Data Sufficiency

If xy ≠ 0, is x > y?

(1) 4x = 3y

(2) |y - x| = x - y

I want to rephrase |y-x| please tell me if Im right.

Removing the absolute bars we get
y-x=x-y when y-x>=0 ...................................(a)
y-x=-(x-y)=y-x when y-x<=0.............................(b)

For equation a lets assume y-x=2
2=x-y ----------->x=y+2
0=x-y------------>x=y

For equation b lets assume y-x=-3
-3=y-x----------->x=y+3
y-x=0------------>x=y

Therefore statement 2 gives us 3 equations to play with.

I rephrase the main question as --

If xy ≠ 0, is x > y?

(1) 4x = 3y

(2) x=y+3 or x=y or x=y+2

Individually st 1 and st 2 are insufficient and thus we rule out option A,B and D

When we combine the St 1 and St2 we get

Pair 1- 4x=3y and x=y+3 we get y=-12 and x=-11 x>y confirmed ----YES

Pair 2- 4x=3y and x=y we get x=0 and y=0 which is not permissible due to conditions in the Question stem.


Pair 3- 4x=3y and x=y+2 we get y=-8 and x=-7 x>y

As a result C is the right answer..Is this the right way of solving this question?Is my mathematics correct when rephrasing the question?


When checking st1 individually x/y=3/4 here x<y and answer to the Question stem is No.

x/y could also be -3/-4 here x>y and the answer to the question stem is Yes.

Yes and No make statement 1 insufficient

When checking for statement 2--

x=y+3 when y is 2 ,x is 5 x>y----Yes
when y is -3, x is 0 x>y---Yes

x=y -----No


x=y+2 when y is 1,x is 3-------Yes
when y is -4 x is -2------Yes

Yes,No,Yes makes statement 2 insufficient.

My concern is that there's no overlap between statement 1 and statement 2 at all..Is that ok? I've done everything mathematically following all the rules.Im just concerned about the overlap not being there.Please clarify.