LalaB wrote:x/y < b/c can be written as xc <by . it is the same as the 1st stmnt (cx-yb<0 or cx<0+by cx<by)

Hi LalaB!

This is true ONLY if we know that C & Y have the same signs (if only one is negative, then the signs will switch direction).

In fact, this is a pretty tough problem. From the stem we actually have a 2-step question:

Question Stem:
If we know that cy>0, then is xc<by?
If we know that cy<0, then is xc>by?

We have to know BOTH the relationship between xc and by, as well as the sign for cy.

Statement 1: cx < yb
We know that xc<by, but we don't know if cy>0... Not Sufficient.

Statement 2: bx < cy
If we know that bx<cy, that doesn't tell us about the xc<by relationship OR enable us to determine if cy is positive or negative... Not Sufficient.

Statement 1+2: cx < yb & bx < cy
The only real way to combine these is to stack and add and hope that something simplifies...

xc<by
+bx<cy
------
xc + bx < by + cy
x(b+c) < y(b+c)

So, if (b+c)>0, then x<y.
and if (b+c)<0, then x>y...
But this doesn't tell us the information me need to know...Not Sufficient.

**Picking Numbers**
I will warn you up front that picking numbers for this problem is fairly AWFUL (it took me a while to come up with sets of numbers for 4 variables that make the statements true, but then give both a Yes and a No answer to the question stem (proving insufficiency). But I will show you a few of those sets here.

Statement 1: cx < yb
Option 1: {b=-1, c=-1, x=6, y=2}
cx < yb --> (-1)(6)<(2)(-1) --> -6 < -2 Fits the constraint of the Statement.

Is x/y < b/c? 6/2<-1/-1 --> 3 < 1 NO!

Option 2: {b=-6, c=-2, x=1, y=-1}
cx < yb --> (-2)(1)<(-1)(-6) --> -2 < 6 Fits the constraint of the Statement.

Is x/y < b/c? --> 1/-1 < -6/-2 --> -1<3 YES!

Two different answers to the question...NOT Sufficient


Statement 2: bx < cy
Option 1: {b=-1, c=-1, x=6, y=2}
bx<cy --> (-1)(6)<(-1)(2) --> -6<-2 Fits the constraint of the Statement.

Is x/y < b/c? 6/2<-1/-1 --> 3<1 NO!

Option 2: {b=-6, c=-2, x=1, y=-1}
bx<cy --> (-6)(1)<(-2)(-1) --> -6<2 Fits the constraint of the Statement.

Is x/y < b/c? --> 1/-1 < -6/-2 --> -1<3 YES!

Two different answers to the question...NOT Sufficient

Statement 1+2: cx < yb & bx < cy
Notice that I used the same numbers for Options 1 and 2 when testing each statement. I did so because it saves me time when looking at them together. I can see that I have 2 sets of numbers that fit all of the Statement constraints, but they give me 2 different answers for the Question Stem... NOT Sufficient

Therefore, the correct answer is E.

Hope this clears up some of the confusion!

Whit