1.If the product of X and Y is a positive number, is the sum of X and Y a negative number?
1. X > Y^5
2. X > Y^6

If xy > 0, is x + y < 0?

Stmt 1. X > Y^5

X and Y can be either positives , negatives or X a positive and Y a negative. Here is an example;

When Y = 1 , X = 2 OR Y = -2 , X = -10 OR Y= (-2), X = 65. So is x + y < 0 , the answers are NO, Yes and No respectively. So insuff.

Stmt 2. X > Y^6
X and Y can only be both positives or both negatives or Y is a negative. Here is an example;

When Y = 1 , X = 2 OR Y = (-2) , X = 65 OR Y = (-5) , X = -5. The answers to whether x + y < 0 are No ,No and Yes respectively.So insuff.

Merging the stmts is not helpful.

Thus E

My opinion is different from Haaress'. I believe that the answer is B. Haaress' mistake is to plug in Y=-2 and X=65. This contradicts the stem "the product of X and Y is a positive number"

We know that xy is positive, so x & y have the same sign. We're asked "is x+y negative?" The answer can only be yes if x and y are both negative (remember, they must have the same sign). So rephrase the question to: "Are x & y negative?" (if one is negative, so will the other be)

(1) x > y^5. Y^5 could be positive or negative. We don't know anything about signs. For instance if (x,y)=(2,1) then x+y will be positive. On the other hand, if (x,y)=(-1,-2) then x+y will be negative. NOT SUFFICIENT

(2) x > y^6. y^6 is a positive number, so X must be positive. We know from the stem that xy is positive meaning x and y have the same sign. Since x is positive y is also positive and x+y must be positive. SUFFICIENT

Pick B

Hope that helps,
-Patrick

Thanks Patrick, I must have overlooked the product condition. I agree with you but I don't harass people but I am Haaress.

1.If the product of X and Y is a positive number, is the sum of X and Y a negative number?
1>X > Y^5
2>X > Y^6

Stmnt 1 is clearly insuff as we have both yes and no
Stmnt 2: X > Y^6
which clearly indicates X is positive and Y could be +ve or -ve.
If we rephrase the eqn X - Y^6 >0 as we know X > y^6

So pick B

Haaress wrote:Thanks Patrick, I must have overlooked the product condition. I agree with you but I don't harass people but I am Haaress.

I tend to overlook limitations like that myself. And I am sorry for misspelling your name Haaress. -Patrick