Vincen wrote: ↑Wed Mar 31, 2021 8:10 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 video:
https://www.gmatprepnow.com/module/gmat- ... cy?id=1103
Cheers,
Brent
