Data Sufficiency

Hi, there! I'm happy to help with this!

Prompt: In the xy-plane, points A, B and C are not on the same line. Is the slope of line BC negative?

A straightforward prompt, from which nothing can be concluded.

Statement #1: The slope of line AB is -1.
OK, this is a rich piece of information. From this, we know line AB makes a 45-degree angle with both the x-axis and the y-axis --- it's slope 45-degrees below any horizontal line that intersects it.
This doesn't tells us one jot about C, so by itself, this statement is not sufficient.

Statement #2: The measure of angle ABC is 37 degrees.
Here, we have to be scrupulously careful to ignore all the discoveries we made in Statement #1, and focus exclusively on Statement #2.
We have the measure of one angle, angle ABC, and this angle could be oriented in any direction, so from this alone, we have absolutely no ideal which way BC points. By itself, this statement is not sufficient.

Combined Statements:
Now we know ---- line AB is 45 degrees below the horizontal.
We know angle ABC equals 37 degrees, which is the same as saying: lines AB and BC intersect at a 37 degree angle. This means, the orientation of BC must be 37 degrees different from the orientation of AB. There are two possibilities
a) BC's slope is less negative than AB -- then AB has orientation of 45 - 37 = 8 degrees below the horizontal.
b) BC's slope is more negative than AB -- then AB has orientation of 45 + 37 = 82 degrees below the horizontal.
In either case, BC is still oriented below the horizontal, which means it has a negative slope. With the combined statements, we are able to give a definitive answer to the question.

Answer = C

Does all that make sense?

Here's a relevant free lesson:
https://gmat.magoosh.com/lessons/260-slope

Here's a relevant practice question:
https://gmat.magoosh.com/questions/1028
When you submit your answer, the following page will have a complete video explanation.

Let me know if you have any questions.

Mike