2019 AMC 10 B
Complete problem set with solutions and individual problem pages
Each piece of candy in a store costs a whole number of cents. Casper has exactly enough money to buy either pieces of red candy, pieces of green candy, pieces of blue candy, or pieces of purple candy. A piece of purple candy costs cents. What is the smallest possible value of ? (2019 AMC 10B Problem, Question#7)
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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 purpe candy costs cems,the smallest possible value of is .
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, cenis) to buy each type of candy, so the minimum value of is .
