For this Q, how do we approach this? I did a table of the y-0/x-0 using the signs and compared the relative signs. I got that L is always positive, and thus bigger slope, but why is it K?

How do you account for the fact that there are multiple possibilities? For example, we can have one junior and two seniors, or two juniors and one senior.

Consider the equation of the line, which is y = mx + c. The y-intercept is c, while the x intercept is \frac{-c}{m}.

If the product is positive (Quantity A), this means that c \times \frac{-c}{m} > 0 \rightarrow \frac{-c^2}{m} > 0. This implies that m must be negative.

Now look at the case where the product is negative (Quantity B). In this case, c \times \frac{-c}{m} < 0 \rightarrow \frac{-c^2}{m} < 0. This implies that m must be positive.

As a result, we can select Quantity B.

Let the number of other marbles be x (there are also other options for this). Then,

\frac{7}{7 + x} = \frac{1}{2}. This implies that x = 7. But, notice that the question is asking for the total number of marbles currently in the bag, which is 10 + 7 = 17.