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X+Y>0

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score780
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X+Y>0 [#permalink] New post   16 Mar 2013, 11:51
Isn't it always the case that if X+Y>0 then X>-Y. I know that it's an easy one, I just can't get my mind around it. I am solving the hard questions but then my mind blocks on the easy ones.

DS question:

Is X+Y positive?
1-X-Y is positive
2-Y>0

What is the answer? C?
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X+Y>0 [#permalink] New post   Updated on: 30 Oct 2021, 11:23
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score780 wrote:
Isn't it always the case that if X+Y>0 then X>-Y.

Yes IT IS TRUE ALWAYS!
X+Y > 0 take Y to the other side or subtract both the sides by Y we get:
X+Y - Y > 0 - Y
=> X > -Y

score780 wrote:
DS question:

Is X+Y positive?
1-X-Y is positive
2-Y>0


Question is is X + Y > 0
STAT1
X-Y > 0
=> X > Y
Only thing which this option tells us is that X is greater than Y
Now, X and Y can both be negative then X + Y < 0
X can be positive and Y can be negative and |Y| > |X| then X + Y <0
X can be positive and Y can be negative and |Y| = |X| then X + Y =0
X can be positive and Y can be negative and |Y| < |X| then X + Y >0
X and Y can both be positive, in this case X + Y > 0
So, NOT Sufficient

STAT2
Y > 0
This is not sufficient as we have no information about X

STAT1 and STAT2 together give us that X > Y and Y is positive so, obviously X will also be positive
Hence, X + Y >0 (because both X and Y are positive)
So, answer will be C

Hope it helps!

Watch the following video to learn the Basics of Inequalities



Check out this post to understand Inequalities in Detail

How to Solve: Inequalities (Basic)

Originally posted by BrushMyQuant on 16 Mar 2013, 12:39.
Last edited by BrushMyQuant on 30 Oct 2021, 11:23, edited 2 times in total.
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Re: X+Y>0 [#permalink] New post   16 Mar 2013, 19:21
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score780 wrote:
nktdotgupta wrote:

Question is is X + Y > 0
STAT1
X-Y > 0
=> X > Y
Only thing which this option tells us is that X is greater than Y
Now, X and Y can both be negative then X + Y < 0
X can be positive and Y can be negative and |Y| > |X| then X + Y <0
X can be positive and Y can be negative and |Y| = |X| then X + Y =0
X can be positive and Y can be negative and |Y| < |X| then X + Y >0
X and Y can both be positive, in this case X + Y > 0
So, NOT Sufficient


Thank you very much. I am just confused about the statements where you included absolute values. You say X+Y can both be negative then X+Y<0, this I understand. Then you say "X can be positive and Y can be negative and |Y| > |X| then X + Y <0". Is it possible for you please to explain this and how it links to assessing if stat 1 is sufficient.


All the cases of STAT1 with examples are explained below in detail:--

-> Now, X and Y can both be negative then X + Y < 0
Ex:- X= -1 Y =-2
then, X+Y = -1 + (-2) = -3 which is less than zero so
X+Y < 0 (it helps in proving that in some cases X + Y < 0 i.e. X+Y is NOT positive)

-> X can be positive and Y can be negative and |Y| > |X| then X + Y <0
X = 6 Y = -9
then |X| = 6 and |Y| = 9
so, |X| < |Y|
so, X + Y = 6 + (-9) = -3 which is less than zero
So, X + Y < 0 (it helps in proving that in some cases X + Y < 0 i.e. X+Y is NOT positive)


-> X can be positive and Y can be negative and |Y| = |X| then X + Y =0
X = 6, Y = -6
then, |Y| = 6 and |X| = 6
so, |X| = |Y|
so, X + Y = 6 + (-6) = 0
X + Y = 0 (it helps in proving that in some cases X + Y = 0 i.e. X+Y is NOT positive)

-> X can be positive and Y can be negative and |Y| < |X| then X + Y >0
X= 7, Y =-3
then |X| = 7 and |Y| = 3
so, |X| > |Y|
X + Y > 0 (it helps in proving that in some cases X + Y > 0 i.e. X+Y is positive)

-> X and Y can both be positive, in this case X + Y > 0
X = 3, Y =4
then, X + Y = 3+4 = 7
So, X + Y > 0 (it helps in proving that in some cases X + Y > 0 i.e. X+Y is positive)

So, in some cases X + Y is positive and in some case it is NOT.
So, Statement 1 is not sufficient.

Hope it helps!
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Re: X+Y>0 [#permalink] New post   24 Mar 2013, 22:56
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score780 wrote:
nktdotgupta wrote:

Question is is X + Y > 0
STAT1
X-Y > 0
=> X > Y
Only thing which this option tells us is that X is greater than Y
Now, X and Y can both be negative then X + Y < 0
X can be positive and Y can be negative and |Y| > |X| then X + Y <0
X can be positive and Y can be negative and |Y| = |X| then X + Y =0
X can be positive and Y can be negative and |Y| < |X| then X + Y >0
X and Y can both be positive, in this case X + Y > 0
So, NOT Sufficient


Thanks again. I understand all your analysis. But what I am not being able to understand is how did you make the link of stat 1 to the analysis you made on X+Y>0 and say it's insufficient.



Its because stat1 in some cases gives X + Y > 0 and in some cases gives X + Y < 0 and in one case X + Y = 0
Since, it is not giving a common answer to whether X + Y > 0
So it is insufficient to answer.

Hope it helps!
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Re: X+Y>0 [#permalink] New post   16 Mar 2013, 13:28
nktdotgupta wrote:

Question is is X + Y > 0
STAT1
X-Y > 0
=> X > Y
Only thing which this option tells us is that X is greater than Y
Now, X and Y can both be negative then X + Y < 0
X can be positive and Y can be negative and |Y| > |X| then X + Y <0
X can be positive and Y can be negative and |Y| = |X| then X + Y =0
X can be positive and Y can be negative and |Y| < |X| then X + Y >0
X and Y can both be positive, in this case X + Y > 0
So, NOT Sufficient


Thank you very much. I am just confused about the statements where you included absolute values. You say X+Y can both be negative then X+Y<0, this I understand. Then you say "X can be positive and Y can be negative and |Y| > |X| then X + Y <0". Is it possible for you please to explain this and how it links to assessing if stat 1 is sufficient.
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Re: X+Y>0 [#permalink] New post   24 Mar 2013, 12:48
nktdotgupta wrote:

Question is is X + Y > 0
STAT1
X-Y > 0
=> X > Y
Only thing which this option tells us is that X is greater than Y
Now, X and Y can both be negative then X + Y < 0
X can be positive and Y can be negative and |Y| > |X| then X + Y <0
X can be positive and Y can be negative and |Y| = |X| then X + Y =0
X can be positive and Y can be negative and |Y| < |X| then X + Y >0
X and Y can both be positive, in this case X + Y > 0
So, NOT Sufficient


Thanks again. I understand all your analysis. But what I am not being able to understand is how did you make the link of stat 1 to the analysis you made on X+Y>0 and say it's insufficient.
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Re: X+Y>0 [#permalink]
24 Mar 2013, 12:48

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