Suppose a, b, and c are positive integers with a < b < c such that
1/a
+
1/b
+
1/c
= 1. What is
a + b + c?  Choose one:
A) 1	B) 4	C) 9	D) 11	E) no such integers exist

Rationale: first note that we must have 1 / a < 1 , so a > 1 . since 1 / a > 1 / b > 1 / c , we must also have 1 / a > 1 / 3 ; so a < 3 . thus , a / 2 . now 1 / b + 1 / c = 1 / 2 where 2 < b < c . similar to before , 1 / b > 1 / 4 , so b < 4 . thus , b = 3 . with a = 2 and b = 3 we have 1 / 2 + 1 / 3 + 1 / c = 1 , which is satisfied when c = 6 . to conclude , a + b + c = 2 + 3 + 6 = 11 . correct answer d
Answer: D