If x and y are integers, then xy(x + y) is

Question

A. Always positive
B. Always negative
C. Positive when x is positive
D. Negative when x is negative
E. It cannot be determined by the information given

msk0657 · Answer

Given x and y are integers, then xy(x + y)

Let's take even as 2 / -2 and odd as 3 / -3..we get the following.. and IMO option D is correct answer..

Anigr16 · Answer

I presume its Option E if am not missing anything.
x=-3 and y=1
xy(x + y) is positive = 6

duahsolo · Answer

If you consider the case where x = 0 or y = 0, the result is zero regardless of the value (be it positive or negative) of the other variable.

so given that x < 0 (i.e, x is negative) and y = 0, the result = 0.

So I think the answer is E

Donnie84 · Answer

We cannot determine the sign of the given expression with absolute certainty.

Few possible combinations:

x = 0; y = 0
x = 1; y = 2
x = -1; y = 2
x = -2, y = -1

Answer (E).

KarishmaB · Answer

The question is straight forward as given. Consider the integer value 0. The expression xy(x+y) can be 0 if either x or y is 0 and hence it needn't be "always positive" or "always negative".
Even when x is positive/negative, if y is 0, the expression will be 0. So it needn't be positive/negative. 
So answer must be (E).

If you were given that xy is not 0, note that xy(x+y) is symmetrical in x and y. So the sign wouldn't depend on the sign of one of the variables. 
If one variable is positive and the other negative, the expression could be either positive or negative. 
Say if x = 2 and y = -5, the expression is positive.
If x = 2 and y = -1, the expression is negative. 
All 4 options (A), (B), (C) and (D) are proved wrong. 
So answer would be (E) in this case too.

sudhirgupta93 · Answer

I think until and unless we don't know which of the two is greater, we can't give an affirmative answer from given info and options.

Ishaan30 · Answer

Made a simple table for this question - X Y + > < - - > < + + > < + - > < - With this table, it streamlines evaluating the options. Check where X and Y are either positive or negative because and it shows that it won't be always positive. From the previous option, we know that it cannot always be negative. Take the scenarios where X is positive and then evaluate using Y. Nope, there is a scenario where X is positive but the solution is negative. Take the scenarios where X is negative. There is a scenario when the solution comes out as positive. Yeah! Since none of the options worked, this would be the correct answer. I always try to streamline things when I know that I have to test it out using multiple cases.

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If x and y are integers, then xy(x + y) is

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If x and y are integers, then xy(x + y) is

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