less than -6, so to go from -2 to -6, that additional "y" has to be greater than 4. With that info, if we look again in (1) if you substract a number bigger than 4 (y) from x it gives you a number bigger than -2, so X must be positive too.
Then (1) + (2) SUFF. Answer C