CAT Exam Model Paper 1 with solutions for free online practice

The sum of the distances from point P to the other two points will be at its lowest only when point P lies on the line segment joining the points (8, 0) and (0, 12).
(8, 0) and (0, 12) are the coordinates of the x and y intercepts of the line respectively.
So, the equation of the line segment joining the points (8, 0) and (0, 12) is $\frac{\mathrm{x}}{8}+\frac{\mathrm{y}}{12}=1$
Or the equation is 12 x + 8y = 96 or 3x + 2 y = 24.
The question states that the elements of set S contain points whose abscissa and ordinate are both natural numbers i.e., their x and y coordinates are positive integers.
The equation of the line is 3x + 2 y = 24. Positive integer values that satisfy the equation will be such that their ‘x’ values will be even and their ‘y’ values will be multiples of 3. The values are
x = 2, y = 9
x = 4, y = 6
x = 6, y= 3
Hence, there are 3 such points that exist in set S.