In the rectangular coordinate system shown above, does the line \(k\) (not shown) intersect quadrant \(\rm II?\)
This topic has expert replies
-
- Legendary Member
- Posts: 2898
- Joined: Thu Sep 07, 2017 2:49 pm
- Thanked: 6 times
- Followed by:5 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
(1) The slope of \(k\) is \(-\dfrac16.\)
(2) The \(y\)-intercept of \(k\) is \(-6.\)
Answer: A
Source: GMAT Prep
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
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Target question: Does line k intersect quadrant II?
Statement 1: The slope of k is -1/6
Here are a few lines with slope -1/6
KEY CONCEPT: As we travel from right to left along a line with slope -1/6, we keep moving up.
So, at some point, the line will surely pass through quadrant II
So, the answer to the target question is YES, line k DOES intersect quadrant II
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: The y-intercept of k is -6
There are several possible cases that satisfy statement 2. Here are two:
Case a: The line is horizontal (i.e., has slope zero)
In this case, the answer to the target question is NO, line k does NOT intersect quadrant II
Case b: The line looks like this
In this case, the answer to the target question is YES, line k DOES intersect quadrant II
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent