VJesus12 wrote: ↑Tue May 04, 2021 6:25 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: GMAT Prep
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
