The lengths of the sides of triangle ABC are such that AB = x + 2, BC = y - 1, and AC = x - 3. Which angle in triangle ABC is the largest?
(1) x - y = 1
(2) y = 8
IMO: C
(1) x - y = 1
(2) y = 8
IMO: C
The largest angle will be opposite to the largest side of the triangle. We are given information about the sides here.GmatKiss wrote:The lengths of the sides of triangle ABC are such that AB = x + 2, BC = y - 1, and AC = x - 3. Which angle in triangle ABC is the largest?
(1) x - y = 1
(2) y = 8
IMO: C
(1) x - y = 1
x = y + 1
AB = x + 2 = y + 1 + 2 = y + 3
BC = y - 1
AC = x - 3 = y + 1 - 3 = y - 2
It can be seen that obviously AB is the largest side. So, angle opposite to side AB is C. Hence C is the largest angle in triangle ABC; SUFFICIENT.
(2) y = 8
AB = x + 2
BC = y - 1 = 8 - 1 = 7
AC = x - 3
No information or relation between x and y is given; NOT sufficient.
The correct answer is A.
