IIn the rectangular coordinate system shown above, does the line \(k\) (not shown) intersect quadrant \(\text{II}?\)

[M7MBA]

In the rectangular coordinate system shown above, does the line \(k\) (not shown) intersect quadrant \(\text{II}?\)

(1) The slope of \(k\) is \(-\dfrac16.\)
(2) The \(y\)-intercept of \(k\) is \(-6.\)

Answer: A

Source: GMAT Prep

[Brent@GMATPrepNow]

GMAT_DS_PREP_100.png

In the rectangular coordinate system shown above, does the line \(k\) (not shown) intersect quadrant \(\text{II}?\)

(1) The slope of \(k\) is \(-\dfrac16.\)
(2) The \(y\)-intercept of \(k\) is \(-6.\)

Answer: A

Source: GMAT Prep

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