GMAT data suffiency / math question - please help!?

Question

Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?

(1) Lines n and p intersect at point (5,1)
(2) The y-intercept of line n is greater than the y-intercept of line p.

You can solve by using both statements - can you help?

Answer 1

The lines intersect at 5, 1; and line n hits the y axis higher than line p.

Line p travels from its y intersect to the point 5,1 and beyond in a straight line. Line n is higher (on the y axis) than line p as it travels from its y intersect; at point 5, 1, they intersect and line n is below line p as it continues upward along x.

Since line n "decreases" in relative value to line p as x increases, the slope of line n must be less than the slope of line p.

Answer 2

Yes, the slope of line n is less than the slope of line p if both given conditions are satisfied.

Proof:

Let the y intercept coordinates be (0, b). Therefore, the slope between (0, b) and (5, 1) is

slope =(1-b)/5......(1)

From (1), we can see that the smaller the b, the larger the slope.

Since the y-intercept of line p is smaller than the y-intercept of line n, the slope of line p is larger than the slope of line n, which is that same as "the slope of line n less than the slope of line p."

End of proof.

Answer 3

First, let us define the word 'slope'. Each line (with the exception of vertical one, which will never cross the Y-axis here) goes from left to right. We will consider the slope as positive in case it goes up, and negative in case it goes down as we move alone the line from left to right. (And, it will be zero if it goes from left to right parallel to X-axis).

Then if the Y axis is at the left of the point (5,1), so, the less is Y-intercept of the line coming through the point (5,1), the greater will be the slope. The intercept here may be as positive or negative, and the slope can be positive or negative.

Hence, if the y-intercept of line n is greater, then the slope of line n is less then the slope of line p.

Answer 4

You again, eh? Making me think! Ok, the lines intersect in the upper right quadrant. Now the Y intercept of line n is higher (greater) than the other line. So the left end of the line is higher than the left end of the other line. So the other one is steeper thus the slope is greater.

Answer 5

Well, first look at (1).
Now, would that be enough information?
No.
Because imagine 2 lines that intersect at (5,1).
You would need to know other points that lies on each line that tell whether 1 slope is more then the other.

Now, look at (2).
Would that be enough information.
No, again.
Because just like above, you would need to know
other points that lies on each line.

Therefore, you need both (1) and (2), since both of those would give you 2 points for each line.

Answer 6

It's easy to see if you draw it. The answer is the same regardless of what values you use for the y-intercepts of the two lines, as long as n's is greater than p's. Line p has the greater slope, and the answer to your question is "Yes."