2016 · Q53
A triangle is formed with vertices (0, 0), (0, 100) and (100, 100). What is the number of points inside the triangle with integer coordinates?
general-mental-abilityquantitative-aptitude
- A5000
- B4999
- C4851
- D4800
Explanation
By Pick's theorem, interior lattice points I = Area - B/2 + 1. The right triangle has area 5000; its boundary has 101 lattice points on each side, i.e. B = 3 x 101 - 3 = 300. Thus I = 5000 - 150 + 1 = 4851 interior integer-coordinate points.