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 twu iron coins and twu copper coins, how many different sums from 1¢ to 14¢ can he make with a combination of his coins?	Choices
A) 8
B) 11
C) 9
D) 4
E) 12
The total sum is 2*2 + 2*5= 
<gadget id="calculator">2*2 + 2*5</gadget>
<output>14</output>
14¢. If you can make each sum from 1 to 14 (1¢, 2¢, 3¢, ..., 14¢), then the answer would be 14 (maximum possible).   Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 13¢ and 11¢ (since total sum is 14¢ we cannot remove 1¢ or 3¢ to get 13¢ or 11¢).   Also discarded 6 and 8, for lack of even numbers after 4   So, out of 14 sums 6 are for sure not possible, so the answer must be   14 - 6= 
<gadget id="calculator">  14 - 6</gadget>
<output>8</output>
8 sums or less. Only A fits.   8nswer: 8.
<result>A</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 twu iron coins and twu copper coins, how many different sums from 1¢ to 14¢ can he make with a combination of his coins?