Probability Simple Question

[gabriel]

O(0,0)
P(0,30)
q(50,0)

How many points on PQ have coordinates both as integers

OA=11

I can deduce that the points lie on 3x+5y = 150 st x,y >0 What is x and y
Also x and y <50 and <30 respectively. Should I go on and check for all points satisfying these conditions ???

ok .. u have the eqn 3x+5y=150 ... in this both x and y have integer values ... from the eqn x = 50 - (5y/3) .. now since x is an integer and 3 cannot divide 5 so y has to be of the form 3a ... that is y has to be a multiple of 3 ... so the values y can take are 0,3,6,9 ... 30 .. which are 11 in number .. similarly for the corresponding values of y we will have 11 values for x ... hence the answer ..