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Question

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

CAT 2021

A
2
CORRECT ANSWER WRONG ANSWER
B
3
CORRECT ANSWER WRONG ANSWER
C
5
CORRECT ANSWER WRONG ANSWER
D
4
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(D)

Explanatory Answer :

any point on the line x/3 + y/5 = 1 will have the shortest distance in total

however , we need to have integral coordinates .

so , we need to find the points with inegral coordinates as close as possible to the line 5x + 3y = 15

put x = 1 , we get y = 2 or 3

put x = 2 , we get y = 1 or 2

sum of distance for (1,2) = sqrt{8} + {sqrt{10}}

sum of distance for (1,2) =sqrt{13} + {sqrt{5}}

sum of distance for (1,2) =sqrt{2} + {sqrt{20}}

sum of distance for (1,2) = sqrt{5} + {sqrt{13}}

sqrt{5} + {sqrt{13}} is the shortest distance

sum of abscissa + ordinate = 4

so , D is the correct option