Few questions on coordinate geometry. These are slightly unconventional questions. CAT has stayed away from raw, brute-force cogeo questions for a while now. The questions that we see in CAT have not been algebraic. They have either been of the visual type or of the type where one has to do trial and error. So, the cogeo basics are important, but no point learning all kinds of fancy formula stuff.

1. Set S contains points whose abscissa and ordinate are both natural numbers. Point P, an element in set S has the property that the sum of the distances from point P to the point (3,0) and the point (0,5) is the lowest among all elements in set S. What is the sum of abscissa and ordinate of point P?

2. Region R is defined as the region in the first quadrant satisfying the condition 3x + 4y < 12. Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2?

3. Region Q is defined by the equation 2x + y < 40. How many points (r, s) exist such that r is a natural number and s is a multiple of r?