Gmat_mission wrote: ↑

Sun Dec 12, 2021 6:46 am

In the \(xy\)-plane, line \(k\) passes through the point \((1, 1)\) and line \(m\) passes through the point \((1, -1).\) Are the lines \(k\) and \(m\) perpendicular to each other?

(1) Lines k and m intersect at the point \((1, -1).\)
(2) Line k intersects the x-axis at the point \((1, 0).\)

Answer: E

Source: GMAT Prep

Target question: Are lines K and m perpendicular to each other?

IMPORTANT: Since line K passes through the point (1, 1), statements 1 and 2 both have the same effect of "locking" line K into exactly one position. In fact, statements 1 and 2 essentially provide the exact same information. As such, it's either the case that each statement is sufficient (D) or each statement is not sufficient (E).

Since neither statement locks line M into any certain position, line M is free to be in lots of different positions, as long as it passes through the point (1, -1)


Okay, let's jump right to . . .
Statements 1 and 2 combined:
Here are two possible scenarios that satisfy statements 1 and 2.
Scenario a:

In this instance, lines M and K are perpendicular.


Scenario b:

In this instance, lines M and K are not perpendicular.


Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Aside: This concept of "locking in" shapes on Geometry DS questions is discussed in much greater detail in this free video: https://www.gmatprepnow.com/module/gmat- ... cy?id=1103

Cheers,
Brent