Data Sufficiency

kishokbabu wrote:A straight line passes through the points (a,b) & (c,d). Is the slope of the line less than 0?

1) (a-c)(b-d)<0
2) Product of the intercepts of the line on the X-axis and on the Y-axis is greater than 0.

Pls explain how to solve this problem?

The question asks if the slope of the line is negative. A line has a negative slope if it is falling as it moves to the right.

From Statement 1, we learn that (a-c) and (b-d) have opposite signs. Now the slope of the line is (b-d)/(a - c) (using the standard slope formula); if (a-c) and (b-d) have opposite signs, then this fraction must be negative, so Statement 1 is sufficient.

From Statement 2, we learn that the x-intercept and y-intercept of the line have the same sign: both are positive or both are negative. If both are positive, then the line crosses the y-axis somewhere above the origin (0,0). For it to then have a positive x-intercept, it must fall as it moves to the right, and thus has a negative slope. Similarly, if the x-intercept is negative, the line crosses the x-axis to the left of the origin. For the line to then have a negative y-intercept, the line must again fall as it moves to the right, so thus has a negative slope. All of this is easier to see if you sketch quick diagrams of course. So Statement 2 is sufficient.

The answer is D.