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(I) Tells us y is positive whatever the value of x is. x can be +ve or -Ve, Hence Insuff. (II) Tess us that x>y. Both can be negative, positive or one negative and the other positive (vice versa). Not Suff

I and II together. Y is positive from I, x>y from II, Hence x and y are bothe +ve. Therefore, xy<0 is False. Suff.
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To find what you seek in the road of life, the best proverb of all is that which says: "Leave no stone unturned." -Edward Bulwer Lytton

From stmt 1, y = x^3(x-1)....here x does not equal 0 and 1 otherwise xy will become 0. Hence, if x > 0, y will always be >0. and if x < 0, y will again be >0. Hence ,insufficient.

Combining this with stmt2, only possibility is of x>0 and y>0. Hence, sufficient.

I have a feeling that it should be E. Reason: when you combine I and II, we are left with two conflicting cases: case 1: x is between 0 and 1 which makes y < 0 and product negative case 2: x is greater than 1 (which makes y > 0) and at some point between 1 and 2 which makes x > y (its important to note that for values of x around 2 or more, x is always less than y). product is positive.

Thus E.

I have to say that this took me a long time and I would have guessed in the real test, or maybe I am missing some trick. is the OA C?

I have a feeling that it should be E. Reason: when you combine I and II, we are left with two conflicting cases: case 1: x is between 0 and 1 which makes y < 0 and product negative case 2: x is greater than 1 (which makes y > 0) and at some point between 1 and 2 which makes x > y (its important to note that for values of x around 2 or more, x is always less than y). product is positive.

Thus E.

I have to say that this took me a long time and I would have guessed in the real test, or maybe I am missing some trick. is the OA C?

And that is the whole problem. There is NO value of x for which it can be an int, positive and greater than 1, AND greater than y.

I have a feeling that it should be E. Reason: when you combine I and II, we are left with two conflicting cases: case 1: x is between 0 and 1 which makes y < 0 and product negative case 2: x is greater than 1 (which makes y > 0) and at some point between 1 and 2 which makes x > y (its important to note that for values of x around 2 or more, x is always less than y). product is positive.

Thus E.

I have to say that this took me a long time and I would have guessed in the real test, or maybe I am missing some trick. is the OA C?

While we are awaiting OA, I think for any value of x > 1, difference between x^4 and x^3 will always be greater than x. I tried with value of x = 1.01 and got this true. Not sure whether there is any such mathematical rule. Can someone confirm please?

St1. since x is integer x^4 -x^3 will always be positive but we dont know the sign of y so insuff. St2 is insuff. since it doesn't tell us abt x

combine: y is positive and since x is on the riht side of y it too ought to be positive. now even if x is 0 or 1 xy would be equal to 1 and not less then 0 so answer is C.

If x and y are integers and xy does not equal 0, is xy < 0?

(1) y = x^4 – x^3

(2) x is to the right of y on the number line

This question looks defective. Check the wording of statement (2)

kevin, why do you think that wording in 2nd statement can be wrong?

question stem clearly says that x y are integers and this makes y either 0 or more than 0 2nd statement says that y < x combining both statements make xy either 0 or more than 0. and this gives the anser of the question that is xy < 0 .....suff.

I have a feeling that it should be E. Reason: when you combine I and II, we are left with two conflicting cases: case 1: x is between 0 and 1 which makes y < 0 and product negative case 2: x is greater than 1 (which makes y > 0) and at some point between 1 and 2 which makes x > y (its important to note that for values of x around 2 or more, x is always less than y). product is positive.

Thus E.

I have to say that this took me a long time and I would have guessed in the real test, or maybe I am missing some trick. is the OA C?

This might be confusing. i forgot that x and y are integers. regardless, the inequality has no solution so IMO answer should be E. @ scthakur - i cannot think of a rule, this function is a parabola which intersects the line y=x somewhere between 1 and 2. just to prove that i spent too much time on this question. (note to self - give up after 3 minutes!!)