Question

A triangle is formed by $X$-axis, $Y$-axis and the line $3 x+4 y=60$ Then the number of points $P ( n , b )$ which lie strictly inside the triangle, where a is an integer and $b$ is a multiple of a, is ____

Answer 1

The correct answer is 31

(1,1)(1,2)−(1,14)⇒14 pts.
If x=2,y=227​=13.5
(2,2)(2,4)…(2,12)⇒6 pts.
If x=3,y=451​=12.75
(3,3)(3,6)−(3,12)⇒4 pts.
If x=4,y=12
(4,4)(4,8)⇒2 pts.
If x=5⋅y=445​=11.25
(5,5),(5,10)⇒2 pts.
If x=6,y=221​=10.5
(6,6)⇒1pt
If x=7,y=439​=9.75
(7,7)⇒1pt
If x=8,y=9
(8,8)⇒1pt
If x=9y=433​=8.25⇒ no pt.
Total =31 pts.