Problem:
Each piece of candy in a store costs a whole number of cents. Casper has exactly enough money to buy either 12 pieces of red candy, 14 pieces of green candy, 15 pieces of blue candy, or pieces of purple candy. A piece of purple candy costs 20 cents. What is the smallest possible value of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If he has enough money to buy pieces of red candy, pieces of green candy, and pieces of blue candy, then the smallest amount of money he could have is cents. Since a piece of purple candy costs cents, the smallest possible value of is .
OR
We simply need to find a value of that is divisible by , and . Observe that is divisible by and , but not is divisible by , and , meaning that we have exact change (in this case, 420 cents) to buy each type of candy, so the minimum value of is .
OR
We can notice that the number of purple candy times has to be divisible by , because of the green candies, and , because of the red candies. , so the answer has to be .
The problems on this page are the property of the MAA's American Mathematics Competitions