If a and b are different positive integers and a + b = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b Pick.
A) I only
B) II only
C) III only
D) I and II
E) I and III
a+b=a(a+b)a+b=a(a+b) --&gt; a(a+b)−(a+b)=0a(a+b)−(a+b)=0 --&gt; (a+b)(a−1)=0(a+b)(a−1)=0 --&gt; as aa and bb are positive the a+b≠0a+b≠0, so a−1=0a−1=0 --&gt; a=1a=1. Also as aa and bb are different positive integers then bb must be more than a=1a=1 --&gt; a&lt;ba&lt;b (bb can not be equal to aa as they are different and bb can not be less than aa as bb is positive integer and thus can not be less than 1).   So we have that: a=1a=1 and a&lt;ba&lt;b.   I. a = 1 --&gt; true;   II. b = 1 --&gt; not true;   III. a &lt; b --&gt; true.   Answer: I and III (I and II only).
<result>E</result>
If a and b are different positive integers and a + b = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b