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DS Rephrasing / Number Props problem

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by ilikaroy » Thu Aug 05, 2010 7:18 pm
MGMAT must have rephrased the second statement which is given as x+y+1 < 0 by taking 1 on the right hand side of the inequality an thus changing it into -1.


From (1) we have z > x+y+1.
z-1 > x+y
2z-1 > x+y+z
Since main question says x+y+z>0, we have 2z -1 > 0 or z>1/2.

So z >0.

Even 1) alone should be sufficient.
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by selango » Thu Aug 05, 2010 8:53 pm
Can check the question again?

is z>1?rt?
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by missrochelle » Fri Aug 06, 2010 3:08 am
The question is worded correctly. It's #84 from the OG10.

If X+Y+Z>0, IS Z>1?

They rephrase based on the fact that they are asking about Z, so what can we say about "X+Y" that would have to be true in order for Z to be greater than 1? In other words (X+Y)+(Z, greater than 1) > 0

Thus, the rephrased question is "Is X+Y Less than -1?" If this is true, then Z will be greater than 1.

1) Z> X+Y+1 -- to rephrase the statement you get Z-1 > X+Y... Tells you nothing about X+Y vs -1
Insuff.

2) X+Y +1 <0 -- becomes X+Y < - 1. Matches our rephrasing. Sufficient.

BUT I STILL DONT UNDERSTAND THE QUESTION REPHRASING!
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by selango » Fri Aug 06, 2010 4:26 am
In the first post you have posted is z>0?

ok now coming to the question.

x+y+z>0

z>1?

The question rephrased is such a way that we are taking x+y as negative and z as positive.

If x+y<-1 surely z must be greater than 1 so that the equation x+y+z>0 is satisfied.

For ex:

If we take x+y<-1,x+y=-2

For the equation x+y+z>0 to satisfy,z must be greater than 1.

x+y=-2,z=3-->x+y+z>0

Hope this clarify.
Last edited by selango on Fri Aug 06, 2010 6:11 am, edited 1 time in total.
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by missrochelle » Fri Aug 06, 2010 5:03 am
Yes, but greater than 1 doesnt have to mean Z =3, it could mean z = 2.

In which case (x+y) + z ===> (-2) + 2 = 0. which is not >0 and doesn't satisfy the statement.

So i'm still a bit confused by how <-1 works for the equation.
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by nithi_mystics » Fri Aug 06, 2010 5:21 am
Exactly! The answer should be D.
ilikaroy wrote:MGMAT must have rephrased the second statement which is given as x+y+1 < 0 by taking 1 on the right hand side of the inequality an thus changing it into -1.


From (1) we have z > x+y+1.
z-1 > x+y
2z-1 > x+y+z
Since main question says x+y+z>0, we have 2z -1 > 0 or z>1/2.

So z >0.

Even 1) alone should be sufficient.
Thanks
Nithi
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by missrochelle » Fri Aug 06, 2010 5:23 am
Does anyone have the OG10th edition to see their methodology and answer? I am confident MGMAT said the answer is B not D. But now that I read your explanation for statement 1, it actually makes sense.
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by selango » Fri Aug 06, 2010 6:25 am
missrochelle,

The confusion occurs bcoz in the first post u have posted "is z>0"

if the question is "z>0",stmt1 is sufficient.

However if the question is "z>1" stmt1 is not sufficient.

z > x+y+1

z-1 > x+y

2z-1 > x+y+z

Since the question says x+y+z>0, we have 2z -1 > 0 or z>1/2.

z=2,z>1

z=0.7,z<1

Hence A is not sufficient.
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by selango » Fri Aug 06, 2010 6:27 am
missrochelle wrote:Yes, but greater than 1 doesnt have to mean Z =3, it could mean z = 2.

In which case (x+y) + z ===> (-2) + 2 = 0. which is not >0 and doesn't satisfy the statement.

So i'm still a bit confused by how <-1 works for the equation.
Given that x+y+z>0

If x+y<-1,z must be surely greater than 1 to satisfy the equation x+y+z>0

If we take x+y=-2, we cannot take z=2 as it does not satisfy the equation.

So we take z=3

Whatever value ur assigning for (x+y),ensure that value of z is such that x+y+z>0
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by missrochelle » Fri Aug 06, 2010 7:06 am
Still not clicking for me. What if X+Y is 2, and Z =2... then all equations are still satisfied and X+Y is not less than -1.



Even when I manipulate it this way --

X+Y+Z > 0, therefore X+Y > - Z.

If we are looking for Z>1, then how do we plug that into the rephrased inequality above?
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by missrochelle » Fri Aug 06, 2010 7:08 am
selango wrote:
The question rephrased is such a way that we are taking x+y as negative and z as positive.

.

Why are we taking x+y as negative? I think that's where I am getting hung up.
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by nithi_mystics » Fri Aug 06, 2010 7:12 am
The second statement is
x+y+1 < 0
Adding -1 to both sides,

x+y+1-1 < -1

===> x+y < -1
missrochelle wrote:
selango wrote:
The question rephrased is such a way that we are taking x+y as negative and z as positive.

.

Why are we taking x+y as negative? I think that's where I am getting hung up.
Thanks
Nithi
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by selango » Fri Aug 06, 2010 7:12 am
...
Last edited by selango on Fri Aug 06, 2010 7:16 am, edited 1 time in total.
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by missrochelle » Fri Aug 06, 2010 7:13 am
Hmmm isn't that against the rules? The whole point of the lab was to rephrase without looking at the statements. This is a weird , and confusing question.
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