Ashley@VeritasPrep wrote:The first statement really doesn't communicate anything beyond what it says at face value, so it's certainly insufficient by itself.
Statement (2) by itself is not terribly helpful either -- it lets us now that line N hits the y-axis higher up than line P does, but we don't know anything about how either of the lines is moving -- falling steeply, falling slowly, rising steeply, rising slowly, etc.
Now let's combine the statements. Remember that slope is rise/run, so we'll consider each line's slope by focusing on its trip from the point where it hits the y-axis to the point (5,1). The "run" in both of these cases is just 5. The "rise" for line N is (1 - N's y-intercept), and the "rise" for line P is (1 - P's y-intercept). But since we KNOW that N's y-intercept > P's y-intercept, we can conclude that we are subtracting a greater number from 1 in our expression for the rise of line N than we are in our expression for the rise of line P. Therefore the rise of line N will turn out to be a smaller number. So, returning to rise/run form, we wind up comparing N's slope "less"/5 to P's slope "greater"/5, so P's slope is definitively greater, i.e. the answer to the question is definitively yes. So the combination of (1) and (2) is sufficient.
Lines N & P lie on the XY plane. Is the slope of N < the slope of P?
1) N & P intersect at (5,1)
2) Y-int. of N > y-int. of P
There is a very simple way of doing this without getting bogged down by all these details...
Every line in a 2D plane is of the form :
y = mx + c ,
where (x,y) are the X-Y co-ordinates , m = slope of the line, c = y-intercept
Let n be the slope of line N, a = y-intercept of line N
p be the slope of line P, b = y-intercept of line P
Here as per
1)
Line N : 1 = 5n+a
Line P : 1 = 5p+b
We cannot say if n>p or n=p or n<p unless we know the relation between a and b
So 1 is not sufficient
2)
Y-int. of N > y-int. of P
or
a > b
This is not at all sufficient
If you combine 1 and 2 you know
Line N : 1 = 5n+a
Line P : 1 = 5p+b
and
a > b
So the relation b/w slopes of Lines N and P (n and p) can be found unambiguously.....
So C is the OA
You can also solve this if you want....But I will never recommend you to solve if you can get the answer without solving...After it is a DATA SUFFICIENCY question and not a PROBLEM SOLVING question.
, since definitively no and definitively yes both mean sufficient! But you're right, it should say "definitively yes."
