n and P line

[kamalakarthi]

Can u help on this.

[MartyMurray]

Statement 1: Lines n and p intersect at point (5,1).

With only one point with which to work and no other information, we cannot determine anything about the slopes of the lines.

Insufficient.

Statement 2: The y intercept of line n is greater than the y intercept of line p.

The lines could have various different slopes irrespective of the relative values of their y intercepts.

Insufficient.

Statements Combined:

From Statement 1 we know that the lines intersect in a particular spot, (5, 1), above the x axis and to the right of the y axis.

From Statement 2 we know that when x = 0, the y value of line n is greater than the y value of line p.

No matter what those y intercepts are, the change in y for n when x goes from 0 to 5 will be less than the change in y for p when x goes from 0 to 5, because n is starting from a higher y when x = 0, and both n and p go to y = 1 when x = 5.

For example if the y intercepts of n and p are 2 and 1 respectively, when x increases from 0 to 5, the change in the y of n will be -1 and the change in the y of p will be 0. So n would have a negative slope and p would have a slope of 0.

Since for a given positive change in x the change in y is less for n than for p, the slope of n is less than the slope of p.

Sufficient.

The correct answer is C.

[GMATGuruNY]

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

Statement 1: Lines n and p intersect at the point (5,1).
No way to determine whether the slope of line n is less than the slope of line p.
INSUFFICIENT.

Statement 2: The y-intercept of line n is greater than the y-intercept of line p.
No way to determine whether the slope of line n is less than the slope of line p.
INSUFFICIENT.

Statements 1 and 2 combined:
Case 1: y-intercept of n is (0,2), line intercept of p is (0,1)
Since (5,1) is on each line, we get:
Slope of n = (1-2)/(5-0) = -1/5.
Slope of p = (1-1)/(5-0) = 0.
The slope of n is less than the slope of p.

Case 2: y-intercept of n is (0,10), line intercept of p is (0,-1)
Since (5,1) is on each line, we get:
Slope of n = (1-10)/(5-0) = -9/5.
Slope of p = (1- (-1))/(5-0) = 2/5.
The slope of n is less than the slope of p.

Case 3: y-intercept of n is (0,-1), line intercept of p is (0,-10)
Since (5,1) is on each line, we get:
Slope of n = (1-(-1))/(5-0) = 2/5
Slope of p = (1- (-10))/(5-0) = 11/5.
The slope of n is less than the slope of p.

In every case, the slope of n is less than the slope of p.
SUFFICIENT.

The correct answer is C.

[Brent@GMATPrepNow]

Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
(1) Lines n and p intersect at (5, 1)
(2) the y-intercept of line n is greater than the y-intercept of line p

Target question: Is slope of line n less than slope of line p?

Statement 1: Lines n and p intersect at (5, 1)
We can use sketches to show that statement (1) is NOT SUFFICIENT



Statement 2: the y-intercept of line n is greater than the y-intercept of line p
We can use sketches to show that statement (2) is NOT SUFFIENT.


Statements 1 and 2 combined
Let n be the y-intercept of line n
Let p be the y-intercept of line p.

So, line n has the points (0,n) and (5,1).
And line p has the points (0,p) and (5,1)

IMPORTANT: We also know that n>p (from statement 2)

When we apply the slope formula, we get:
Slope of line n = (1-n)/(5-0)= (1-n)/5
Slope of line p = (1-p)/(5-0)= (1-p)/5
Since n>p, we know that (1-p)/5 (the slope of line p) WILL BE GREATER than (1-n)/5 (the slope of line n)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent