nzk5053 wrote:

sarathvr wrote:

Essentially I think the question is asking 'are the slopes equal?'

So I got B

How did you get B? I got E...

Bunuel would you be able to provide us explanation?

Let me try to answer.

You are given that l1: y=ax+b and l2: y=cx+d

Also, for ac=a^2 ---> a^2-ac=0 ---> a(a-c)=0 ---> either a=0 (line l1 is parallel to the y-axis) or a=c (slopes of lines l1 and l2 are equal). Thus for answering this question for "sufficiency", any statement or a combination that gives you either a=0 or a=c will be sufficient.

Per statement 1, d=b+2 ---> y-cx=y-ax+2 ---> x(a-c)=2. Not sufficient.

Per statement 1, what it means in simpler terms is that there is a point (x,y) on l1 such that for every single one of these points you have a corresponding point on l2 with coordinates (x,y+k) . In other words, if there is a point (m,n) on l1 then the corresponding point on l2 will be = (m,n+k), k being constant. Clearly, the 'x' coordinate of the 2 corresponding points on lines l1 and l2 is the same while the y coordinates differs just by a constant. Thus the slopes of lines l1 and l2 are equal ---> a=c.

You can think of it by drawing (l1) y=x+2 and (l2) y =x+4 follows what is mentioned in statement 2. If there is a point (1,3) on l1, you will get a corresponding (1,5=3+2) point on l2. This shows that the x-coordinates are the same , giving you the same slope of value 1.

Thus this statement is sufficient.

Hope this helps.