what is the largest amount of postage in cents that cannot be made by using only 3 cent and 5 cent stamps?

The largest you can't make is 7 cents.

Step-by-step explanation:

Once you get 3 consecutive amounts, you can get all larger ones just by adding 3 cent stamps.  So let's see what you can make:

1 no

2 no

3 yes

4 no

5 yes

6 yes

7 no

8 yes, and this will give you 11 14 17 etc

9 yes, and this will give you 12 15 18 etc

10 yes, and this will give you 13 16 19 etc.

associative property of multiplication