Is this GRE math problem wrong?

Question

I'm working out of the Manhattan GRE test prep book and I've come across a question that I can't figure out why they chose the answer they did. "Perpendicular lines m and n intersect at point (a,b), where a>b>0. The slope of m is between 0 and 1. Which of the following statements must be true? Indicate all that apply" a: The x-intercept of line m is positive b: The y-intercept of line m is negative c: The x-intercept of line n is positive d: The y-intercept of line n is positive e: The product of the x and y intercepts of line m is negative f: The sum of the x intercepts of lines m and n is positive The book answer is C and E I understand C, but I can't comprehend how E MUST be true. The slope of line m can go through the origin. 0*0=0 is not negative. The book solution says the intersections of m will always have opposite signs.

Answer 1

Breonna, Yes, you are correct. When line m goes through the origin, there are no intercepts, or they are zero. However, for all other situations, line m will have one +ve and one -ve intercept, making the product -ve. Therefore, for situations when line m has x and y intercepts, the product is indeed -ve. It's a tricky one. I would have the same doubts as you and contemplate whether to pick "e" or not! It seems like word play. For situations when there are intercepts, the product is indeed -ve.