In a ring toss game at a carnival, three rings are tossed over any of three pegs. A ring over peg $A$ is worth one point, over peg $B$ three points and over peg $C$ five points. If all three rings land on pegs, how many different point totals are possible? (It is possible to have more than one ring on a peg.)
(A) 12
(B) 7
(C) 10
(D) 13
(E) 6
In a ring toss game at a carnival, three rings are tossed over any of three pegs. A ring over peg $A$ is worth one point, over peg $B$ three points and over peg $C$ five points. If all three rings land on pegs, how many different point totals are possible? (It is possible to have more than one ring on a peg.)
(A) 12
(B) 7
(C) 10
(D) 13
(E) 6

## Solution

The lowest possible score is 3 and the highest is 15 .

It is not possible to get an even score because this would require 3 odd numbers to add to an even number. Starting at a score of 3 , it is possible to achieve every odd score between 3 and 15 . This implies that $3,5,7,9,11,13$, and 15 are possible scores.

There are 7 possible scores.

ANSWER: (B)