How many positive integers less than 15 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
Pick.
A) 14  B) 13  C) 12  D) 8  E) 10
The number = 2a + 3b &lt; 20   When a = 1, b = 1, 2, 3, 4, 5 -&gt; 2a = 2; 3b = 3, 6, 9-&gt; the number = 5, 8, 11 --&gt; 3 numbers   when a =2, b = 1,2,3-&gt; ....--&gt; 3 numbers   when a =3, b = 1,2,3,4 --&gt; ....--&gt; 2 numbers   Total number is already 8. Look at the answer there is no number greater than 8 --&gt; we dont need to try any more   Answer must be 8
<result>D</result>
How many positive integers less than 15 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?