Is this GRE math problem about the $x$,$y$-intercepts of two perpendicular lines 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

Community wiki answer so the question can be marked as answered:

As Dr. MV noted in a comment, you're right and the book is wrong.

Answer 2

Are you sure option e says “negative” and not “not positive”. Because my book says “not positive”. The book solution says it has opposite signs IF the intercepts are nonzero. If one of the intercepts is zero, the product is still not positive. So the book is right