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?  Answers.
A) 1 B) 4 C) 9 D) 11 E) no such integers exist
First note that we must have 1/a &lt; 1, so a &gt; 1. Since 1/a &gt; 1/b &gt; 1/c, we   must also have 1/a &gt; 1/3; so a &lt; 3. Thus, a/ 2. Now 1/b + 1/c = 1/2 where 2 &lt; b &lt; c.   Similar to before, 1/b &gt; 1/4, so b &lt; 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= 
<gadget id="calculator">2+3+6</gadget>
<output>11</output>
11.   correct answer 11
<result>D</result>
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?