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In the xy-plane, points A, B and C are not on the same line

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In the xy-plane, points A, B and C are not on the same line

by AAPL » Tue Jul 17, 2018 6:00 am
In the xy-plane, points A, B, and C are not on the same line. Is the slope of line BC negative?

(1) The slope of line Ab is -1.
(2) The measure of angle ABC is 37 degrees.

The OA is C.

Why can't the line AB be at a different degree? The slope is given as -1. Is it not possible to have the line/slope(-1) AB at any other degree other than 45?
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Source: — Data Sufficiency |

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In the xy-plane, points A, B and C are not on the same line

by Brent@GMATPrepNow » Tue Jul 17, 2018 6:12 am
In the xy-plane, points A, B and C are not on the same line. Is the slope of line BC negative?

1. The slope of line AB is -1.
2. The measure of angle ABC is 37 degrees.
Target question: Is the slope of line BC negative?


We can quickly see that statements 1 and 2 (alone) are NOT SUFFICIENT.

This brings us to...
Statements 1 and 2 combined
If we draw the line segment AB with slope -1, then we get something like this:
Image

If we add some lines parallel to the x- and y-axes, we need to recognize that we get 45-degree angles at point B
Image

So, if we add a 37-degree angle at point B, we get two possible scenarios:
Scenario #1
Image
or
Scenario #2
Image

In BOTH possible scenarios, the slope of line BC is definitely negative.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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