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since r is non zero (mentioned in Ques) hence, x and y, they cannot be both +ve or both -ve (as |x| = |y|)

so one has to +ve and other -ve, so that x-y still remains a non zero number, and since their mod values are same, x-y = 2x (assuming y = -x, there cant be any other valid assumption) and the denominator (2x + y) will be equal to x, so the value of the exp is 2x/x = 2.

stmt 2 alone is obviously not sufficient as there is no way to determine y.

(1) is not sufficient. x can be a negavtive of y, and vice versa. Similarly, both could be similar negative or postive values.
We can try by putting in some numbers, same x = 10, y = -10, then r=2
Or x = -10, y=10, then r = 2
Or x = 10, y=10, then r=0
And x = -10, y=-10, then r = 0

So we don't really know the value of r from this statement.

2) Not sufficient as well as we know nothing about y.

(1) and (2), x=-3, |x|=3=|y|
so y=+3, or -3
If y=+3, x=-3, r=-3-3/2(-3)+3, and r = 2
If y=-3, x=-3, r=-3+3/2(-3)-3 and r = 0
So again, we don't really know the value or r.

In the question it is specifically mentioned that r, x and y are non zero numbers, so r = 0 is not even of our concern. We need to know the value of r, while we know r is not 0, so r could be of an negative value or positive value. Using x and y as I mentioned all we get is an positive value.

hah ! alex, my bad. I did not spot the limits 'r x and y are non-zero'. No excuses, but i was working that at my workplace, so perhaps I missed it. Great work !

If x, y, and r are all nonzero numbers, what is the value of
r = (x-y) / (2x+y)

1) lxl = lyl
2) x = -3

By 1) alone, there are 4 possibilities:

+x, +y or +x, +x
+x, -y or +x, -x
-x, -y or -x, -x
-x, +y or -x, +x

+x, +y will give (x-x) / (2x+x) = 0
+x, -y will give (x-(-x)) / (2x-x) = 2x / x = 2
-x, -y will give (-x-(-x)) / (-2x-x) = 0 / -3x = 0
-x, +y will give (-x-x) / (-2x+x) = -2x / -x = 2

Now in the question, it says r cannot be 0, and from the above 4 possibilities, we can eliminate the first and 4th possibilities. This leads us to say r=2, and this allows us to answer the question - what is the value of r if it is a nonzero? We can test by substituting any number into the equation. Let's say x=5 and y=-5, we will get r=2. If we let x-8, y=-8, we will still get r=2. Same apply to x=-5, y=5 or x=-8, y=8. Why don't we consider x=5, y=5? Because in the question, it says r cannot be 0.

By 2) alone, we have no clue to answer the question.

So my answer is A. Pls post the correct answer....

OA is A guys. I thought this was a good catch question where the key lay in the opening sentence r is not equal to 0 so x = -y or y = -x according to A which is sufficient _________________