Data Sufficiency

I would appreciate any help with the following:

Q1. Are x and y both positive?
(1) 2x- 2y = 1;
(2) (x/y) > 1.

Q2. In the xy-plane, does the line with the equation y = 3x + 2 contain the point (r,s)?
(1) (3r + 2 - s)(4r+9-s) =0;
(2) (4r-6-s)(3r + 2 - s) =0.

Q3. Is |x - y| > |x| - |y|?
(1) y < x;
(2) xy < 0.

Thanks,

1. E

1. 2x - 2y = 1 -- x = 1, y = 1/2

x = -1/2, y = -1

in suff

2. x/y > 1, only tells us that x and y should be of same sign...

1. + 2. does not tell anything therefore, E

2. C, put (r,s ) in the equation of line 3x - y + 2 =0,

x = r and y = s,

1. 3r - s + 2 might be 0 -- insuff
2. again tells us that 3r - s + 2 might be 0 -- insuff

1. + 2. tells us that 3r- s + 2 = 0 hence suff

3. c

let me know if the answer is right..i will explain

I actually got different answers. Like the post above though, I do not want to post all of my work only to find out I am wrong.

My differing answers are:
1)C
3)B

A brief overview of why I think C works for #1 is because in statement 1 you can move things around and get x=y+1/2

Plug that into statement two and you have (Y+1/2)/Y, which reduces to Y/2>0. This implies that Y is greater than 0.

Now if as you said in statement 1, both x and y need to be either both positive OR both negative. You know they are both positive.

Let us know the OA, thanks!

I agree with B for 3. Questions rephrase is is x > 0 & y > 0.

zskhan wrote:I would appreciate any help with the following:

Q3. Is |x - y| > |x| - |y|?
(1) y < x;
(2) xy < 0.

|x-y| >= |x| - |y| (triangle inequality).

|x-y| + |y| = |x| (extreme condition)
This can happen ---0===y===x--- or when ---x===y==0---
In other words, this is true when xy >= 0.

(2) is sufficient on its own. B

zskhan wrote:I would appreciate any help with the following:

Q1. Are x and y both positive?
(1) 2x- 2y = 1;
(2) (x/y) > 1.

Thanks,

2. y(y-x) < 0

1. x-y = 1/2

1. If y is positive, x is positive. Insuff

2. 0 < y < x or x < y < 0 (on its own)

Combining two gives us y is +ve. Sufficient.

C is the answer