Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has five iron coins and five copper coins, how many different sums from 1¢ to 35¢ can he make with a combination of his coins?
Choose the correct choice from the following answers:
A) 20  B) 21  C) 35  D) 33  E) 31
The total sum is 5*2 + 5*5= 
<gadget id="calculator">5*2 + 5*5</gadget>
<output>35</output>
35¢. If you can make each sum from 1 to 35 (1¢, 2¢, 3¢, ..., 35¢), then the answer would be 35 (maximum possible).   Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 32¢ and 34¢ (since total sum is 35¢ we cannot remove 1¢ or 3¢ to get 34¢ or 32¢).   So, out of 35 sums 4 are for sure not possible, so the answer must be   35 - 4= 
<gadget id="calculator">  35 - 4</gadget>
<output>31</output>
31 sums or less. Only A fits.   Answer: 31.
<result>E</result>
Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has five iron coins and five copper coins, how many different sums from 1¢ to 35¢ can he make with a combination of his coins?