How many positive integers less than 22 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?  Choose the correct choice from the following.
A) 14  B) 17  C) 12  D) 11  E) 10
The number = 2a + 3b &lt; 20   When a = 1, b = 1, 2, 3, 4, 5, 6 -&gt; 2a = 2; 3b = 3, 6, 9, 12, 15, 18 -&gt; the number = 5, 8, 11, 14, 17, 20 --&gt; 6 numbers   when a =2, b = 1,2,3,4,5, 6 -&gt; ....--&gt; 6 numbers   when a =3, b = 1,2,3,4, 5 --&gt; ....--&gt; 5 numbers   Total number is already 17. Look at the answer there is no number greater than 17 --&gt; we dont need to try any more   Answer must be 17
<result>B</result>
How many positive integers less than 22 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?