BTGModeratorVI wrote: ↑

Thu Nov 05, 2020 7:57 am

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.

Answer: C
Source: Official guide

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