Given that they intersect at a point (5,1) in this case, the other point is important in determining the slope.
If one line always hits the y-axis higher than the other, then that means
1. their slopes are different
2. If the slopes are positive, the slope of the line hitting highest on the y-axis (but below 1) is smaller than the slope of the other line
3. I the slope are negative, the slope of the line hitting lowest on the y-axis (but above 1) will be "larger" than the slope of the other line.
While the absolute values of the slopes switch, the line hitting higher on the y-axis will always have a lower slope, whether +/- or 0.
Slope
This topic has expert replies
Source: Beat The GMAT — Data Sufficiency |
-
grockit_jake
- GMAT Instructor
- Posts: 80
- Joined: Wed Aug 12, 2009 8:49 pm
- Location: San Francisco, CA
- Thanked: 16 times
-
mridul_dave
- Senior | Next Rank: 100 Posts
- Posts: 41
- Joined: Tue Oct 06, 2009 9:49 am
- Thanked: 4 times
Do we have to respond based on absolute values ?grockit_jake wrote:Given that they intersect at a point (5,1) in this case, the other point is important in determining the slope.
If one line always hits the y-axis higher than the other, then that means
1. their slopes are different
2. If the slopes are positive, the slope of the line hitting highest on the y-axis (but below 1) is smaller than the slope of the other line
3. I the slope are negative, the slope of the line hitting lowest on the y-axis (but above 1) will be "larger" than the slope of the other line.
While the absolute values of the slopes switch, the line hitting higher on the y-axis will always have a lower slope, whether +/- or 0.
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
You have some other options such as sketching and applying the slope formula.mridul_dave wrote:Do we have to respond based on absolute values ?grockit_jake wrote:Given that they intersect at a point (5,1) in this case, the other point is important in determining the slope.
If one line always hits the y-axis higher than the other, then that means
1. their slopes are different
2. If the slopes are positive, the slope of the line hitting highest on the y-axis (but below 1) is smaller than the slope of the other line
3. I the slope are negative, the slope of the line hitting lowest on the y-axis (but above 1) will be "larger" than the slope of the other line.
While the absolute values of the slopes switch, the line hitting higher on the y-axis will always have a lower slope, whether +/- or 0.
Statement (1): lines pass through (5,1). We can sketch this to show that statement (1) is INSUFFICIENT
Statement (2): the y-intercept of line n is greater than y intercept of line p.
We can use sketches to show that statement (2) is INSUFFIENT.
Statements 1 and 2: Let n be the y-intercept of line n, and let p be the y-intercept of line p.
So, the two points of intersection with the y-axis are (0,n) and (0,p). 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 p) will be greater than (1-n)/5 (the slope of n)
So, statements 1&2 combined are SUFFICIENT
Answer = C
Brent Hanneson - Creator of GMATPrepNow.com
-
palvarez
- Master | Next Rank: 500 Posts
- Posts: 199
- Joined: Sat Oct 24, 2009 4:43 pm
- Thanked: 22 times
- GMAT Score:710
okigbo wrote:Lines n and p lie in xy plane. Is slope of line n less than slope of line p?
a. Lines n and p intersect at (5, 1)
b. Y-intercept of line n is greater than y intercept of line p
Let n and p be slopes of n and p.
N: y = nx+a
P: y = px+b
1 = 5n +a = 5p +b
5(p-n) = a - b > 0
p - n > 0
C is the answer
