the above post is wrong; the correct answer should be (c), not (e).
Is x + y > x y?
it's probably best not to rephrase this statement, since the two elements on either side of the inequality -- a sum on one side, and a product on the other side -- are really easy to think about.
it's possible to move things over and factor the expression, as the poster above me just did, but that creates an expression that is much harder to think about with any significant degree of intuition.
(1) x > 0 > y. [/quote]
this just means that x is positive and y is negative.
getting a "yes" to the question is easy; xy is always negative, so, if you create a situation in which x is positive, then you will get a "yes".
try x = 3, y = -2.
1 > -6, so "yes".
to get a "no" to the question, you need to make (x + y) even more negative than xy. one way to do this is to take advantage of the fact that multiplying by a tiny decimal creates a really small number, but adding to a really tiny decimal doesn't have much of an effect:
try x = 0.001, y = -10.
then -9.999 < -0.01, so "no".
insufficient.
(2) |y| = x.
this means that x is positive or 0, and y is either x or -x.
the easiest way to get a "no" is to let x = y = 0, in which case 0 = 0 (not ">").
to get a "yes", just let y = -x. in this case, the product will be negative, but the sum will be zero (since the numbers are opposites).
e.g., if x = 2 and y = -2, then 0 > -4, so "yes".
insufficient.
--
together:
in this case, x is positive, and y is the opposite of x.
if that's true, then the sum of (x + y) must be 0, and the product (xy) must be negative.
0 is always greater than a negative number, so these statements together are sufficient.
answer (c)
--
to the poster in the previous post -- it doesn't look as though you actually thought about considering the statements together! it seems that you just thought you were done, and picked (e), as soon as you ascertained that both individual statements are insufficient.
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