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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.

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

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.

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.

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.

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.