umaa wrote:In the xy-plane, if line k has negative slope and passes
through the point (s, -2), is the x-intercept of line k positive?
(1) s = 0
(2) The y-intercept of line k is negative.
Don't know the original answer. IMO E.
Let me know your answers and explanations.
(Edited)
Very tough question to answer in words as opposed to a sketch (which is what you should always draw on your scratch paper for geometry word problems).
Let's break the question down.
Step 1 of the Kaplan Method for DS: Focus on the question stem
We know that our line has a negative slope (goes from top left to bottom right) and passes through the point (s, -2), i.e. it travels below the x-axis. There are three possibilities for the location of that point:
1) (s, -2) could be in the lower left quadrant (-, -). If a line with a negative slope passes through the lower left quadrant, then it's x-intercept will be negative.
2) (s, -2) could be on the y-axis, i.e. (0, -2). If a line with a negative slope has a negative y-intercept, then it's x-intercept will be negative.
3) (s, -2) could be in the lower right quadrant (+, -). If a line with a negative slope passes through the lower right quadrant, then it's x-intercept could be negative, 0 or positive.
So, if we can narrow it down to one of the first two possibilities, we can answer the question. If we can only narrow it down to the 3rd possibility, then without further info we can't answer the question.
Step 2 of the Kaplan Method for DS: consider each statement independently
(1) s = 0
Perfect! Based on our preliminary work, we know we're in case #2 and the x-intercept will definitely be negative: sufficient.
(2) The y-intercept of line k is negative.
Good enough! Identical to our reasoning for case #2 - we have a line with a negative slope and a negative y-intercept, therefore the x-intercept will also be negative: sufficient.
Step 3 of the Kaplan Method for DS: If necessary, combine the statements
No need for step 3 on this question!
Each of (1) and (2) is sufficient alone: choose (D).
