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In xy plane, line k passes through (1,1) . . .

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In xy plane, line k passes through (1,1) . . .

by Vincen » Thu Nov 02, 2017 8:24 am
In xy plane, line k passes through (1,1) and m through (1, -1). Are lines k and m perpendicular?

(1) k and m intersect at (1, -1)
(2) k intersects x -axis at (1, 0)

The OA is E.

I am confused. Both statements implies that k is a vertical line? Am I wrong? Why aren't they sufficient?

Experts, I would appreciate your help here.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Thu Nov 02, 2017 8:29 am
Vincen wrote:In xy plane, line k passes through (1,1) and m through (1, -1). Are lines k and m perpendicular?

(1) k and m intersect at (1, -1)
(2) k intersects x -axis at (1, 0)
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 ALONE is sufficient (answer D) or the statements COMBINED are not sufficient (answer 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:
Image
In this instance, lines M and K are perpendicular.


Scenario b:
Image
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

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by GMATGuruNY » Thu Nov 02, 2017 8:34 am
Vincen wrote:In xy plane, line k passes through (1,1) and m through (1, -1). Are lines k and m perpendicular?

(1) k and m intersect at (1, -1)
(2) k intersects x -axis at (1, 0)
Statements combined:
Only one fact is known about line m:
It passes through (1, -1).
Implication:
Line m can have any ANY SLOPE.
Thus, it cannot be determined whether line m is perpendicular to line k.
INSUFFICIENT.

The correct answer is E.
Both statements implies that k is a vertical line? Am I wrong? Why aren't they sufficient?
Each statement implies that line k is vertical.
If line m is HORIZONTAL, then it WILL be perpendicular to line k, with the result that the answer to the question stem is YES.
If line m is NOT horizontal, then it will NOT be perpendicular to line k, with the result that the answer to the question stem is NO.
Since the answer is YES in the first case but NO in the second case, the two statements combined are INSUFFICIENT.
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