I have twenty 3g stamps and twenty 5g stamps. Using one or more of these stamps, how many
different amounts of postage can I make? Pick:
A) 150
B) 152
C) 154
D) 396
E) 400
We need to find how many positive integers can be represented in the form 3n+5m   where n and m are integers between 0 and 20, but not with both of them 0. First, let us see   which integers divisible by 3 can be represented in this form. These are 3; 6; 9; ; 60 if we   set m = 0, and if we let m be 3; 6; 9; 12; 15; or 18, we get that the multiples of 3 we can   represent are 3; 6; 9; ; 150. There are thus 50 multiples of 3 we can represent. Working   similarly, we get that 5; 8; 11; ; 155 are the integers which give remainder 2 when divided   by 3, and which we can represent, giving 51 numbers of this form. Finally, the numbers which   give remainder 1 when divided by 3, and which can be represented in the desired form, are   10; 13; 16; ; 160. There are 51 of them. So, the answer is 50 + 51 + 51= 
<gadget id="calculator">50 + 51 + 51</gadget>
<output>152</output>
152.   correct answer 152
<result>B</result>
I have twenty 3g stamps and twenty 5g stamps. Using one or more of these stamps, how many
different amounts of postage can I make?