Is the slope of Line L 0? 1) Line L passes through Quandrant II 2)

Question

Is the slope of Line L > 0? 1) Line L passes through Quandrant II 2) Line L has negative Y-intercept Source: https://www.GMATinsight.com

ArunSharma12 · Answer

If a line makes acute angle with X-axis,slope is positive
If a line makes obtuse angle with X-axis, slope is negative.

statement 1:
It does not specify the slope of line. It can be either positive or negative depending on the angle made with X-axis.
not sufficient

statement 2:
This also does not restrict a line to have a certain slope. It can still be positive or negative intercepting the Y-axis below the X-axis.
not sufficient

combining both statements,
This restricts any lines making acute angle with X-axis. 
Allowed lines can only make obtuse angle with X-axis hence slope will be negative for such lines.
Ans: C

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Condition 2) tells the followings. If L has a positive slope, the line L passes through the quadrants 1, 3 and 4. If L has a negative slope, the line L passes through the quadrants 2, 3 and 4. Thus, when we consider both conditions together, the slope of the line L is positive. Since both conditions together yield a unique solution, they are sufficient. Therefore, C is the answer.

GMATinsight · Answer

Please check the solution as mentioned below:

SUGGESTION: ALways draw the figure to answer questions of coordinate geometry

Kherarohan8 · Answer

can we generalise the specifics about the lines with positive and negative slopes? in terms of quadrants and intercepts

TaizKaran · Answer

MathRevolution  Sir/Ma'am though your answer is correct but your reasoning is not. On using both the conditions we figure out that the slope is negative. But you've mentioned that it's positive which is incorrect. Please correct me if I'm wrong.

bumpbot · Answer

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Is the slope of Line L > 0? 1) Line L passes through Quandrant II 2)

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