I say the answer is D.
Looking at (1):
If x is greater than y and, (as the problem states) x + y is greater than 0 then x must always be positive.
if x is positive and is greater than y then:
4 + 3 is greater than 0 and 4 is greater than 3; if y is negative then it still must satisfy x + y is greater than 0 so the absolute | y | must be less than x; for example using the -5 you have x would need to be a positive number greater than |-5| for x + y greater than 0; i.e. 6 + (-5) is greater than 0
If you use a number less than 5 then the equation x + y is greater than 0 cannot be satisfied; i.e. 4 + (-5) = -1 and this is not greater than zero.
After doing (1) we know the answer cannot be (E) so now we go to (2) to see if the answer is possibly (D) or (A)
Looking at (2):
(2) states y is less than 0
We know from the problem that x + y is greater than 0; thus if
y is less than 0 , x must be positive which is similar to the answer
above. Consequently, | y | must be less than x, otherwise x + y
is greater than 0 cannot be satisfied.
Looking at the -5 you posted, we can insert that in the equations:
x + y is greater than 0; if y = -5 then x must be a number greater than positive 5
for the equation to be true; thus we can use 6 + (-5) is greater than 0.
Checking to see if x is greater than | y | we get 6 is greater than | -5 | or 6 is greater than 5
Just to make sure I am correct we can play with the numbers and pick a
number less than | y |, such as 4; 4 + (-5) = -1 wich does not
satisfy the equation x + y is greater than 0 so we see we cannot use a number X
that is less than the absolute value of Y.
