Question

12. In the figure below, x > 90 and y = z + 1. If z is an integer, what is the greatest possible

value of y?
(A) 30
(B) 45
(C) 60
(D) 61
(E) 89

Answer 1

Hi,

Answer B: 45

Explanation:

`x > 90 \Longrightarrow\ 0 > 90-x \Longrightarrow\ 90 > 180-x\\\\y=z+1 \Longrightarrow\ z=y-1\\x+y+z=180\\y+z=180-x\\y+y-1 =180- x < 90\\2y-1 < 90\\y < 45.5\\Hence\ y\ is\ an\ integer \Longrightarrow\ y=45\\`