How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?
Choose one:  A) 14  B) 13  C) 12  D) 11  E) 10
The numbers must be of the form 2a+3b,2a+3b, where aa and bb are positive integers.   The smallest number is 5=2∗1+3∗1.5=2∗1+3∗1. Starting with 55, we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list. Adding either 22 or 33 to 2a+3b2a+3b will give another number of the same form.   So, after 55, we get   5+2= 
<gadget id="calculator">  5+2</gadget>
<output>7</output>
7,5+3=8,7+2=9,8+2=10,...5+2=7,5+3=8,7+2=9,8+2=10,... We will get all the numbers up to 1919 inclusive, except 1,2,3,4,1,2,3,4,and 6,6, because once we have 77 and 8,8, by adding 22 all the time we can get any odd or even number.   We get a total of 19−5=1419−5=14 numbers.   14nswer 14
<result>A</result>
How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?